TDA.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Time Series Classification Using Topological Data Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook shows the basic pipeline of applying Topological Data Analysis for time series classification. We use [Giotto-TDA](https://github.com/giotto-ai/giotto-tda) for working with topology and [UCR](http://www.timeseriesclassification.com/) collection of datasets."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 0. Imports and Data Loading"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Giotto Installation:\n",
    "# !pip install -U giotto-tda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "from xgboost import XGBClassifier\n",
    "from catboost import CatBoostClassifier\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "from sklearn.ensemble import RandomForestClassifier, StackingClassifier\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.svm import SVC\n",
    "\n",
    "from sklearn.model_selection import GridSearchCV, StratifiedKFold\n",
    "\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "from gtda.time_series import TakensEmbedding\n",
    "from gtda.homology import VietorisRipsPersistence\n",
    "from gtda.diagrams import Scaler, BettiCurve, PersistenceLandscape, PersistenceEntropy\n",
    "from gtda.plotting import plot_diagram, plot_betti_curves\n",
    "\n",
    "import torch\n",
    "from torch import nn\n",
    "import torch.nn.functional as F\n",
    "from torch.autograd import Variable\n",
    "from torch.utils.data import DataLoader, Dataset\n",
    "\n",
    "from src.utils import *\n",
    "from src.TFE import *\n",
    "from src.nn import *\n",
    "from src import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset:  GunPoint\n",
      "X_train shape:  (50, 150)\n",
      "y_train shape:  (50,)\n",
      "X_test shape:   (150, 150)\n",
      "y_test shape:   (150,)\n",
      "num. of class:  2\n"
     ]
    }
   ],
   "source": [
    "directory_list = get_files_directory_list()\n",
    "directory_list = sorted(directory_list)\n",
    "\n",
    "random_index =  51\n",
    "random_path = directory_list[random_index]\n",
    "\n",
    "X_train, X_test, y_train, y_test = get_data_from_directory(random_path)\n",
    "X_train = X_train.squeeze()\n",
    "y_train = y_train.squeeze()\n",
    "X_test = X_test.squeeze()\n",
    "y_test = y_test.squeeze()\n",
    "num_classes = np.unique(y_train).shape[0]\n",
    "\n",
    "print('Dataset: ', random_path)\n",
    "print('X_train shape: ', X_train.shape)\n",
    "print('y_train shape: ', y_train.shape)\n",
    "print('X_test shape:  ', X_test.shape)\n",
    "print('y_test shape:  ', y_test.shape)\n",
    "print('num. of class: ', num_classes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Background"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1. Common Pipeline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The core idea of Topological Data Analysis (TDA) is to exploit the topological and geometrical properties of data, like shape, connectivity, and etc. to extract informative features. One of the ways of numerical description of such properties is the *Persistent Homology*. Persistent Homology considers data as a point cloud, and tries to find so called holes in point clouds using discretization and triangulation of initial data space space with simplical complexes. The structure of those wholes are described with *Persistence Diagram* (PD) that is a 2D plot that indicates the birth and death of n-dimensional holes in the induced topological spaces. Then, we can utilize different features to describe PD and use them as a input of classifier."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2. Point Clouds and Takens' Embedding"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we are going to work with time series data, we need to represent them in some form that will have informative topological behaviour and allow to extract topological features. One way is to utilize the Taken's embedding theorem [1] as it was proposed, for example, in [2]. This theorem states that time series can be reconstructed in so called *phase space* as:\n",
    "\n",
    "$$\n",
    "x_n(m, \\tau) = (x_n, x_{n+\\tau}, ..., x_{n+(m-1)\\tau}),\n",
    "$$\n",
    "\n",
    "where $m$ is embedding dimension, $\\tau$ is the time delay.\n",
    "\n",
    "Let's look how it can look like for a sample time series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_embedding(series, time_delay, class_index):\n",
    "    fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(12, 5))\n",
    "    ax1.plot(series)\n",
    "    ax1.set_xlabel(\"Time\")\n",
    "    ax1.set_ylabel(\"Value\")\n",
    "    ax1.set_title(\"Initial time seriesm class \" + str(class_index))\n",
    "    ax1.grid()\n",
    "    sample_embedding = TakensEmbedding(dimension=2, \n",
    "                                       time_delay=time_delay, \n",
    "                                       parameters_type='fixed').fit_transform(series)\n",
    "    ax2.scatter(sample_embedding[:,0], sample_embedding[:,1])\n",
    "    ax2.set_xlabel(\"$x_t$\")\n",
    "    ax2.set_ylabel(\"$x_{t+\\\\tau}$\")\n",
    "    ax2.set_title(\"Takens Embedding for $m=2$ and $\\\\tau=\" + str(time_delay) + \" $, class \" + str(class_index))\n",
    "    ax2.grid()\n",
    "    plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_embedding(X_train[0], 10, int(y_train[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_embedding(X_train[14], 10, int(y_train[14]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_embedding(X_train[3], 10, int(y_train[3]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_embedding(X_train[13], 10, int(y_train[13]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that for different classes the embeddings (point clouds) have distinguishable difference in this \"tail\" part in bottom left of the plot. This difference can be potentially described with topology."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3. Persistence Diagram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After obtaining point cloud, it is possible to build a Persistence Diagram (PD). One of the ways of obtaining the PD is the Vietoris-Rips Persistent Homology, as proposed, for example, in [3]. PD shows the distribution of holes - their birth and death - for each *homology dimension*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample_embedding = TakensEmbedding(dimension=2, \n",
    "                                   time_delay=10, \n",
    "                                   parameters_type='fixed').fit_transform(X_train[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since Giotto-TDA uses Plotly and doesn't make inline plots, we will duplicate them with static images."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"images/sample_pd.png\" />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "hoverinfo": "none",
         "line": {
          "color": "black",
          "dash": "dash",
          "width": 1
         },
         "mode": "lines",
         "showlegend": false,
         "type": "scatter",
         "x": [
          -215.72299003601074,
          215.72299003601074
         ],
         "y": [
          -215.72299003601074,
          215.72299003601074
         ]
        },
        {
         "mode": "markers",
         "name": "H0",
         "type": "scatter",
         "x": [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0
         ],
         "y": [
          3.1115465390030295e-05,
          0.00011724147771019489,
          0.00018083618488162756,
          0.00030200701439753175,
          0.0003210972936358303,
          0.00032163949799723923,
          0.00034711218904703856,
          0.00040335001540370286,
          0.0004294600512366742,
          0.00044809546670876443,
          0.00045218432205729187,
          0.0004985016421414912,
          0.0006946500507183373,
          0.0007524000247940421,
          0.0007821202161721885,
          0.0008903918205760419,
          0.0008979983394965529,
          0.0009090504609048367,
          0.0009277918725274503,
          0.0009387360187247396,
          0.0009700138471089303,
          0.0009723960538394749,
          0.0009990863036364317,
          0.001057142042554915,
          0.0010927460389211774,
          0.0011640521697700024,
          0.0011711467523127794,
          0.0012091384269297123,
          0.0013271733187139034,
          0.0013361260062083602,
          0.0014009801670908928,
          0.0014329892583191395,
          0.0014770843554288149,
          0.0015520630404353142,
          0.0017055911011993885,
          0.0017181670991703868,
          0.001718968152999878,
          0.0017451574094593525,
          0.0018401487031951547,
          0.001997033366933465,
          0.0021304611582309008,
          0.0022279394324868917,
          0.0024083165917545557,
          0.002469613216817379,
          0.002636025892570615,
          0.003008101601153612,
          0.003009792882949114,
          0.0030583005864173174,
          0.003233747323974967,
          0.003272024681791663,
          0.003427602117881179,
          0.0034404327161610126,
          0.0036608928348869085,
          0.003673546714708209,
          0.0037313185166567564,
          0.0037498981691896915,
          0.003782292827963829,
          0.004389222711324692,
          0.0045432886108756065,
          0.004573663230985403,
          0.004673801362514496,
          0.005345672834664583,
          0.005503309890627861,
          0.005838809069246054,
          0.00617360370233655,
          0.006209418177604675,
          0.0063294656574726105,
          0.006551452912390232,
          0.006726308725774288,
          0.006891865748912096,
          0.007111506536602974,
          0.007183264009654522,
          0.00865400955080986,
          0.008829085156321526,
          0.00927064847201109,
          0.010975435376167297,
          0.011464009992778301,
          0.012786324135959148,
          0.014875533059239388,
          0.015044189058244228,
          0.01533709280192852,
          0.016633369028568268,
          0.021069874987006187,
          0.024333905428647995,
          0.02459896355867386,
          0.025049136951565742,
          0.025928784161806107,
          0.026079507544636726,
          0.05318451672792435,
          0.05566033720970154,
          0.06598460674285889,
          0.072403684258461,
          0.07274448126554489,
          0.07540038228034973,
          0.07894501090049744,
          0.08755286782979965,
          0.09078233689069748,
          0.09111286699771881,
          0.09442399442195892,
          0.10571727901697159,
          0.10649972409009933,
          0.11773419380187988,
          0.11926567554473877,
          0.12149273604154587,
          0.1219441145658493,
          0.12209657579660416,
          0.12383794784545898,
          0.125274658203125,
          0.13216683268547058,
          0.13217337429523468,
          0.14249977469444275,
          0.1573610007762909,
          0.15896303951740265,
          0.17133337259292603,
          0.17970013618469238,
          0.18315866589546204,
          0.1881297379732132,
          0.1897231638431549,
          0.1904776394367218,
          0.19223806262016296,
          0.19262565672397614,
          0.19357822835445404,
          0.19691163301467896,
          0.1972905546426773,
          0.20275619626045227,
          0.2038634717464447,
          0.204138845205307,
          0.21361592411994934,
          0.2167135775089264,
          0.2216271162033081,
          0.22368580102920532,
          0.22803379595279694,
          0.2290230542421341,
          0.25358492136001587,
          0.2643882632255554,
          0.2646411061286926,
          0.33282220363616943,
          0.33572152256965637,
          0.34103888273239136
         ]
        },
        {
         "mode": "markers",
         "name": "H1",
         "type": "scatter",
         "x": [
          0.3421160876750946,
          0.012406336143612862,
          0.00836150348186493,
          0.008062447421252728,
          0.0071426331996917725,
          0.0015118992887437344,
          0.0011205206392332911,
          0.0009748348384164274
         ],
         "y": [
          2.1572299003601074,
          0.01435124035924673,
          0.008417228236794472,
          0.009965289384126663,
          0.012665953487157822,
          0.0018643250223249197,
          0.0012951800599694252,
          0.001064925454556942
         ]
        }
       ],
       "layout": {
        "height": 500,
        "plot_bgcolor": "white",
        "template": {
         "data": {
          "bar": [
           {
            "error_x": {
             "color": "#2a3f5f"
            },
            "error_y": {
             "color": "#2a3f5f"
            },
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             }
            },
            "type": "bar"
           }
          ],
          "barpolar": [
           {
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             }
            },
            "type": "barpolar"
           }
          ],
          "carpet": [
           {
            "aaxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "baxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "type": "carpet"
           }
          ],
          "choropleth": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "choropleth"
           }
          ],
          "contour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "contour"
           }
          ],
          "contourcarpet": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "contourcarpet"
           }
          ],
          "heatmap": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmap"
           }
          ],
          "heatmapgl": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmapgl"
           }
          ],
          "histogram": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "histogram"
           }
          ],
          "histogram2d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2d"
           }
          ],
          "histogram2dcontour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2dcontour"
           }
          ],
          "mesh3d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "mesh3d"
           }
          ],
          "parcoords": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "parcoords"
           }
          ],
          "pie": [
           {
            "automargin": true,
            "type": "pie"
           }
          ],
          "scatter": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter"
           }
          ],
          "scatter3d": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter3d"
           }
          ],
          "scattercarpet": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattercarpet"
           }
          ],
          "scattergeo": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergeo"
           }
          ],
          "scattergl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergl"
           }
          ],
          "scattermapbox": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolar"
           }
          ],
          "scatterpolargl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolargl"
           }
          ],
          "scatterternary": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterternary"
           }
          ],
          "surface": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "surface"
           }
          ],
          "table": [
           {
            "cells": {
             "fill": {
              "color": "#EBF0F8"
             },
             "line": {
              "color": "white"
             }
            },
            "header": {
             "fill": {
              "color": "#C8D4E3"
             },
             "line": {
              "color": "white"
             }
            },
            "type": "table"
           }
          ]
         },
         "layout": {
          "annotationdefaults": {
           "arrowcolor": "#2a3f5f",
           "arrowhead": 0,
           "arrowwidth": 1
          },
          "coloraxis": {
           "colorbar": {
            "outlinewidth": 0,
            "ticks": ""
           }
          },
          "colorscale": {
           "diverging": [
            [
             0,
             "#8e0152"
            ],
            [
             0.1,
             "#c51b7d"
            ],
            [
             0.2,
             "#de77ae"
            ],
            [
             0.3,
             "#f1b6da"
            ],
            [
             0.4,
             "#fde0ef"
            ],
            [
             0.5,
             "#f7f7f7"
            ],
            [
             0.6,
             "#e6f5d0"
            ],
            [
             0.7,
             "#b8e186"
            ],
            [
             0.8,
             "#7fbc41"
            ],
            [
             0.9,
             "#4d9221"
            ],
            [
             1,
             "#276419"
            ]
           ],
           "sequential": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ],
           "sequentialminus": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        },
        "width": 500,
        "xaxis": {
         "anchor": "y",
         "exponentformat": "e",
         "linecolor": "black",
         "linewidth": 1,
         "mirror": false,
         "range": [
          0,
          2.3729528903961183
         ],
         "showexponent": "all",
         "showline": true,
         "side": "bottom",
         "ticks": "outside",
         "title": {
          "text": "Birth"
         },
         "type": "linear",
         "zeroline": true
        },
        "yaxis": {
         "anchor": "x",
         "exponentformat": "e",
         "linecolor": "black",
         "linewidth": 1,
         "mirror": false,
         "range": [
          0,
          2.3729528903961183
         ],
         "showexponent": "all",
         "showline": true,
         "side": "left",
         "ticks": "outside",
         "title": {
          "text": "Death"
         },
         "type": "linear",
         "zeroline": true
        }
       }
      },
      "text/html": [
       "<div>\n",
       "        \n",
       "        \n",
       "            <div id=\"62149eef-e8f0-4eb3-9316-699e42d40451\" class=\"plotly-graph-div\" style=\"height:500px; width:500px;\"></div>\n",
       "            <script type=\"text/javascript\">\n",
       "                require([\"plotly\"], function(Plotly) {\n",
       "                    window.PLOTLYENV=window.PLOTLYENV || {};\n",
       "                    \n",
       "                if (document.getElementById(\"62149eef-e8f0-4eb3-9316-699e42d40451\")) {\n",
       "                    Plotly.newPlot(\n",
       "                        '62149eef-e8f0-4eb3-9316-699e42d40451',\n",
       "                        [{\"hoverinfo\": \"none\", \"line\": {\"color\": \"black\", \"dash\": \"dash\", \"width\": 1}, \"mode\": \"lines\", \"showlegend\": false, \"type\": \"scatter\", \"x\": [-215.72299003601074, 215.72299003601074], \"y\": [-215.72299003601074, 215.72299003601074]}, {\"mode\": \"markers\", \"name\": \"H0\", \"type\": \"scatter\", \"x\": [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], \"y\": [3.1115465390030295e-05, 0.00011724147771019489, 0.00018083618488162756, 0.00030200701439753175, 0.0003210972936358303, 0.00032163949799723923, 0.00034711218904703856, 0.00040335001540370286, 0.0004294600512366742, 0.00044809546670876443, 0.00045218432205729187, 0.0004985016421414912, 0.0006946500507183373, 0.0007524000247940421, 0.0007821202161721885, 0.0008903918205760419, 0.0008979983394965529, 0.0009090504609048367, 0.0009277918725274503, 0.0009387360187247396, 0.0009700138471089303, 0.0009723960538394749, 0.0009990863036364317, 0.001057142042554915, 0.0010927460389211774, 0.0011640521697700024, 0.0011711467523127794, 0.0012091384269297123, 0.0013271733187139034, 0.0013361260062083602, 0.0014009801670908928, 0.0014329892583191395, 0.0014770843554288149, 0.0015520630404353142, 0.0017055911011993885, 0.0017181670991703868, 0.001718968152999878, 0.0017451574094593525, 0.0018401487031951547, 0.001997033366933465, 0.0021304611582309008, 0.0022279394324868917, 0.0024083165917545557, 0.002469613216817379, 0.002636025892570615, 0.003008101601153612, 0.003009792882949114, 0.0030583005864173174, 0.003233747323974967, 0.003272024681791663, 0.003427602117881179, 0.0034404327161610126, 0.0036608928348869085, 0.003673546714708209, 0.0037313185166567564, 0.0037498981691896915, 0.003782292827963829, 0.004389222711324692, 0.0045432886108756065, 0.004573663230985403, 0.004673801362514496, 0.005345672834664583, 0.005503309890627861, 0.005838809069246054, 0.00617360370233655, 0.006209418177604675, 0.0063294656574726105, 0.006551452912390232, 0.006726308725774288, 0.006891865748912096, 0.007111506536602974, 0.007183264009654522, 0.00865400955080986, 0.008829085156321526, 0.00927064847201109, 0.010975435376167297, 0.011464009992778301, 0.012786324135959148, 0.014875533059239388, 0.015044189058244228, 0.01533709280192852, 0.016633369028568268, 0.021069874987006187, 0.024333905428647995, 0.02459896355867386, 0.025049136951565742, 0.025928784161806107, 0.026079507544636726, 0.05318451672792435, 0.05566033720970154, 0.06598460674285889, 0.072403684258461, 0.07274448126554489, 0.07540038228034973, 0.07894501090049744, 0.08755286782979965, 0.09078233689069748, 0.09111286699771881, 0.09442399442195892, 0.10571727901697159, 0.10649972409009933, 0.11773419380187988, 0.11926567554473877, 0.12149273604154587, 0.1219441145658493, 0.12209657579660416, 0.12383794784545898, 0.125274658203125, 0.13216683268547058, 0.13217337429523468, 0.14249977469444275, 0.1573610007762909, 0.15896303951740265, 0.17133337259292603, 0.17970013618469238, 0.18315866589546204, 0.1881297379732132, 0.1897231638431549, 0.1904776394367218, 0.19223806262016296, 0.19262565672397614, 0.19357822835445404, 0.19691163301467896, 0.1972905546426773, 0.20275619626045227, 0.2038634717464447, 0.204138845205307, 0.21361592411994934, 0.2167135775089264, 0.2216271162033081, 0.22368580102920532, 0.22803379595279694, 0.2290230542421341, 0.25358492136001587, 0.2643882632255554, 0.2646411061286926, 0.33282220363616943, 0.33572152256965637, 0.34103888273239136]}, {\"mode\": \"markers\", \"name\": \"H1\", \"type\": \"scatter\", \"x\": [0.3421160876750946, 0.012406336143612862, 0.00836150348186493, 0.008062447421252728, 0.0071426331996917725, 0.0015118992887437344, 0.0011205206392332911, 0.0009748348384164274], \"y\": [2.1572299003601074, 0.01435124035924673, 0.008417228236794472, 0.009965289384126663, 0.012665953487157822, 0.0018643250223249197, 0.0012951800599694252, 0.001064925454556942]}],\n",
       "                        {\"height\": 500, \"plot_bgcolor\": \"white\", \"template\": {\"data\": {\"bar\": [{\"error_x\": {\"color\": \"#2a3f5f\"}, \"error_y\": {\"color\": \"#2a3f5f\"}, \"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"bar\"}], \"barpolar\": [{\"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"barpolar\"}], \"carpet\": [{\"aaxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"baxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"type\": \"carpet\"}], \"choropleth\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"choropleth\"}], \"contour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"contour\"}], \"contourcarpet\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"contourcarpet\"}], \"heatmap\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmap\"}], \"heatmapgl\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmapgl\"}], \"histogram\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"histogram\"}], \"histogram2d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2d\"}], \"histogram2dcontour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2dcontour\"}], \"mesh3d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"mesh3d\"}], \"parcoords\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"parcoords\"}], \"pie\": [{\"automargin\": true, \"type\": \"pie\"}], \"scatter\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter\"}], \"scatter3d\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter3d\"}], \"scattercarpet\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattercarpet\"}], \"scattergeo\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergeo\"}], \"scattergl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergl\"}], \"scattermapbox\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattermapbox\"}], \"scatterpolar\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolar\"}], \"scatterpolargl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolargl\"}], \"scatterternary\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterternary\"}], \"surface\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"surface\"}], \"table\": [{\"cells\": {\"fill\": {\"color\": \"#EBF0F8\"}, \"line\": {\"color\": \"white\"}}, \"header\": {\"fill\": {\"color\": \"#C8D4E3\"}, \"line\": {\"color\": \"white\"}}, \"type\": \"table\"}]}, \"layout\": {\"annotationdefaults\": {\"arrowcolor\": \"#2a3f5f\", \"arrowhead\": 0, \"arrowwidth\": 1}, \"coloraxis\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"colorscale\": {\"diverging\": [[0, \"#8e0152\"], [0.1, \"#c51b7d\"], [0.2, \"#de77ae\"], [0.3, \"#f1b6da\"], [0.4, \"#fde0ef\"], [0.5, \"#f7f7f7\"], [0.6, \"#e6f5d0\"], [0.7, \"#b8e186\"], [0.8, \"#7fbc41\"], [0.9, \"#4d9221\"], [1, \"#276419\"]], \"sequential\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"sequentialminus\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]]}, \"colorway\": [\"#636efa\", \"#EF553B\", \"#00cc96\", \"#ab63fa\", \"#FFA15A\", \"#19d3f3\", \"#FF6692\", \"#B6E880\", \"#FF97FF\", \"#FECB52\"], \"font\": {\"color\": \"#2a3f5f\"}, \"geo\": {\"bgcolor\": \"white\", \"lakecolor\": \"white\", \"landcolor\": \"#E5ECF6\", \"showlakes\": true, \"showland\": true, \"subunitcolor\": \"white\"}, \"hoverlabel\": {\"align\": \"left\"}, \"hovermode\": \"closest\", \"mapbox\": {\"style\": \"light\"}, \"paper_bgcolor\": \"white\", \"plot_bgcolor\": \"#E5ECF6\", \"polar\": {\"angularaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"radialaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"scene\": {\"xaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"yaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"zaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}}, \"shapedefaults\": {\"line\": {\"color\": \"#2a3f5f\"}}, \"ternary\": {\"aaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"baxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"caxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"title\": {\"x\": 0.05}, \"xaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}, \"yaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}}}, \"width\": 500, \"xaxis\": {\"anchor\": \"y\", \"exponentformat\": \"e\", \"linecolor\": \"black\", \"linewidth\": 1, \"mirror\": false, \"range\": [0, 2.3729528903961183], \"showexponent\": \"all\", \"showline\": true, \"side\": \"bottom\", \"ticks\": \"outside\", \"title\": {\"text\": \"Birth\"}, \"type\": \"linear\", \"zeroline\": true}, \"yaxis\": {\"anchor\": \"x\", \"exponentformat\": \"e\", \"linecolor\": \"black\", \"linewidth\": 1, \"mirror\": false, \"range\": [0, 2.3729528903961183], \"showexponent\": \"all\", \"showline\": true, \"side\": \"left\", \"ticks\": \"outside\", \"title\": {\"text\": \"Death\"}, \"type\": \"linear\", \"zeroline\": true}},\n",
       "                        {\"responsive\": true}\n",
       "                    ).then(function(){\n",
       "                            \n",
       "var gd = document.getElementById('62149eef-e8f0-4eb3-9316-699e42d40451');\n",
       "var x = new MutationObserver(function (mutations, observer) {{\n",
       "        var display = window.getComputedStyle(gd).display;\n",
       "        if (!display || display === 'none') {{\n",
       "            console.log([gd, 'removed!']);\n",
       "            Plotly.purge(gd);\n",
       "            observer.disconnect();\n",
       "        }}\n",
       "}});\n",
       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
       "if (notebookContainer) {{\n",
       "    x.observe(notebookContainer, {childList: true});\n",
       "}}\n",
       "\n",
       "// Listen for the clearing of the current output cell\n",
       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
       "}}\n",
       "\n",
       "                        })\n",
       "                };\n",
       "                });\n",
       "            </script>\n",
       "        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_pd = VietorisRipsPersistence(homology_dimensions=(0, 1)).fit_transform([sample_embedding])[0]\n",
    "plot_diagram(sample_pd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Diagram also can be scaled for normalization."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"images/sample_pd_scaled.png\" />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "hoverinfo": "none",
         "line": {
          "color": "black",
          "dash": "dash",
          "width": 1
         },
         "mode": "lines",
         "showlegend": false,
         "type": "scatter",
         "x": [
          -237.69637862752177,
          237.69637862752177
         ],
         "y": [
          -237.69637862752177,
          237.69637862752177
         ]
        },
        {
         "mode": "markers",
         "name": "H0",
         "type": "scatter",
         "x": [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0
         ],
         "y": [
          3.428486431272609e-05,
          0.00012918361029578093,
          0.00019925602859484064,
          0.0003327692316448046,
          0.00035380403299432346,
          0.0003544014659019679,
          0.00038246878693911957,
          0.00044443495783555974,
          0.00047320454313704333,
          0.00049373814862432,
          0.0004982434918374587,
          0.0005492786608285252,
          0.0007654066052098122,
          0.0008290389501042384,
          0.0008617864187978766,
          0.0009810864909445287,
          0.0009894678044107725,
          0.0010016456869557076,
          0.001022296085285155,
          0.0010343549943417722,
          0.0010688187598264533,
          0.0010714436164210057,
          0.0011008525158634876,
          0.0011648217705876353,
          0.0012040523644131487,
          0.0012826216864584095,
          0.0012904389180757288,
          0.0013323003973410245,
          0.0014623582382976615,
          0.001472222840100469,
          0.001543682999159693,
          0.0015789525133957144,
          0.0016275391053785582,
          0.0017101550653062577,
          0.0018793213839041723,
          0.0018931783639823474,
          0.0018940610125786977,
          0.0019229178878627153,
          0.0020275849264494426,
          0.0022004497491860823,
          0.002347468399327984,
          0.002454875740481756,
          0.00265362598744378,
          0.0027211662426437004,
          0.0029045295938454297,
          0.003314504666463717,
          0.0033163682210063383,
          0.00336981688425732,
          0.003563134500300492,
          0.0036053107622507816,
          0.0037767352040706335,
          0.0037908727178619633,
          0.004033788745700218,
          0.004047731540617944,
          0.0041113879367566395,
          0.00413186009933189,
          0.004167554454746681,
          0.004836305779450733,
          0.005006064720707439,
          0.00503953327777259,
          0.005149871407348017,
          0.005890179224361672,
          0.006063873077454105,
          0.0064335459610755505,
          0.006802442534668641,
          0.00684190504662556,
          0.006974180476440459,
          0.00721877919346443,
          0.00741144569422275,
          0.00759386623664913,
          0.007835879476982499,
          0.007914946114622593,
          0.009535500738665405,
          0.009728409419419352,
          0.010214950056820353,
          0.012093385328749,
          0.012631725804367196,
          0.0140887299150073,
          0.016390744156406047,
          0.016576579334152127,
          0.01689931804247699,
          0.01832763203312668,
          0.023216037297229875,
          0.02681253953177954,
          0.0271045962922686,
          0.02760062402314236,
          0.028569871465471217,
          0.02873594742365883,
          0.05860185334521915,
          0.06132985912036646,
          0.07270575132173222,
          0.07977867145571177,
          0.0801541818007956,
          0.0830806109825295,
          0.08698629292420819,
          0.09647093996853762,
          0.10002936042496137,
          0.10039355809092744,
          0.10404195457284514,
          0.11648556501323624,
          0.1173477093786855,
          0.1297265140941451,
          0.1314139914657083,
          0.13386789874275415,
          0.13436525435885818,
          0.13453324518090953,
          0.13645199213405942,
          0.13803504477530482,
          0.14562925119275288,
          0.14563645912618206,
          0.1570146992420817,
          0.1733896791226707,
          0.17515490037757586,
          0.1887852666819615,
          0.1980042627948166,
          0.20181507585414052,
          0.20729249775794686,
          0.20904822884081997,
          0.20987955477563927,
          0.21181929339824063,
          0.21224636755866458,
          0.21329596745022047,
          0.21696891031135596,
          0.21738642862381685,
          0.22340879656524076,
          0.22462885833575252,
          0.2249322811370533,
          0.23537468849290208,
          0.23878786662788065,
          0.24420189483927235,
          0.2464702758206852,
          0.2512611543796003,
          0.25235117780669747,
          0.27941489904139905,
          0.2913186615383178,
          0.291597258837694,
          0.36672323389335143,
          0.36991787536786935,
          0.3757768580119045
         ]
        },
        {
         "mode": "markers",
         "name": "H1",
         "type": "scatter",
         "x": [
          0.376963786275218,
          0.013670036619093048,
          0.009213200211942796,
          0.00888368251611322,
          0.007870176679583535,
          0.0016659002627579067,
          0.001234656065534268,
          0.0010741308138407033
         ],
         "y": [
          2.3769637862752178,
          0.015813047379125623,
          0.00927460105032561,
          0.010980346592575898,
          0.013956098398503916,
          0.0020542238280552897,
          0.0014271061692308165,
          0.0011733979953374358
         ]
        }
       ],
       "layout": {
        "height": 500,
        "plot_bgcolor": "white",
        "template": {
         "data": {
          "bar": [
           {
            "error_x": {
             "color": "#2a3f5f"
            },
            "error_y": {
             "color": "#2a3f5f"
            },
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             }
            },
            "type": "bar"
           }
          ],
          "barpolar": [
           {
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             }
            },
            "type": "barpolar"
           }
          ],
          "carpet": [
           {
            "aaxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "baxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "type": "carpet"
           }
          ],
          "choropleth": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "choropleth"
           }
          ],
          "contour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "contour"
           }
          ],
          "contourcarpet": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "contourcarpet"
           }
          ],
          "heatmap": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmap"
           }
          ],
          "heatmapgl": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmapgl"
           }
          ],
          "histogram": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "histogram"
           }
          ],
          "histogram2d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2d"
           }
          ],
          "histogram2dcontour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2dcontour"
           }
          ],
          "mesh3d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "mesh3d"
           }
          ],
          "parcoords": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "parcoords"
           }
          ],
          "pie": [
           {
            "automargin": true,
            "type": "pie"
           }
          ],
          "scatter": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter"
           }
          ],
          "scatter3d": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter3d"
           }
          ],
          "scattercarpet": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattercarpet"
           }
          ],
          "scattergeo": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergeo"
           }
          ],
          "scattergl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergl"
           }
          ],
          "scattermapbox": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolar"
           }
          ],
          "scatterpolargl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolargl"
           }
          ],
          "scatterternary": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterternary"
           }
          ],
          "surface": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "surface"
           }
          ],
          "table": [
           {
            "cells": {
             "fill": {
              "color": "#EBF0F8"
             },
             "line": {
              "color": "white"
             }
            },
            "header": {
             "fill": {
              "color": "#C8D4E3"
             },
             "line": {
              "color": "white"
             }
            },
            "type": "table"
           }
          ]
         },
         "layout": {
          "annotationdefaults": {
           "arrowcolor": "#2a3f5f",
           "arrowhead": 0,
           "arrowwidth": 1
          },
          "coloraxis": {
           "colorbar": {
            "outlinewidth": 0,
            "ticks": ""
           }
          },
          "colorscale": {
           "diverging": [
            [
             0,
             "#8e0152"
            ],
            [
             0.1,
             "#c51b7d"
            ],
            [
             0.2,
             "#de77ae"
            ],
            [
             0.3,
             "#f1b6da"
            ],
            [
             0.4,
             "#fde0ef"
            ],
            [
             0.5,
             "#f7f7f7"
            ],
            [
             0.6,
             "#e6f5d0"
            ],
            [
             0.7,
             "#b8e186"
            ],
            [
             0.8,
             "#7fbc41"
            ],
            [
             0.9,
             "#4d9221"
            ],
            [
             1,
             "#276419"
            ]
           ],
           "sequential": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ],
           "sequentialminus": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        },
        "width": 500,
        "xaxis": {
         "anchor": "y",
         "exponentformat": "e",
         "linecolor": "black",
         "linewidth": 1,
         "mirror": false,
         "range": [
          0,
          2.6146601649027397
         ],
         "showexponent": "all",
         "showline": true,
         "side": "bottom",
         "ticks": "outside",
         "title": {
          "text": "Birth"
         },
         "type": "linear",
         "zeroline": true
        },
        "yaxis": {
         "anchor": "x",
         "exponentformat": "e",
         "linecolor": "black",
         "linewidth": 1,
         "mirror": false,
         "range": [
          0,
          2.6146601649027397
         ],
         "showexponent": "all",
         "showline": true,
         "side": "left",
         "ticks": "outside",
         "title": {
          "text": "Death"
         },
         "type": "linear",
         "zeroline": true
        }
       }
      },
      "text/html": [
       "<div>\n",
       "        \n",
       "        \n",
       "            <div id=\"567dcba1-d4a5-4c31-9a24-5b3aaa87ea10\" class=\"plotly-graph-div\" style=\"height:500px; width:500px;\"></div>\n",
       "            <script type=\"text/javascript\">\n",
       "                require([\"plotly\"], function(Plotly) {\n",
       "                    window.PLOTLYENV=window.PLOTLYENV || {};\n",
       "                    \n",
       "                if (document.getElementById(\"567dcba1-d4a5-4c31-9a24-5b3aaa87ea10\")) {\n",
       "                    Plotly.newPlot(\n",
       "                        '567dcba1-d4a5-4c31-9a24-5b3aaa87ea10',\n",
       "                        [{\"hoverinfo\": \"none\", \"line\": {\"color\": \"black\", \"dash\": \"dash\", \"width\": 1}, \"mode\": \"lines\", \"showlegend\": false, \"type\": \"scatter\", \"x\": [-237.69637862752177, 237.69637862752177], \"y\": [-237.69637862752177, 237.69637862752177]}, {\"mode\": \"markers\", \"name\": \"H0\", \"type\": \"scatter\", \"x\": [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], \"y\": [3.428486431272609e-05, 0.00012918361029578093, 0.00019925602859484064, 0.0003327692316448046, 0.00035380403299432346, 0.0003544014659019679, 0.00038246878693911957, 0.00044443495783555974, 0.00047320454313704333, 0.00049373814862432, 0.0004982434918374587, 0.0005492786608285252, 0.0007654066052098122, 0.0008290389501042384, 0.0008617864187978766, 0.0009810864909445287, 0.0009894678044107725, 0.0010016456869557076, 0.001022296085285155, 0.0010343549943417722, 0.0010688187598264533, 0.0010714436164210057, 0.0011008525158634876, 0.0011648217705876353, 0.0012040523644131487, 0.0012826216864584095, 0.0012904389180757288, 0.0013323003973410245, 0.0014623582382976615, 0.001472222840100469, 0.001543682999159693, 0.0015789525133957144, 0.0016275391053785582, 0.0017101550653062577, 0.0018793213839041723, 0.0018931783639823474, 0.0018940610125786977, 0.0019229178878627153, 0.0020275849264494426, 0.0022004497491860823, 0.002347468399327984, 0.002454875740481756, 0.00265362598744378, 0.0027211662426437004, 0.0029045295938454297, 0.003314504666463717, 0.0033163682210063383, 0.00336981688425732, 0.003563134500300492, 0.0036053107622507816, 0.0037767352040706335, 0.0037908727178619633, 0.004033788745700218, 0.004047731540617944, 0.0041113879367566395, 0.00413186009933189, 0.004167554454746681, 0.004836305779450733, 0.005006064720707439, 0.00503953327777259, 0.005149871407348017, 0.005890179224361672, 0.006063873077454105, 0.0064335459610755505, 0.006802442534668641, 0.00684190504662556, 0.006974180476440459, 0.00721877919346443, 0.00741144569422275, 0.00759386623664913, 0.007835879476982499, 0.007914946114622593, 0.009535500738665405, 0.009728409419419352, 0.010214950056820353, 0.012093385328749, 0.012631725804367196, 0.0140887299150073, 0.016390744156406047, 0.016576579334152127, 0.01689931804247699, 0.01832763203312668, 0.023216037297229875, 0.02681253953177954, 0.0271045962922686, 0.02760062402314236, 0.028569871465471217, 0.02873594742365883, 0.05860185334521915, 0.06132985912036646, 0.07270575132173222, 0.07977867145571177, 0.0801541818007956, 0.0830806109825295, 0.08698629292420819, 0.09647093996853762, 0.10002936042496137, 0.10039355809092744, 0.10404195457284514, 0.11648556501323624, 0.1173477093786855, 0.1297265140941451, 0.1314139914657083, 0.13386789874275415, 0.13436525435885818, 0.13453324518090953, 0.13645199213405942, 0.13803504477530482, 0.14562925119275288, 0.14563645912618206, 0.1570146992420817, 0.1733896791226707, 0.17515490037757586, 0.1887852666819615, 0.1980042627948166, 0.20181507585414052, 0.20729249775794686, 0.20904822884081997, 0.20987955477563927, 0.21181929339824063, 0.21224636755866458, 0.21329596745022047, 0.21696891031135596, 0.21738642862381685, 0.22340879656524076, 0.22462885833575252, 0.2249322811370533, 0.23537468849290208, 0.23878786662788065, 0.24420189483927235, 0.2464702758206852, 0.2512611543796003, 0.25235117780669747, 0.27941489904139905, 0.2913186615383178, 0.291597258837694, 0.36672323389335143, 0.36991787536786935, 0.3757768580119045]}, {\"mode\": \"markers\", \"name\": \"H1\", \"type\": \"scatter\", \"x\": [0.376963786275218, 0.013670036619093048, 0.009213200211942796, 0.00888368251611322, 0.007870176679583535, 0.0016659002627579067, 0.001234656065534268, 0.0010741308138407033], \"y\": [2.3769637862752178, 0.015813047379125623, 0.00927460105032561, 0.010980346592575898, 0.013956098398503916, 0.0020542238280552897, 0.0014271061692308165, 0.0011733979953374358]}],\n",
       "                        {\"height\": 500, \"plot_bgcolor\": \"white\", \"template\": {\"data\": {\"bar\": [{\"error_x\": {\"color\": \"#2a3f5f\"}, \"error_y\": {\"color\": \"#2a3f5f\"}, \"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"bar\"}], \"barpolar\": [{\"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"barpolar\"}], \"carpet\": [{\"aaxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"baxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"type\": \"carpet\"}], \"choropleth\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"choropleth\"}], \"contour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"contour\"}], \"contourcarpet\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"contourcarpet\"}], \"heatmap\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmap\"}], \"heatmapgl\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmapgl\"}], \"histogram\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"histogram\"}], \"histogram2d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2d\"}], \"histogram2dcontour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2dcontour\"}], \"mesh3d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"mesh3d\"}], \"parcoords\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"parcoords\"}], \"pie\": [{\"automargin\": true, \"type\": \"pie\"}], \"scatter\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter\"}], \"scatter3d\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter3d\"}], \"scattercarpet\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattercarpet\"}], \"scattergeo\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergeo\"}], \"scattergl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergl\"}], \"scattermapbox\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattermapbox\"}], \"scatterpolar\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolar\"}], \"scatterpolargl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolargl\"}], \"scatterternary\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterternary\"}], \"surface\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"surface\"}], \"table\": [{\"cells\": {\"fill\": {\"color\": \"#EBF0F8\"}, \"line\": {\"color\": \"white\"}}, \"header\": {\"fill\": {\"color\": \"#C8D4E3\"}, \"line\": {\"color\": \"white\"}}, \"type\": \"table\"}]}, \"layout\": {\"annotationdefaults\": {\"arrowcolor\": \"#2a3f5f\", \"arrowhead\": 0, \"arrowwidth\": 1}, \"coloraxis\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"colorscale\": {\"diverging\": [[0, \"#8e0152\"], [0.1, \"#c51b7d\"], [0.2, \"#de77ae\"], [0.3, \"#f1b6da\"], [0.4, \"#fde0ef\"], [0.5, \"#f7f7f7\"], [0.6, \"#e6f5d0\"], [0.7, \"#b8e186\"], [0.8, \"#7fbc41\"], [0.9, \"#4d9221\"], [1, \"#276419\"]], \"sequential\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"sequentialminus\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]]}, \"colorway\": [\"#636efa\", \"#EF553B\", \"#00cc96\", \"#ab63fa\", \"#FFA15A\", \"#19d3f3\", \"#FF6692\", \"#B6E880\", \"#FF97FF\", \"#FECB52\"], \"font\": {\"color\": \"#2a3f5f\"}, \"geo\": {\"bgcolor\": \"white\", \"lakecolor\": \"white\", \"landcolor\": \"#E5ECF6\", \"showlakes\": true, \"showland\": true, \"subunitcolor\": \"white\"}, \"hoverlabel\": {\"align\": \"left\"}, \"hovermode\": \"closest\", \"mapbox\": {\"style\": \"light\"}, \"paper_bgcolor\": \"white\", \"plot_bgcolor\": \"#E5ECF6\", \"polar\": {\"angularaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"radialaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"scene\": {\"xaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"yaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"zaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}}, \"shapedefaults\": {\"line\": {\"color\": \"#2a3f5f\"}}, \"ternary\": {\"aaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"baxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"caxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"title\": {\"x\": 0.05}, \"xaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}, \"yaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}}}, \"width\": 500, \"xaxis\": {\"anchor\": \"y\", \"exponentformat\": \"e\", \"linecolor\": \"black\", \"linewidth\": 1, \"mirror\": false, \"range\": [0, 2.6146601649027397], \"showexponent\": \"all\", \"showline\": true, \"side\": \"bottom\", \"ticks\": \"outside\", \"title\": {\"text\": \"Birth\"}, \"type\": \"linear\", \"zeroline\": true}, \"yaxis\": {\"anchor\": \"x\", \"exponentformat\": \"e\", \"linecolor\": \"black\", \"linewidth\": 1, \"mirror\": false, \"range\": [0, 2.6146601649027397], \"showexponent\": \"all\", \"showline\": true, \"side\": \"left\", \"ticks\": \"outside\", \"title\": {\"text\": \"Death\"}, \"type\": \"linear\", \"zeroline\": true}},\n",
       "                        {\"responsive\": true}\n",
       "                    ).then(function(){\n",
       "                            \n",
       "var gd = document.getElementById('567dcba1-d4a5-4c31-9a24-5b3aaa87ea10');\n",
       "var x = new MutationObserver(function (mutations, observer) {{\n",
       "        var display = window.getComputedStyle(gd).display;\n",
       "        if (!display || display === 'none') {{\n",
       "            console.log([gd, 'removed!']);\n",
       "            Plotly.purge(gd);\n",
       "            observer.disconnect();\n",
       "        }}\n",
       "}});\n",
       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
       "if (notebookContainer) {{\n",
       "    x.observe(notebookContainer, {childList: true});\n",
       "}}\n",
       "\n",
       "// Listen for the clearing of the current output cell\n",
       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
       "}}\n",
       "\n",
       "                        })\n",
       "                };\n",
       "                });\n",
       "            </script>\n",
       "        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_pd = Scaler().fit_transform([sample_pd])[0]\n",
    "plot_diagram(sample_pd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4. Alternative Persistence Homology Representation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PD is not the only way to represent Persistence Homology. There are some extensions over PD that can also be useful for feature engineering."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.4.1. Betti Curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $D$ be a PD. *Betti Curve* is a function $\\beta_{D}: \\mathbb{R} \\rightarrow \\mathbb{N}$ whose value $s \\in \\mathbb{R}$ is the number, counted with multiplicity, of points $(b_i , d_i)$ such that $b_i \\leq s < d_i$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"images/sample_bc.png\" />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "mode": "lines",
         "name": "H0",
         "showlegend": true,
         "type": "scatter",
         "x": [
          0,
          0.0037957258385040863,
          0.0075914516770081725,
          0.01138717751551226,
          0.015182903354016345,
          0.01897862919252043,
          0.02277435503102452,
          0.026570080869528605,
          0.03036580670803269,
          0.034161532546536776,
          0.03795725838504086,
          0.041752984223544946,
          0.04554871006204904,
          0.049344435900553124,
          0.05314016173905721,
          0.056935887577561295,
          0.06073161341606538,
          0.06452733925456947,
          0.06832306509307355,
          0.07211879093157764,
          0.07591451677008172,
          0.07971024260858581,
          0.08350596844708989,
          0.08730169428559398,
          0.09109742012409808,
          0.09489314596260216,
          0.09868887180110625,
          0.10248459763961033,
          0.10628032347811442,
          0.1100760493166185,
          0.11387177515512259,
          0.11766750099362668,
          0.12146322683213076,
          0.12525895267063486,
          0.12905467850913893,
          0.13285040434764303,
          0.1366461301861471,
          0.1404418560246512,
          0.14423758186315527,
          0.14803330770165937,
          0.15182903354016344,
          0.15562475937866754,
          0.15942048521717161,
          0.16321621105567571,
          0.16701193689417979,
          0.17080766273268388,
          0.17460338857118796,
          0.17839911440969206,
          0.18219484024819615,
          0.18599056608670023,
          0.18978629192520433,
          0.1935820177637084,
          0.1973777436022125,
          0.20117346944071657,
          0.20496919527922067,
          0.20876492111772474,
          0.21256064695622884,
          0.2163563727947329,
          0.220152098633237,
          0.22394782447174108,
          0.22774355031024518,
          0.23153927614874925,
          0.23533500198725335,
          0.23913072782575742,
          0.24292645366426152,
          0.24672217950276562,
          0.2505179053412697,
          0.2543136311797738,
          0.25810935701827786,
          0.26190508285678193,
          0.26570080869528606,
          0.26949653453379013,
          0.2732922603722942,
          0.2770879862107983,
          0.2808837120493024,
          0.2846794378878065,
          0.28847516372631055,
          0.2922708895648146,
          0.29606661540331874,
          0.2998623412418228,
          0.3036580670803269,
          0.307453792918831,
          0.3112495187573351,
          0.31504524459583916,
          0.31884097043434323,
          0.32263669627284736,
          0.32643242211135143,
          0.3302281479498555,
          0.33402387378835957,
          0.3378195996268637,
          0.34161532546536777,
          0.34541105130387184,
          0.3492067771423759,
          0.35300250298088004,
          0.3567982288193841,
          0.3605939546578882,
          0.3643896804963923,
          0.3681854063348964,
          0.37198113217340045,
          0.3757768580119045
         ],
         "y": [
          139,
          87,
          70,
          64,
          61,
          57,
          57,
          56,
          51,
          51,
          51,
          51,
          51,
          51,
          51,
          51,
          50,
          49,
          49,
          49,
          48,
          48,
          45,
          44,
          44,
          44,
          43,
          41,
          40,
          40,
          40,
          38,
          38,
          38,
          38,
          36,
          32,
          31,
          31,
          29,
          29,
          29,
          28,
          28,
          28,
          28,
          27,
          26,
          26,
          26,
          25,
          25,
          25,
          24,
          23,
          22,
          18,
          17,
          15,
          14,
          12,
          12,
          12,
          10,
          10,
          8,
          8,
          6,
          6,
          6,
          6,
          6,
          6,
          6,
          5,
          5,
          5,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          3,
          2,
          1,
          0
         ]
        },
        {
         "mode": "lines",
         "name": "H1",
         "showlegend": true,
         "type": "scatter",
         "x": [
          0.0010741308138407033,
          0.025073016222541482,
          0.04907190163124226,
          0.07307078703994305,
          0.09706967244864383,
          0.1210685578573446,
          0.14506744326604537,
          0.16906632867474616,
          0.19306521408344693,
          0.2170640994921477,
          0.2410629849008485,
          0.2650618703095493,
          0.2890607557182501,
          0.31305964112695084,
          0.33705852653565166,
          0.3610574119443524,
          0.3850562973530532,
          0.40905518276175395,
          0.4330540681704547,
          0.45705295357915554,
          0.4810518389878563,
          0.5050507243965571,
          0.5290496098052578,
          0.5530484952139586,
          0.5770473806226594,
          0.6010462660313601,
          0.6250451514400609,
          0.6490440368487617,
          0.6730429222574625,
          0.6970418076661633,
          0.7210406930748641,
          0.7450395784835648,
          0.7690384638922656,
          0.7930373493009664,
          0.8170362347096671,
          0.8410351201183679,
          0.8650340055270687,
          0.8890328909357695,
          0.9130317763444703,
          0.9370306617531711,
          0.9610295471618718,
          0.9850284325705726,
          1.0090273179792735,
          1.0330262033879742,
          1.057025088796675,
          1.0810239742053758,
          1.1050228596140765,
          1.1290217450227773,
          1.153020630431478,
          1.1770195158401788,
          1.2010184012488796,
          1.2250172866575804,
          1.2490161720662811,
          1.273015057474982,
          1.2970139428836827,
          1.3210128282923834,
          1.3450117137010844,
          1.3690105991097852,
          1.393009484518486,
          1.4170083699271867,
          1.4410072553358875,
          1.4650061407445882,
          1.489005026153289,
          1.5130039115619898,
          1.5370027969706905,
          1.5610016823793913,
          1.585000567788092,
          1.6089994531967928,
          1.6329983386054936,
          1.6569972240141944,
          1.6809961094228951,
          1.704994994831596,
          1.7289938802402967,
          1.7529927656489976,
          1.7769916510576984,
          1.8009905364663992,
          1.8249894218751,
          1.8489883072838007,
          1.8729871926925015,
          1.8969860781012022,
          1.920984963509903,
          1.9449838489186038,
          1.9689827343273045,
          1.9929816197360053,
          2.0169805051447063,
          2.040979390553407,
          2.064978275962108,
          2.0889771613708086,
          2.1129760467795093,
          2.13697493218821,
          2.160973817596911,
          2.1849727030056116,
          2.2089715884143124,
          2.232970473823013,
          2.256969359231714,
          2.2809682446404147,
          2.3049671300491155,
          2.3289660154578162,
          2.352964900866517,
          2.3769637862752178
         ],
         "y": [
          1,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          0
         ]
        }
       ],
       "layout": {
        "plot_bgcolor": "white",
        "template": {
         "data": {
          "bar": [
           {
            "error_x": {
             "color": "#2a3f5f"
            },
            "error_y": {
             "color": "#2a3f5f"
            },
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             }
            },
            "type": "bar"
           }
          ],
          "barpolar": [
           {
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             }
            },
            "type": "barpolar"
           }
          ],
          "carpet": [
           {
            "aaxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "baxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "type": "carpet"
           }
          ],
          "choropleth": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "choropleth"
           }
          ],
          "contour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "contour"
           }
          ],
          "contourcarpet": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "contourcarpet"
           }
          ],
          "heatmap": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmap"
           }
          ],
          "heatmapgl": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmapgl"
           }
          ],
          "histogram": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "histogram"
           }
          ],
          "histogram2d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2d"
           }
          ],
          "histogram2dcontour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2dcontour"
           }
          ],
          "mesh3d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "mesh3d"
           }
          ],
          "parcoords": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "parcoords"
           }
          ],
          "pie": [
           {
            "automargin": true,
            "type": "pie"
           }
          ],
          "scatter": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter"
           }
          ],
          "scatter3d": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter3d"
           }
          ],
          "scattercarpet": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattercarpet"
           }
          ],
          "scattergeo": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergeo"
           }
          ],
          "scattergl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergl"
           }
          ],
          "scattermapbox": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolar"
           }
          ],
          "scatterpolargl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolargl"
           }
          ],
          "scatterternary": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterternary"
           }
          ],
          "surface": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "surface"
           }
          ],
          "table": [
           {
            "cells": {
             "fill": {
              "color": "#EBF0F8"
             },
             "line": {
              "color": "white"
             }
            },
            "header": {
             "fill": {
              "color": "#C8D4E3"
             },
             "line": {
              "color": "white"
             }
            },
            "type": "table"
           }
          ]
         },
         "layout": {
          "annotationdefaults": {
           "arrowcolor": "#2a3f5f",
           "arrowhead": 0,
           "arrowwidth": 1
          },
          "coloraxis": {
           "colorbar": {
            "outlinewidth": 0,
            "ticks": ""
           }
          },
          "colorscale": {
           "diverging": [
            [
             0,
             "#8e0152"
            ],
            [
             0.1,
             "#c51b7d"
            ],
            [
             0.2,
             "#de77ae"
            ],
            [
             0.3,
             "#f1b6da"
            ],
            [
             0.4,
             "#fde0ef"
            ],
            [
             0.5,
             "#f7f7f7"
            ],
            [
             0.6,
             "#e6f5d0"
            ],
            [
             0.7,
             "#b8e186"
            ],
            [
             0.8,
             "#7fbc41"
            ],
            [
             0.9,
             "#4d9221"
            ],
            [
             1,
             "#276419"
            ]
           ],
           "sequential": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ],
           "sequentialminus": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        },
        "xaxis": {
         "anchor": "x",
         "exponentformat": "e",
         "linecolor": "black",
         "linewidth": 1,
         "mirror": false,
         "showexponent": "all",
         "showline": true,
         "side": "bottom",
         "ticks": "outside",
         "title": {
          "text": "Filtration parameter"
         },
         "type": "linear",
         "zeroline": true
        },
        "yaxis": {
         "anchor": "y",
         "exponentformat": "e",
         "linecolor": "black",
         "linewidth": 1,
         "mirror": false,
         "showexponent": "all",
         "showline": true,
         "side": "left",
         "ticks": "outside",
         "title": {
          "text": "Betti number"
         },
         "type": "linear",
         "zeroline": true
        }
       }
      },
      "text/html": [
       "<div>\n",
       "        \n",
       "        \n",
       "            <div id=\"6a04a6f1-a846-46ed-8377-93ad8665f5d2\" class=\"plotly-graph-div\" style=\"height:525px; width:100%;\"></div>\n",
       "            <script type=\"text/javascript\">\n",
       "                require([\"plotly\"], function(Plotly) {\n",
       "                    window.PLOTLYENV=window.PLOTLYENV || {};\n",
       "                    \n",
       "                if (document.getElementById(\"6a04a6f1-a846-46ed-8377-93ad8665f5d2\")) {\n",
       "                    Plotly.newPlot(\n",
       "                        '6a04a6f1-a846-46ed-8377-93ad8665f5d2',\n",
       "                        [{\"mode\": \"lines\", \"name\": \"H0\", \"showlegend\": true, \"type\": \"scatter\", \"x\": [0.0, 0.0037957258385040863, 0.0075914516770081725, 0.01138717751551226, 0.015182903354016345, 0.01897862919252043, 0.02277435503102452, 0.026570080869528605, 0.03036580670803269, 0.034161532546536776, 0.03795725838504086, 0.041752984223544946, 0.04554871006204904, 0.049344435900553124, 0.05314016173905721, 0.056935887577561295, 0.06073161341606538, 0.06452733925456947, 0.06832306509307355, 0.07211879093157764, 0.07591451677008172, 0.07971024260858581, 0.08350596844708989, 0.08730169428559398, 0.09109742012409808, 0.09489314596260216, 0.09868887180110625, 0.10248459763961033, 0.10628032347811442, 0.1100760493166185, 0.11387177515512259, 0.11766750099362668, 0.12146322683213076, 0.12525895267063486, 0.12905467850913893, 0.13285040434764303, 0.1366461301861471, 0.1404418560246512, 0.14423758186315527, 0.14803330770165937, 0.15182903354016344, 0.15562475937866754, 0.15942048521717161, 0.16321621105567571, 0.16701193689417979, 0.17080766273268388, 0.17460338857118796, 0.17839911440969206, 0.18219484024819615, 0.18599056608670023, 0.18978629192520433, 0.1935820177637084, 0.1973777436022125, 0.20117346944071657, 0.20496919527922067, 0.20876492111772474, 0.21256064695622884, 0.2163563727947329, 0.220152098633237, 0.22394782447174108, 0.22774355031024518, 0.23153927614874925, 0.23533500198725335, 0.23913072782575742, 0.24292645366426152, 0.24672217950276562, 0.2505179053412697, 0.2543136311797738, 0.25810935701827786, 0.26190508285678193, 0.26570080869528606, 0.26949653453379013, 0.2732922603722942, 0.2770879862107983, 0.2808837120493024, 0.2846794378878065, 0.28847516372631055, 0.2922708895648146, 0.29606661540331874, 0.2998623412418228, 0.3036580670803269, 0.307453792918831, 0.3112495187573351, 0.31504524459583916, 0.31884097043434323, 0.32263669627284736, 0.32643242211135143, 0.3302281479498555, 0.33402387378835957, 0.3378195996268637, 0.34161532546536777, 0.34541105130387184, 0.3492067771423759, 0.35300250298088004, 0.3567982288193841, 0.3605939546578882, 0.3643896804963923, 0.3681854063348964, 0.37198113217340045, 0.3757768580119045], \"y\": [139, 87, 70, 64, 61, 57, 57, 56, 51, 51, 51, 51, 51, 51, 51, 51, 50, 49, 49, 49, 48, 48, 45, 44, 44, 44, 43, 41, 40, 40, 40, 38, 38, 38, 38, 36, 32, 31, 31, 29, 29, 29, 28, 28, 28, 28, 27, 26, 26, 26, 25, 25, 25, 24, 23, 22, 18, 17, 15, 14, 12, 12, 12, 10, 10, 8, 8, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 0]}, {\"mode\": \"lines\", \"name\": \"H1\", \"showlegend\": true, \"type\": \"scatter\", \"x\": [0.0010741308138407033, 0.025073016222541482, 0.04907190163124226, 0.07307078703994305, 0.09706967244864383, 0.1210685578573446, 0.14506744326604537, 0.16906632867474616, 0.19306521408344693, 0.2170640994921477, 0.2410629849008485, 0.2650618703095493, 0.2890607557182501, 0.31305964112695084, 0.33705852653565166, 0.3610574119443524, 0.3850562973530532, 0.40905518276175395, 0.4330540681704547, 0.45705295357915554, 0.4810518389878563, 0.5050507243965571, 0.5290496098052578, 0.5530484952139586, 0.5770473806226594, 0.6010462660313601, 0.6250451514400609, 0.6490440368487617, 0.6730429222574625, 0.6970418076661633, 0.7210406930748641, 0.7450395784835648, 0.7690384638922656, 0.7930373493009664, 0.8170362347096671, 0.8410351201183679, 0.8650340055270687, 0.8890328909357695, 0.9130317763444703, 0.9370306617531711, 0.9610295471618718, 0.9850284325705726, 1.0090273179792735, 1.0330262033879742, 1.057025088796675, 1.0810239742053758, 1.1050228596140765, 1.1290217450227773, 1.153020630431478, 1.1770195158401788, 1.2010184012488796, 1.2250172866575804, 1.2490161720662811, 1.273015057474982, 1.2970139428836827, 1.3210128282923834, 1.3450117137010844, 1.3690105991097852, 1.393009484518486, 1.4170083699271867, 1.4410072553358875, 1.4650061407445882, 1.489005026153289, 1.5130039115619898, 1.5370027969706905, 1.5610016823793913, 1.585000567788092, 1.6089994531967928, 1.6329983386054936, 1.6569972240141944, 1.6809961094228951, 1.704994994831596, 1.7289938802402967, 1.7529927656489976, 1.7769916510576984, 1.8009905364663992, 1.8249894218751, 1.8489883072838007, 1.8729871926925015, 1.8969860781012022, 1.920984963509903, 1.9449838489186038, 1.9689827343273045, 1.9929816197360053, 2.0169805051447063, 2.040979390553407, 2.064978275962108, 2.0889771613708086, 2.1129760467795093, 2.13697493218821, 2.160973817596911, 2.1849727030056116, 2.2089715884143124, 2.232970473823013, 2.256969359231714, 2.2809682446404147, 2.3049671300491155, 2.3289660154578162, 2.352964900866517, 2.3769637862752178], \"y\": [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]}],\n",
       "                        {\"plot_bgcolor\": \"white\", \"template\": {\"data\": {\"bar\": [{\"error_x\": {\"color\": \"#2a3f5f\"}, \"error_y\": {\"color\": \"#2a3f5f\"}, \"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"bar\"}], \"barpolar\": [{\"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"barpolar\"}], \"carpet\": [{\"aaxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"baxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"type\": \"carpet\"}], \"choropleth\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"choropleth\"}], \"contour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"contour\"}], \"contourcarpet\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"contourcarpet\"}], \"heatmap\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmap\"}], \"heatmapgl\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmapgl\"}], \"histogram\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"histogram\"}], \"histogram2d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2d\"}], \"histogram2dcontour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2dcontour\"}], \"mesh3d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"mesh3d\"}], \"parcoords\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"parcoords\"}], \"pie\": [{\"automargin\": true, \"type\": \"pie\"}], \"scatter\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter\"}], \"scatter3d\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter3d\"}], \"scattercarpet\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattercarpet\"}], \"scattergeo\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergeo\"}], \"scattergl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergl\"}], \"scattermapbox\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattermapbox\"}], \"scatterpolar\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolar\"}], \"scatterpolargl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolargl\"}], \"scatterternary\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterternary\"}], \"surface\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"surface\"}], \"table\": [{\"cells\": {\"fill\": {\"color\": \"#EBF0F8\"}, \"line\": {\"color\": \"white\"}}, \"header\": {\"fill\": {\"color\": \"#C8D4E3\"}, \"line\": {\"color\": \"white\"}}, \"type\": \"table\"}]}, \"layout\": {\"annotationdefaults\": {\"arrowcolor\": \"#2a3f5f\", \"arrowhead\": 0, \"arrowwidth\": 1}, \"coloraxis\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"colorscale\": {\"diverging\": [[0, \"#8e0152\"], [0.1, \"#c51b7d\"], [0.2, \"#de77ae\"], [0.3, \"#f1b6da\"], [0.4, \"#fde0ef\"], [0.5, \"#f7f7f7\"], [0.6, \"#e6f5d0\"], [0.7, \"#b8e186\"], [0.8, \"#7fbc41\"], [0.9, \"#4d9221\"], [1, \"#276419\"]], \"sequential\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"sequentialminus\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]]}, \"colorway\": [\"#636efa\", \"#EF553B\", \"#00cc96\", \"#ab63fa\", \"#FFA15A\", \"#19d3f3\", \"#FF6692\", \"#B6E880\", \"#FF97FF\", \"#FECB52\"], \"font\": {\"color\": \"#2a3f5f\"}, \"geo\": {\"bgcolor\": \"white\", \"lakecolor\": \"white\", \"landcolor\": \"#E5ECF6\", \"showlakes\": true, \"showland\": true, \"subunitcolor\": \"white\"}, \"hoverlabel\": {\"align\": \"left\"}, \"hovermode\": \"closest\", \"mapbox\": {\"style\": \"light\"}, \"paper_bgcolor\": \"white\", \"plot_bgcolor\": \"#E5ECF6\", \"polar\": {\"angularaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"radialaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"scene\": {\"xaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"yaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"zaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}}, \"shapedefaults\": {\"line\": {\"color\": \"#2a3f5f\"}}, \"ternary\": {\"aaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"baxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"caxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"title\": {\"x\": 0.05}, \"xaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}, \"yaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}}}, \"xaxis\": {\"anchor\": \"x\", \"exponentformat\": \"e\", \"linecolor\": \"black\", \"linewidth\": 1, \"mirror\": false, \"showexponent\": \"all\", \"showline\": true, \"side\": \"bottom\", \"ticks\": \"outside\", \"title\": {\"text\": \"Filtration parameter\"}, \"type\": \"linear\", \"zeroline\": true}, \"yaxis\": {\"anchor\": \"y\", \"exponentformat\": \"e\", \"linecolor\": \"black\", \"linewidth\": 1, \"mirror\": false, \"showexponent\": \"all\", \"showline\": true, \"side\": \"left\", \"ticks\": \"outside\", \"title\": {\"text\": \"Betti number\"}, \"type\": \"linear\", \"zeroline\": true}},\n",
       "                        {\"responsive\": true}\n",
       "                    ).then(function(){\n",
       "                            \n",
       "var gd = document.getElementById('6a04a6f1-a846-46ed-8377-93ad8665f5d2');\n",
       "var x = new MutationObserver(function (mutations, observer) {{\n",
       "        var display = window.getComputedStyle(gd).display;\n",
       "        if (!display || display === 'none') {{\n",
       "            console.log([gd, 'removed!']);\n",
       "            Plotly.purge(gd);\n",
       "            observer.disconnect();\n",
       "        }}\n",
       "}});\n",
       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
       "if (notebookContainer) {{\n",
       "    x.observe(notebookContainer, {childList: true});\n",
       "}}\n",
       "\n",
       "// Listen for the clearing of the current output cell\n",
       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
       "}}\n",
       "\n",
       "                        })\n",
       "                };\n",
       "                });\n",
       "            </script>\n",
       "        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "betti_curve_extractor = BettiCurve()\n",
    "sample_betti_curve = betti_curve_extractor.fit_transform([sample_pd])[0]\n",
    "betti_curve_extractor.plot([sample_betti_curve])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.4.2. Persistence Landscape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A *Persistence Landscape* is a set of $\\{{\\lambda_k}\\}_{k \\in \\mathbb{N}}$ of functions $\\lambda: \\mathbb{R} \\rightarrow \\overline{\\mathbb{R}}$, where $\\lambda_k$ is the $k$-th *layer* of Persistence Landscape. For the PD $\\{ (b_i, d_i) \\}$ Persistence Landscape $\\lambda$ can defined as letting $\\lambda_k$ be $k$-th largest value on set $\\{ \\Lambda_i(t) \\}$, where $\\Lambda_i(t) = \\left[ min \\{ t-b_i, d_i-t \\} \\right]_+$ and $c_+ := max(c, 0)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"images/sample_pl0.png\" />\n",
    "<img src=\"images/sample_pl1.png\" />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "hoverinfo": "none",
         "mode": "lines",
         "name": "Layer 1",
         "showlegend": true,
         "type": "scatter",
         "x": [
          0,
          0.0037957258385040863,
          0.0075914516770081725,
          0.01138717751551226,
          0.015182903354016345,
          0.01897862919252043,
          0.02277435503102452,
          0.026570080869528605,
          0.03036580670803269,
          0.034161532546536776,
          0.03795725838504086,
          0.041752984223544946,
          0.04554871006204904,
          0.049344435900553124,
          0.05314016173905721,
          0.056935887577561295,
          0.06073161341606538,
          0.06452733925456947,
          0.06832306509307355,
          0.07211879093157764,
          0.07591451677008172,
          0.07971024260858581,
          0.08350596844708989,
          0.08730169428559398,
          0.09109742012409808,
          0.09489314596260216,
          0.09868887180110625,
          0.10248459763961033,
          0.10628032347811442,
          0.1100760493166185,
          0.11387177515512259,
          0.11766750099362668,
          0.12146322683213076,
          0.12525895267063486,
          0.12905467850913893,
          0.13285040434764303,
          0.1366461301861471,
          0.1404418560246512,
          0.14423758186315527,
          0.14803330770165937,
          0.15182903354016344,
          0.15562475937866754,
          0.15942048521717161,
          0.16321621105567571,
          0.16701193689417979,
          0.17080766273268388,
          0.17460338857118796,
          0.17839911440969206,
          0.18219484024819615,
          0.18599056608670023,
          0.18978629192520433,
          0.1935820177637084,
          0.1973777436022125,
          0.20117346944071657,
          0.20496919527922067,
          0.20876492111772474,
          0.21256064695622884,
          0.2163563727947329,
          0.220152098633237,
          0.22394782447174108,
          0.22774355031024518,
          0.23153927614874925,
          0.23533500198725335,
          0.23913072782575742,
          0.24292645366426152,
          0.24672217950276562,
          0.2505179053412697,
          0.2543136311797738,
          0.25810935701827786,
          0.26190508285678193,
          0.26570080869528606,
          0.26949653453379013,
          0.2732922603722942,
          0.2770879862107983,
          0.2808837120493024,
          0.2846794378878065,
          0.28847516372631055,
          0.2922708895648146,
          0.29606661540331874,
          0.2998623412418228,
          0.3036580670803269,
          0.307453792918831,
          0.3112495187573351,
          0.31504524459583916,
          0.31884097043434323,
          0.32263669627284736,
          0.32643242211135143,
          0.3302281479498555,
          0.33402387378835957,
          0.3378195996268637,
          0.34161532546536777,
          0.34541105130387184,
          0.3492067771423759,
          0.35300250298088004,
          0.3567982288193841,
          0.3605939546578882,
          0.3643896804963923,
          0.3681854063348964,
          0.37198113217340045,
          0.3757768580119045
         ],
         "y": [
          0,
          0.0037957258385040993,
          0.007591451677008174,
          0.01138717751551227,
          0.015182903354016349,
          0.01897862919252044,
          0.022774355031024526,
          0.02657008086952861,
          0.030365806708032697,
          0.03416153254653678,
          0.03795725838504087,
          0.04175298422354495,
          0.04554871006204905,
          0.049344435900553124,
          0.05314016173905722,
          0.056935887577561295,
          0.06073161341606538,
          0.06452733925456947,
          0.06832306509307355,
          0.07211879093157764,
          0.07591451677008172,
          0.07971024260858581,
          0.08350596844708989,
          0.08730169428559398,
          0.09109742012409808,
          0.09489314596260216,
          0.09868887180110625,
          0.10248459763961033,
          0.10628032347811442,
          0.1100760493166185,
          0.11387177515512259,
          0.11766750099362668,
          0.12146322683213076,
          0.12525895267063486,
          0.12905467850913893,
          0.13285040434764303,
          0.1366461301861471,
          0.1404418560246512,
          0.14423758186315527,
          0.14803330770165937,
          0.15182903354016344,
          0.15562475937866754,
          0.15942048521717161,
          0.16321621105567571,
          0.16701193689417979,
          0.17080766273268388,
          0.17460338857118796,
          0.17839911440969206,
          0.18219484024819615,
          0.18599056608670023,
          0.1859905660867002,
          0.18219484024819613,
          0.17839911440969203,
          0.17460338857118796,
          0.17080766273268386,
          0.16701193689417979,
          0.1632162110556757,
          0.15942048521717161,
          0.15562475937866752,
          0.15182903354016344,
          0.14803330770165934,
          0.14423758186315527,
          0.14044185602465117,
          0.1366461301861471,
          0.132850404347643,
          0.1290546785091389,
          0.1252589526706348,
          0.12146322683213073,
          0.11766750099362666,
          0.11387177515512259,
          0.11007604931661846,
          0.10628032347811439,
          0.10248459763961032,
          0.09868887180110625,
          0.09489314596260212,
          0.09109742012409805,
          0.08730169428559398,
          0.0835059684470899,
          0.07971024260858578,
          0.07591451677008171,
          0.07211879093157764,
          0.06832306509307351,
          0.06452733925456944,
          0.060731613416065366,
          0.056935887577561295,
          0.05314016173905717,
          0.049344435900553096,
          0.045548710062049025,
          0.04175298422354495,
          0.037957258385040826,
          0.034161532546536755,
          0.030365806708032683,
          0.02657008086952861,
          0.022774355031024485,
          0.018978629192520413,
          0.015182903354016342,
          0.011387177515512215,
          0.007591451677008143,
          0.0037957258385040715,
          0
         ]
        },
        {
         "hoverinfo": "none",
         "mode": "lines",
         "name": "Layer 2",
         "showlegend": true,
         "type": "scatter",
         "x": [
          0,
          0.0037957258385040863,
          0.0075914516770081725,
          0.01138717751551226,
          0.015182903354016345,
          0.01897862919252043,
          0.02277435503102452,
          0.026570080869528605,
          0.03036580670803269,
          0.034161532546536776,
          0.03795725838504086,
          0.041752984223544946,
          0.04554871006204904,
          0.049344435900553124,
          0.05314016173905721,
          0.056935887577561295,
          0.06073161341606538,
          0.06452733925456947,
          0.06832306509307355,
          0.07211879093157764,
          0.07591451677008172,
          0.07971024260858581,
          0.08350596844708989,
          0.08730169428559398,
          0.09109742012409808,
          0.09489314596260216,
          0.09868887180110625,
          0.10248459763961033,
          0.10628032347811442,
          0.1100760493166185,
          0.11387177515512259,
          0.11766750099362668,
          0.12146322683213076,
          0.12525895267063486,
          0.12905467850913893,
          0.13285040434764303,
          0.1366461301861471,
          0.1404418560246512,
          0.14423758186315527,
          0.14803330770165937,
          0.15182903354016344,
          0.15562475937866754,
          0.15942048521717161,
          0.16321621105567571,
          0.16701193689417979,
          0.17080766273268388,
          0.17460338857118796,
          0.17839911440969206,
          0.18219484024819615,
          0.18599056608670023,
          0.18978629192520433,
          0.1935820177637084,
          0.1973777436022125,
          0.20117346944071657,
          0.20496919527922067,
          0.20876492111772474,
          0.21256064695622884,
          0.2163563727947329,
          0.220152098633237,
          0.22394782447174108,
          0.22774355031024518,
          0.23153927614874925,
          0.23533500198725335,
          0.23913072782575742,
          0.24292645366426152,
          0.24672217950276562,
          0.2505179053412697,
          0.2543136311797738,
          0.25810935701827786,
          0.26190508285678193,
          0.26570080869528606,
          0.26949653453379013,
          0.2732922603722942,
          0.2770879862107983,
          0.2808837120493024,
          0.2846794378878065,
          0.28847516372631055,
          0.2922708895648146,
          0.29606661540331874,
          0.2998623412418228,
          0.3036580670803269,
          0.307453792918831,
          0.3112495187573351,
          0.31504524459583916,
          0.31884097043434323,
          0.32263669627284736,
          0.32643242211135143,
          0.3302281479498555,
          0.33402387378835957,
          0.3378195996268637,
          0.34161532546536777,
          0.34541105130387184,
          0.3492067771423759,
          0.35300250298088004,
          0.3567982288193841,
          0.3605939546578882,
          0.3643896804963923,
          0.3681854063348964,
          0.37198113217340045,
          0.3757768580119045
         ],
         "y": [
          0,
          0.0037957258385040993,
          0.007591451677008174,
          0.01138717751551227,
          0.015182903354016349,
          0.01897862919252044,
          0.022774355031024526,
          0.02657008086952861,
          0.030365806708032697,
          0.03416153254653678,
          0.03795725838504087,
          0.04175298422354495,
          0.04554871006204904,
          0.049344435900553124,
          0.05314016173905722,
          0.056935887577561295,
          0.06073161341606538,
          0.06452733925456947,
          0.06832306509307355,
          0.07211879093157764,
          0.07591451677008172,
          0.07971024260858581,
          0.08350596844708989,
          0.08730169428559398,
          0.09109742012409808,
          0.09489314596260216,
          0.09868887180110625,
          0.10248459763961033,
          0.10628032347811442,
          0.1100760493166185,
          0.11387177515512259,
          0.11766750099362668,
          0.12146322683213076,
          0.12525895267063486,
          0.12905467850913893,
          0.13285040434764303,
          0.1366461301861471,
          0.1404418560246512,
          0.14423758186315527,
          0.14803330770165937,
          0.15182903354016344,
          0.15562475937866754,
          0.15942048521717161,
          0.16321621105567571,
          0.16701193689417979,
          0.17080766273268388,
          0.17460338857118796,
          0.17839911440969206,
          0.18219484024819615,
          0.18392730928116913,
          0.18013158344266503,
          0.17633585760416096,
          0.17254013176565686,
          0.16874440592715279,
          0.16494868008864869,
          0.16115295425014461,
          0.15735722841164052,
          0.15356150257313644,
          0.14976577673463234,
          0.14597005089612827,
          0.14217432505762417,
          0.1383785992191201,
          0.134582873380616,
          0.13078714754211193,
          0.12699142170360783,
          0.12319569586510373,
          0.11939997002659963,
          0.11560424418809556,
          0.11180851834959149,
          0.10801279251108742,
          0.10421706667258329,
          0.10042134083407922,
          0.09662561499557515,
          0.09282988915707108,
          0.08903416331856695,
          0.08523843748006288,
          0.08144271164155881,
          0.07764698580305474,
          0.07385125996455061,
          0.07005553412604654,
          0.06625980828754247,
          0.06246408244903834,
          0.05866835661053427,
          0.054872630772030195,
          0.051076904933526124,
          0.047281179095022,
          0.043485453256517925,
          0.039689727418013854,
          0.03589400157950978,
          0.032098275741005655,
          0.028302549902501584,
          0.024506824063997512,
          0.02071109822549344,
          0.016915372386989314,
          0.013119646548485242,
          0.00932392070998117,
          0.0055281948714770435,
          0.001732469032972972,
          0,
          0
         ]
        }
       ],
       "layout": {
        "plot_bgcolor": "white",
        "template": {
         "data": {
          "bar": [
           {
            "error_x": {
             "color": "#2a3f5f"
            },
            "error_y": {
             "color": "#2a3f5f"
            },
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             }
            },
            "type": "bar"
           }
          ],
          "barpolar": [
           {
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             }
            },
            "type": "barpolar"
           }
          ],
          "carpet": [
           {
            "aaxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "baxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "type": "carpet"
           }
          ],
          "choropleth": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "choropleth"
           }
          ],
          "contour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "contour"
           }
          ],
          "contourcarpet": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "contourcarpet"
           }
          ],
          "heatmap": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmap"
           }
          ],
          "heatmapgl": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmapgl"
           }
          ],
          "histogram": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "histogram"
           }
          ],
          "histogram2d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2d"
           }
          ],
          "histogram2dcontour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2dcontour"
           }
          ],
          "mesh3d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "mesh3d"
           }
          ],
          "parcoords": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "parcoords"
           }
          ],
          "pie": [
           {
            "automargin": true,
            "type": "pie"
           }
          ],
          "scatter": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter"
           }
          ],
          "scatter3d": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter3d"
           }
          ],
          "scattercarpet": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattercarpet"
           }
          ],
          "scattergeo": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergeo"
           }
          ],
          "scattergl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergl"
           }
          ],
          "scattermapbox": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolar"
           }
          ],
          "scatterpolargl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolargl"
           }
          ],
          "scatterternary": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterternary"
           }
          ],
          "surface": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "surface"
           }
          ],
          "table": [
           {
            "cells": {
             "fill": {
              "color": "#EBF0F8"
             },
             "line": {
              "color": "white"
             }
            },
            "header": {
             "fill": {
              "color": "#C8D4E3"
             },
             "line": {
              "color": "white"
             }
            },
            "type": "table"
           }
          ]
         },
         "layout": {
          "annotationdefaults": {
           "arrowcolor": "#2a3f5f",
           "arrowhead": 0,
           "arrowwidth": 1
          },
          "coloraxis": {
           "colorbar": {
            "outlinewidth": 0,
            "ticks": ""
           }
          },
          "colorscale": {
           "diverging": [
            [
             0,
             "#8e0152"
            ],
            [
             0.1,
             "#c51b7d"
            ],
            [
             0.2,
             "#de77ae"
            ],
            [
             0.3,
             "#f1b6da"
            ],
            [
             0.4,
             "#fde0ef"
            ],
            [
             0.5,
             "#f7f7f7"
            ],
            [
             0.6,
             "#e6f5d0"
            ],
            [
             0.7,
             "#b8e186"
            ],
            [
             0.8,
             "#7fbc41"
            ],
            [
             0.9,
             "#4d9221"
            ],
            [
             1,
             "#276419"
            ]
           ],
           "sequential": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ],
           "sequentialminus": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        },
        "title": {
         "text": "Persistence landscape for homology dimension 0"
        },
        "xaxis": {
         "anchor": "y",
         "exponentformat": "e",
         "linecolor": "black",
         "linewidth": 1,
         "mirror": false,
         "showexponent": "all",
         "showline": true,
         "side": "bottom",
         "ticks": "outside",
         "type": "linear",
         "zeroline": true
        },
        "yaxis": {
         "anchor": "x",
         "exponentformat": "e",
         "linecolor": "black",
         "linewidth": 1,
         "mirror": false,
         "showexponent": "all",
         "showline": true,
         "side": "left",
         "ticks": "outside",
         "type": "linear",
         "zeroline": true
        }
       }
      },
      "text/html": [
       "<div>\n",
       "        \n",
       "        \n",
       "            <div id=\"69465ae3-fd08-4e0d-9508-16aa75ad3169\" class=\"plotly-graph-div\" style=\"height:525px; width:100%;\"></div>\n",
       "            <script type=\"text/javascript\">\n",
       "                require([\"plotly\"], function(Plotly) {\n",
       "                    window.PLOTLYENV=window.PLOTLYENV || {};\n",
       "                    \n",
       "                if (document.getElementById(\"69465ae3-fd08-4e0d-9508-16aa75ad3169\")) {\n",
       "                    Plotly.newPlot(\n",
       "                        '69465ae3-fd08-4e0d-9508-16aa75ad3169',\n",
       "                        [{\"hoverinfo\": \"none\", \"mode\": \"lines\", \"name\": \"Layer 1\", \"showlegend\": true, \"type\": \"scatter\", \"x\": [0.0, 0.0037957258385040863, 0.0075914516770081725, 0.01138717751551226, 0.015182903354016345, 0.01897862919252043, 0.02277435503102452, 0.026570080869528605, 0.03036580670803269, 0.034161532546536776, 0.03795725838504086, 0.041752984223544946, 0.04554871006204904, 0.049344435900553124, 0.05314016173905721, 0.056935887577561295, 0.06073161341606538, 0.06452733925456947, 0.06832306509307355, 0.07211879093157764, 0.07591451677008172, 0.07971024260858581, 0.08350596844708989, 0.08730169428559398, 0.09109742012409808, 0.09489314596260216, 0.09868887180110625, 0.10248459763961033, 0.10628032347811442, 0.1100760493166185, 0.11387177515512259, 0.11766750099362668, 0.12146322683213076, 0.12525895267063486, 0.12905467850913893, 0.13285040434764303, 0.1366461301861471, 0.1404418560246512, 0.14423758186315527, 0.14803330770165937, 0.15182903354016344, 0.15562475937866754, 0.15942048521717161, 0.16321621105567571, 0.16701193689417979, 0.17080766273268388, 0.17460338857118796, 0.17839911440969206, 0.18219484024819615, 0.18599056608670023, 0.18978629192520433, 0.1935820177637084, 0.1973777436022125, 0.20117346944071657, 0.20496919527922067, 0.20876492111772474, 0.21256064695622884, 0.2163563727947329, 0.220152098633237, 0.22394782447174108, 0.22774355031024518, 0.23153927614874925, 0.23533500198725335, 0.23913072782575742, 0.24292645366426152, 0.24672217950276562, 0.2505179053412697, 0.2543136311797738, 0.25810935701827786, 0.26190508285678193, 0.26570080869528606, 0.26949653453379013, 0.2732922603722942, 0.2770879862107983, 0.2808837120493024, 0.2846794378878065, 0.28847516372631055, 0.2922708895648146, 0.29606661540331874, 0.2998623412418228, 0.3036580670803269, 0.307453792918831, 0.3112495187573351, 0.31504524459583916, 0.31884097043434323, 0.32263669627284736, 0.32643242211135143, 0.3302281479498555, 0.33402387378835957, 0.3378195996268637, 0.34161532546536777, 0.34541105130387184, 0.3492067771423759, 0.35300250298088004, 0.3567982288193841, 0.3605939546578882, 0.3643896804963923, 0.3681854063348964, 0.37198113217340045, 0.3757768580119045], \"y\": [0.0, 0.0037957258385040993, 0.007591451677008174, 0.01138717751551227, 0.015182903354016349, 0.01897862919252044, 0.022774355031024526, 0.02657008086952861, 0.030365806708032697, 0.03416153254653678, 0.03795725838504087, 0.04175298422354495, 0.04554871006204905, 0.049344435900553124, 0.05314016173905722, 0.056935887577561295, 0.06073161341606538, 0.06452733925456947, 0.06832306509307355, 0.07211879093157764, 0.07591451677008172, 0.07971024260858581, 0.08350596844708989, 0.08730169428559398, 0.09109742012409808, 0.09489314596260216, 0.09868887180110625, 0.10248459763961033, 0.10628032347811442, 0.1100760493166185, 0.11387177515512259, 0.11766750099362668, 0.12146322683213076, 0.12525895267063486, 0.12905467850913893, 0.13285040434764303, 0.1366461301861471, 0.1404418560246512, 0.14423758186315527, 0.14803330770165937, 0.15182903354016344, 0.15562475937866754, 0.15942048521717161, 0.16321621105567571, 0.16701193689417979, 0.17080766273268388, 0.17460338857118796, 0.17839911440969206, 0.18219484024819615, 0.18599056608670023, 0.1859905660867002, 0.18219484024819613, 0.17839911440969203, 0.17460338857118796, 0.17080766273268386, 0.16701193689417979, 0.1632162110556757, 0.15942048521717161, 0.15562475937866752, 0.15182903354016344, 0.14803330770165934, 0.14423758186315527, 0.14044185602465117, 0.1366461301861471, 0.132850404347643, 0.1290546785091389, 0.1252589526706348, 0.12146322683213073, 0.11766750099362666, 0.11387177515512259, 0.11007604931661846, 0.10628032347811439, 0.10248459763961032, 0.09868887180110625, 0.09489314596260212, 0.09109742012409805, 0.08730169428559398, 0.0835059684470899, 0.07971024260858578, 0.07591451677008171, 0.07211879093157764, 0.06832306509307351, 0.06452733925456944, 0.060731613416065366, 0.056935887577561295, 0.05314016173905717, 0.049344435900553096, 0.045548710062049025, 0.04175298422354495, 0.037957258385040826, 0.034161532546536755, 0.030365806708032683, 0.02657008086952861, 0.022774355031024485, 0.018978629192520413, 0.015182903354016342, 0.011387177515512215, 0.007591451677008143, 0.0037957258385040715, 0.0]}, {\"hoverinfo\": \"none\", \"mode\": \"lines\", \"name\": \"Layer 2\", \"showlegend\": true, \"type\": \"scatter\", \"x\": [0.0, 0.0037957258385040863, 0.0075914516770081725, 0.01138717751551226, 0.015182903354016345, 0.01897862919252043, 0.02277435503102452, 0.026570080869528605, 0.03036580670803269, 0.034161532546536776, 0.03795725838504086, 0.041752984223544946, 0.04554871006204904, 0.049344435900553124, 0.05314016173905721, 0.056935887577561295, 0.06073161341606538, 0.06452733925456947, 0.06832306509307355, 0.07211879093157764, 0.07591451677008172, 0.07971024260858581, 0.08350596844708989, 0.08730169428559398, 0.09109742012409808, 0.09489314596260216, 0.09868887180110625, 0.10248459763961033, 0.10628032347811442, 0.1100760493166185, 0.11387177515512259, 0.11766750099362668, 0.12146322683213076, 0.12525895267063486, 0.12905467850913893, 0.13285040434764303, 0.1366461301861471, 0.1404418560246512, 0.14423758186315527, 0.14803330770165937, 0.15182903354016344, 0.15562475937866754, 0.15942048521717161, 0.16321621105567571, 0.16701193689417979, 0.17080766273268388, 0.17460338857118796, 0.17839911440969206, 0.18219484024819615, 0.18599056608670023, 0.18978629192520433, 0.1935820177637084, 0.1973777436022125, 0.20117346944071657, 0.20496919527922067, 0.20876492111772474, 0.21256064695622884, 0.2163563727947329, 0.220152098633237, 0.22394782447174108, 0.22774355031024518, 0.23153927614874925, 0.23533500198725335, 0.23913072782575742, 0.24292645366426152, 0.24672217950276562, 0.2505179053412697, 0.2543136311797738, 0.25810935701827786, 0.26190508285678193, 0.26570080869528606, 0.26949653453379013, 0.2732922603722942, 0.2770879862107983, 0.2808837120493024, 0.2846794378878065, 0.28847516372631055, 0.2922708895648146, 0.29606661540331874, 0.2998623412418228, 0.3036580670803269, 0.307453792918831, 0.3112495187573351, 0.31504524459583916, 0.31884097043434323, 0.32263669627284736, 0.32643242211135143, 0.3302281479498555, 0.33402387378835957, 0.3378195996268637, 0.34161532546536777, 0.34541105130387184, 0.3492067771423759, 0.35300250298088004, 0.3567982288193841, 0.3605939546578882, 0.3643896804963923, 0.3681854063348964, 0.37198113217340045, 0.3757768580119045], \"y\": [0.0, 0.0037957258385040993, 0.007591451677008174, 0.01138717751551227, 0.015182903354016349, 0.01897862919252044, 0.022774355031024526, 0.02657008086952861, 0.030365806708032697, 0.03416153254653678, 0.03795725838504087, 0.04175298422354495, 0.04554871006204904, 0.049344435900553124, 0.05314016173905722, 0.056935887577561295, 0.06073161341606538, 0.06452733925456947, 0.06832306509307355, 0.07211879093157764, 0.07591451677008172, 0.07971024260858581, 0.08350596844708989, 0.08730169428559398, 0.09109742012409808, 0.09489314596260216, 0.09868887180110625, 0.10248459763961033, 0.10628032347811442, 0.1100760493166185, 0.11387177515512259, 0.11766750099362668, 0.12146322683213076, 0.12525895267063486, 0.12905467850913893, 0.13285040434764303, 0.1366461301861471, 0.1404418560246512, 0.14423758186315527, 0.14803330770165937, 0.15182903354016344, 0.15562475937866754, 0.15942048521717161, 0.16321621105567571, 0.16701193689417979, 0.17080766273268388, 0.17460338857118796, 0.17839911440969206, 0.18219484024819615, 0.18392730928116913, 0.18013158344266503, 0.17633585760416096, 0.17254013176565686, 0.16874440592715279, 0.16494868008864869, 0.16115295425014461, 0.15735722841164052, 0.15356150257313644, 0.14976577673463234, 0.14597005089612827, 0.14217432505762417, 0.1383785992191201, 0.134582873380616, 0.13078714754211193, 0.12699142170360783, 0.12319569586510373, 0.11939997002659963, 0.11560424418809556, 0.11180851834959149, 0.10801279251108742, 0.10421706667258329, 0.10042134083407922, 0.09662561499557515, 0.09282988915707108, 0.08903416331856695, 0.08523843748006288, 0.08144271164155881, 0.07764698580305474, 0.07385125996455061, 0.07005553412604654, 0.06625980828754247, 0.06246408244903834, 0.05866835661053427, 0.054872630772030195, 0.051076904933526124, 0.047281179095022, 0.043485453256517925, 0.039689727418013854, 0.03589400157950978, 0.032098275741005655, 0.028302549902501584, 0.024506824063997512, 0.02071109822549344, 0.016915372386989314, 0.013119646548485242, 0.00932392070998117, 0.0055281948714770435, 0.001732469032972972, 0.0, 0.0]}],\n",
       "                        {\"plot_bgcolor\": \"white\", \"template\": {\"data\": {\"bar\": [{\"error_x\": {\"color\": \"#2a3f5f\"}, \"error_y\": {\"color\": \"#2a3f5f\"}, \"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"bar\"}], \"barpolar\": [{\"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"barpolar\"}], \"carpet\": [{\"aaxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"baxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"type\": \"carpet\"}], \"choropleth\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"choropleth\"}], \"contour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"contour\"}], \"contourcarpet\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"contourcarpet\"}], \"heatmap\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmap\"}], \"heatmapgl\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmapgl\"}], \"histogram\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"histogram\"}], \"histogram2d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2d\"}], \"histogram2dcontour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2dcontour\"}], \"mesh3d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"mesh3d\"}], \"parcoords\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"parcoords\"}], \"pie\": [{\"automargin\": true, \"type\": \"pie\"}], \"scatter\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter\"}], \"scatter3d\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter3d\"}], \"scattercarpet\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattercarpet\"}], \"scattergeo\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergeo\"}], \"scattergl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergl\"}], \"scattermapbox\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattermapbox\"}], \"scatterpolar\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolar\"}], \"scatterpolargl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolargl\"}], \"scatterternary\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterternary\"}], \"surface\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"surface\"}], \"table\": [{\"cells\": {\"fill\": {\"color\": \"#EBF0F8\"}, \"line\": {\"color\": \"white\"}}, \"header\": {\"fill\": {\"color\": \"#C8D4E3\"}, \"line\": {\"color\": \"white\"}}, \"type\": \"table\"}]}, \"layout\": {\"annotationdefaults\": {\"arrowcolor\": \"#2a3f5f\", \"arrowhead\": 0, \"arrowwidth\": 1}, \"coloraxis\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"colorscale\": {\"diverging\": [[0, \"#8e0152\"], [0.1, \"#c51b7d\"], [0.2, \"#de77ae\"], [0.3, \"#f1b6da\"], [0.4, \"#fde0ef\"], [0.5, \"#f7f7f7\"], [0.6, \"#e6f5d0\"], [0.7, \"#b8e186\"], [0.8, \"#7fbc41\"], [0.9, \"#4d9221\"], [1, \"#276419\"]], \"sequential\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"sequentialminus\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]]}, \"colorway\": [\"#636efa\", \"#EF553B\", \"#00cc96\", \"#ab63fa\", \"#FFA15A\", \"#19d3f3\", \"#FF6692\", \"#B6E880\", \"#FF97FF\", \"#FECB52\"], \"font\": {\"color\": \"#2a3f5f\"}, \"geo\": {\"bgcolor\": \"white\", \"lakecolor\": \"white\", \"landcolor\": \"#E5ECF6\", \"showlakes\": true, \"showland\": true, \"subunitcolor\": \"white\"}, \"hoverlabel\": {\"align\": \"left\"}, \"hovermode\": \"closest\", \"mapbox\": {\"style\": \"light\"}, \"paper_bgcolor\": \"white\", \"plot_bgcolor\": \"#E5ECF6\", \"polar\": {\"angularaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"radialaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"scene\": {\"xaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"yaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"zaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}}, \"shapedefaults\": {\"line\": {\"color\": \"#2a3f5f\"}}, \"ternary\": {\"aaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"baxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"caxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"title\": {\"x\": 0.05}, \"xaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}, \"yaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}}}, \"title\": {\"text\": \"Persistence landscape for homology dimension 0\"}, \"xaxis\": {\"anchor\": \"y\", \"exponentformat\": \"e\", \"linecolor\": \"black\", \"linewidth\": 1, \"mirror\": false, \"showexponent\": \"all\", \"showline\": true, \"side\": \"bottom\", \"ticks\": \"outside\", \"type\": \"linear\", \"zeroline\": true}, \"yaxis\": {\"anchor\": \"x\", \"exponentformat\": \"e\", \"linecolor\": \"black\", \"linewidth\": 1, \"mirror\": false, \"showexponent\": \"all\", \"showline\": true, \"side\": \"left\", \"ticks\": \"outside\", \"type\": \"linear\", \"zeroline\": true}},\n",
       "                        {\"responsive\": true}\n",
       "                    ).then(function(){\n",
       "                            \n",
       "var gd = document.getElementById('69465ae3-fd08-4e0d-9508-16aa75ad3169');\n",
       "var x = new MutationObserver(function (mutations, observer) {{\n",
       "        var display = window.getComputedStyle(gd).display;\n",
       "        if (!display || display === 'none') {{\n",
       "            console.log([gd, 'removed!']);\n",
       "            Plotly.purge(gd);\n",
       "            observer.disconnect();\n",
       "        }}\n",
       "}});\n",
       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
       "if (notebookContainer) {{\n",
       "    x.observe(notebookContainer, {childList: true});\n",
       "}}\n",
       "\n",
       "// Listen for the clearing of the current output cell\n",
       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
       "}}\n",
       "\n",
       "                        })\n",
       "                };\n",
       "                });\n",
       "            </script>\n",
       "        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "hoverinfo": "none",
         "mode": "lines",
         "name": "Layer 1",
         "showlegend": true,
         "type": "scatter",
         "x": [
          0.0010741308138407033,
          0.025073016222541482,
          0.04907190163124226,
          0.07307078703994305,
          0.09706967244864383,
          0.1210685578573446,
          0.14506744326604537,
          0.16906632867474616,
          0.19306521408344693,
          0.2170640994921477,
          0.2410629849008485,
          0.2650618703095493,
          0.2890607557182501,
          0.31305964112695084,
          0.33705852653565166,
          0.3610574119443524,
          0.3850562973530532,
          0.40905518276175395,
          0.4330540681704547,
          0.45705295357915554,
          0.4810518389878563,
          0.5050507243965571,
          0.5290496098052578,
          0.5530484952139586,
          0.5770473806226594,
          0.6010462660313601,
          0.6250451514400609,
          0.6490440368487617,
          0.6730429222574625,
          0.6970418076661633,
          0.7210406930748641,
          0.7450395784835648,
          0.7690384638922656,
          0.7930373493009664,
          0.8170362347096671,
          0.8410351201183679,
          0.8650340055270687,
          0.8890328909357695,
          0.9130317763444703,
          0.9370306617531711,
          0.9610295471618718,
          0.9850284325705726,
          1.0090273179792735,
          1.0330262033879742,
          1.057025088796675,
          1.0810239742053758,
          1.1050228596140765,
          1.1290217450227773,
          1.153020630431478,
          1.1770195158401788,
          1.2010184012488796,
          1.2250172866575804,
          1.2490161720662811,
          1.273015057474982,
          1.2970139428836827,
          1.3210128282923834,
          1.3450117137010844,
          1.3690105991097852,
          1.393009484518486,
          1.4170083699271867,
          1.4410072553358875,
          1.4650061407445882,
          1.489005026153289,
          1.5130039115619898,
          1.5370027969706905,
          1.5610016823793913,
          1.585000567788092,
          1.6089994531967928,
          1.6329983386054936,
          1.6569972240141944,
          1.6809961094228951,
          1.704994994831596,
          1.7289938802402967,
          1.7529927656489976,
          1.7769916510576984,
          1.8009905364663992,
          1.8249894218751,
          1.8489883072838007,
          1.8729871926925015,
          1.8969860781012022,
          1.920984963509903,
          1.9449838489186038,
          1.9689827343273045,
          1.9929816197360053,
          2.0169805051447063,
          2.040979390553407,
          2.064978275962108,
          2.0889771613708086,
          2.1129760467795093,
          2.13697493218821,
          2.160973817596911,
          2.1849727030056116,
          2.2089715884143124,
          2.232970473823013,
          2.256969359231714,
          2.2809682446404147,
          2.3049671300491155,
          2.3289660154578162,
          2.352964900866517,
          2.3769637862752178
         ],
         "y": [
          1.0842021724855044e-19,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0.008092511077835263,
          0.03209139648653603,
          0.05609028189523679,
          0.08008916730393767,
          0.10408805271263843,
          0.1280869381213392,
          0.15208582353003997,
          0.17608470893874073,
          0.2000835943474415,
          0.22408247975614226,
          0.24808136516484303,
          0.2720802505735438,
          0.29607913598224467,
          0.32007802139094543,
          0.3440769067996462,
          0.36807579220834696,
          0.39207467761704773,
          0.4160735630257485,
          0.44007244843444926,
          0.46407133384315,
          0.4880702192518508,
          0.5120691046605517,
          0.5360679900692524,
          0.5600668754779532,
          0.584065760886654,
          0.6080646462953547,
          0.6320635317040556,
          0.6560624171127564,
          0.6800613025214571,
          0.7040601879301579,
          0.7280590733388587,
          0.7520579587475594,
          0.7760568441562602,
          0.800055729564961,
          0.8240546149736617,
          0.8480535003823625,
          0.8720523857910633,
          0.896051271199764,
          0.9200501566084648,
          0.9440490420171656,
          0.9680479274258665,
          0.9920468128345673,
          0.9839543017567317,
          0.9599554163480309,
          0.9359565309393302,
          0.9119576455306294,
          0.8879587601219286,
          0.8639598747132279,
          0.8399609893045271,
          0.8159621038958264,
          0.7919632184871256,
          0.7679643330784248,
          0.7439654476697241,
          0.7199665622610233,
          0.6959676768523225,
          0.6719687914436218,
          0.647969906034921,
          0.62397102062622,
          0.5999721352175192,
          0.5759732498088185,
          0.5519743644001177,
          0.527975478991417,
          0.5039765935827162,
          0.4799777081740154,
          0.45597882276531465,
          0.4319799373566139,
          0.4079810519479131,
          0.38398216653921236,
          0.35998328113051137,
          0.3359843957218106,
          0.31198551031310984,
          0.28798662490440907,
          0.2639877394957083,
          0.23998885408700754,
          0.21598996867830678,
          0.191991083269606,
          0.16799219786090525,
          0.14399331245220448,
          0.11999442704350372,
          0.09599554163480295,
          0.07199665622610218,
          0.04799777081740142,
          0.023998885408700654,
          0
         ]
        },
        {
         "hoverinfo": "none",
         "mode": "lines",
         "name": "Layer 2",
         "showlegend": true,
         "type": "scatter",
         "x": [
          0.0010741308138407033,
          0.025073016222541482,
          0.04907190163124226,
          0.07307078703994305,
          0.09706967244864383,
          0.1210685578573446,
          0.14506744326604537,
          0.16906632867474616,
          0.19306521408344693,
          0.2170640994921477,
          0.2410629849008485,
          0.2650618703095493,
          0.2890607557182501,
          0.31305964112695084,
          0.33705852653565166,
          0.3610574119443524,
          0.3850562973530532,
          0.40905518276175395,
          0.4330540681704547,
          0.45705295357915554,
          0.4810518389878563,
          0.5050507243965571,
          0.5290496098052578,
          0.5530484952139586,
          0.5770473806226594,
          0.6010462660313601,
          0.6250451514400609,
          0.6490440368487617,
          0.6730429222574625,
          0.6970418076661633,
          0.7210406930748641,
          0.7450395784835648,
          0.7690384638922656,
          0.7930373493009664,
          0.8170362347096671,
          0.8410351201183679,
          0.8650340055270687,
          0.8890328909357695,
          0.9130317763444703,
          0.9370306617531711,
          0.9610295471618718,
          0.9850284325705726,
          1.0090273179792735,
          1.0330262033879742,
          1.057025088796675,
          1.0810239742053758,
          1.1050228596140765,
          1.1290217450227773,
          1.153020630431478,
          1.1770195158401788,
          1.2010184012488796,
          1.2250172866575804,
          1.2490161720662811,
          1.273015057474982,
          1.2970139428836827,
          1.3210128282923834,
          1.3450117137010844,
          1.3690105991097852,
          1.393009484518486,
          1.4170083699271867,
          1.4410072553358875,
          1.4650061407445882,
          1.489005026153289,
          1.5130039115619898,
          1.5370027969706905,
          1.5610016823793913,
          1.585000567788092,
          1.6089994531967928,
          1.6329983386054936,
          1.6569972240141944,
          1.6809961094228951,
          1.704994994831596,
          1.7289938802402967,
          1.7529927656489976,
          1.7769916510576984,
          1.8009905364663992,
          1.8249894218751,
          1.8489883072838007,
          1.8729871926925015,
          1.8969860781012022,
          1.920984963509903,
          1.9449838489186038,
          1.9689827343273045,
          1.9929816197360053,
          2.0169805051447063,
          2.040979390553407,
          2.064978275962108,
          2.0889771613708086,
          2.1129760467795093,
          2.13697493218821,
          2.160973817596911,
          2.1849727030056116,
          2.2089715884143124,
          2.232970473823013,
          2.256969359231714,
          2.2809682446404147,
          2.3049671300491155,
          2.3289660154578162,
          2.352964900866517,
          2.3769637862752178
         ],
         "y": [
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0
         ]
        }
       ],
       "layout": {
        "plot_bgcolor": "white",
        "template": {
         "data": {
          "bar": [
           {
            "error_x": {
             "color": "#2a3f5f"
            },
            "error_y": {
             "color": "#2a3f5f"
            },
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             }
            },
            "type": "bar"
           }
          ],
          "barpolar": [
           {
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             }
            },
            "type": "barpolar"
           }
          ],
          "carpet": [
           {
            "aaxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "baxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "type": "carpet"
           }
          ],
          "choropleth": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "choropleth"
           }
          ],
          "contour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "contour"
           }
          ],
          "contourcarpet": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "contourcarpet"
           }
          ],
          "heatmap": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmap"
           }
          ],
          "heatmapgl": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmapgl"
           }
          ],
          "histogram": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "histogram"
           }
          ],
          "histogram2d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2d"
           }
          ],
          "histogram2dcontour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2dcontour"
           }
          ],
          "mesh3d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "mesh3d"
           }
          ],
          "parcoords": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "parcoords"
           }
          ],
          "pie": [
           {
            "automargin": true,
            "type": "pie"
           }
          ],
          "scatter": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter"
           }
          ],
          "scatter3d": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter3d"
           }
          ],
          "scattercarpet": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattercarpet"
           }
          ],
          "scattergeo": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergeo"
           }
          ],
          "scattergl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergl"
           }
          ],
          "scattermapbox": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolar"
           }
          ],
          "scatterpolargl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolargl"
           }
          ],
          "scatterternary": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterternary"
           }
          ],
          "surface": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "surface"
           }
          ],
          "table": [
           {
            "cells": {
             "fill": {
              "color": "#EBF0F8"
             },
             "line": {
              "color": "white"
             }
            },
            "header": {
             "fill": {
              "color": "#C8D4E3"
             },
             "line": {
              "color": "white"
             }
            },
            "type": "table"
           }
          ]
         },
         "layout": {
          "annotationdefaults": {
           "arrowcolor": "#2a3f5f",
           "arrowhead": 0,
           "arrowwidth": 1
          },
          "coloraxis": {
           "colorbar": {
            "outlinewidth": 0,
            "ticks": ""
           }
          },
          "colorscale": {
           "diverging": [
            [
             0,
             "#8e0152"
            ],
            [
             0.1,
             "#c51b7d"
            ],
            [
             0.2,
             "#de77ae"
            ],
            [
             0.3,
             "#f1b6da"
            ],
            [
             0.4,
             "#fde0ef"
            ],
            [
             0.5,
             "#f7f7f7"
            ],
            [
             0.6,
             "#e6f5d0"
            ],
            [
             0.7,
             "#b8e186"
            ],
            [
             0.8,
             "#7fbc41"
            ],
            [
             0.9,
             "#4d9221"
            ],
            [
             1,
             "#276419"
            ]
           ],
           "sequential": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ],
           "sequentialminus": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        },
        "title": {
         "text": "Persistence landscape for homology dimension 1"
        },
        "xaxis": {
         "anchor": "y",
         "exponentformat": "e",
         "linecolor": "black",
         "linewidth": 1,
         "mirror": false,
         "showexponent": "all",
         "showline": true,
         "side": "bottom",
         "ticks": "outside",
         "type": "linear",
         "zeroline": true
        },
        "yaxis": {
         "anchor": "x",
         "exponentformat": "e",
         "linecolor": "black",
         "linewidth": 1,
         "mirror": false,
         "showexponent": "all",
         "showline": true,
         "side": "left",
         "ticks": "outside",
         "type": "linear",
         "zeroline": true
        }
       }
      },
      "text/html": [
       "<div>\n",
       "        \n",
       "        \n",
       "            <div id=\"fff19cf7-6f0e-462a-9f17-4181dfd78236\" class=\"plotly-graph-div\" style=\"height:525px; width:100%;\"></div>\n",
       "            <script type=\"text/javascript\">\n",
       "                require([\"plotly\"], function(Plotly) {\n",
       "                    window.PLOTLYENV=window.PLOTLYENV || {};\n",
       "                    \n",
       "                if (document.getElementById(\"fff19cf7-6f0e-462a-9f17-4181dfd78236\")) {\n",
       "                    Plotly.newPlot(\n",
       "                        'fff19cf7-6f0e-462a-9f17-4181dfd78236',\n",
       "                        [{\"hoverinfo\": \"none\", \"mode\": \"lines\", \"name\": \"Layer 1\", \"showlegend\": true, \"type\": \"scatter\", \"x\": [0.0010741308138407033, 0.025073016222541482, 0.04907190163124226, 0.07307078703994305, 0.09706967244864383, 0.1210685578573446, 0.14506744326604537, 0.16906632867474616, 0.19306521408344693, 0.2170640994921477, 0.2410629849008485, 0.2650618703095493, 0.2890607557182501, 0.31305964112695084, 0.33705852653565166, 0.3610574119443524, 0.3850562973530532, 0.40905518276175395, 0.4330540681704547, 0.45705295357915554, 0.4810518389878563, 0.5050507243965571, 0.5290496098052578, 0.5530484952139586, 0.5770473806226594, 0.6010462660313601, 0.6250451514400609, 0.6490440368487617, 0.6730429222574625, 0.6970418076661633, 0.7210406930748641, 0.7450395784835648, 0.7690384638922656, 0.7930373493009664, 0.8170362347096671, 0.8410351201183679, 0.8650340055270687, 0.8890328909357695, 0.9130317763444703, 0.9370306617531711, 0.9610295471618718, 0.9850284325705726, 1.0090273179792735, 1.0330262033879742, 1.057025088796675, 1.0810239742053758, 1.1050228596140765, 1.1290217450227773, 1.153020630431478, 1.1770195158401788, 1.2010184012488796, 1.2250172866575804, 1.2490161720662811, 1.273015057474982, 1.2970139428836827, 1.3210128282923834, 1.3450117137010844, 1.3690105991097852, 1.393009484518486, 1.4170083699271867, 1.4410072553358875, 1.4650061407445882, 1.489005026153289, 1.5130039115619898, 1.5370027969706905, 1.5610016823793913, 1.585000567788092, 1.6089994531967928, 1.6329983386054936, 1.6569972240141944, 1.6809961094228951, 1.704994994831596, 1.7289938802402967, 1.7529927656489976, 1.7769916510576984, 1.8009905364663992, 1.8249894218751, 1.8489883072838007, 1.8729871926925015, 1.8969860781012022, 1.920984963509903, 1.9449838489186038, 1.9689827343273045, 1.9929816197360053, 2.0169805051447063, 2.040979390553407, 2.064978275962108, 2.0889771613708086, 2.1129760467795093, 2.13697493218821, 2.160973817596911, 2.1849727030056116, 2.2089715884143124, 2.232970473823013, 2.256969359231714, 2.2809682446404147, 2.3049671300491155, 2.3289660154578162, 2.352964900866517, 2.3769637862752178], \"y\": [1.0842021724855044e-19, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.008092511077835263, 0.03209139648653603, 0.05609028189523679, 0.08008916730393767, 0.10408805271263843, 0.1280869381213392, 0.15208582353003997, 0.17608470893874073, 0.2000835943474415, 0.22408247975614226, 0.24808136516484303, 0.2720802505735438, 0.29607913598224467, 0.32007802139094543, 0.3440769067996462, 0.36807579220834696, 0.39207467761704773, 0.4160735630257485, 0.44007244843444926, 0.46407133384315, 0.4880702192518508, 0.5120691046605517, 0.5360679900692524, 0.5600668754779532, 0.584065760886654, 0.6080646462953547, 0.6320635317040556, 0.6560624171127564, 0.6800613025214571, 0.7040601879301579, 0.7280590733388587, 0.7520579587475594, 0.7760568441562602, 0.800055729564961, 0.8240546149736617, 0.8480535003823625, 0.8720523857910633, 0.896051271199764, 0.9200501566084648, 0.9440490420171656, 0.9680479274258665, 0.9920468128345673, 0.9839543017567317, 0.9599554163480309, 0.9359565309393302, 0.9119576455306294, 0.8879587601219286, 0.8639598747132279, 0.8399609893045271, 0.8159621038958264, 0.7919632184871256, 0.7679643330784248, 0.7439654476697241, 0.7199665622610233, 0.6959676768523225, 0.6719687914436218, 0.647969906034921, 0.62397102062622, 0.5999721352175192, 0.5759732498088185, 0.5519743644001177, 0.527975478991417, 0.5039765935827162, 0.4799777081740154, 0.45597882276531465, 0.4319799373566139, 0.4079810519479131, 0.38398216653921236, 0.35998328113051137, 0.3359843957218106, 0.31198551031310984, 0.28798662490440907, 0.2639877394957083, 0.23998885408700754, 0.21598996867830678, 0.191991083269606, 0.16799219786090525, 0.14399331245220448, 0.11999442704350372, 0.09599554163480295, 0.07199665622610218, 0.04799777081740142, 0.023998885408700654, 0.0]}, {\"hoverinfo\": \"none\", \"mode\": \"lines\", \"name\": \"Layer 2\", \"showlegend\": true, \"type\": \"scatter\", \"x\": [0.0010741308138407033, 0.025073016222541482, 0.04907190163124226, 0.07307078703994305, 0.09706967244864383, 0.1210685578573446, 0.14506744326604537, 0.16906632867474616, 0.19306521408344693, 0.2170640994921477, 0.2410629849008485, 0.2650618703095493, 0.2890607557182501, 0.31305964112695084, 0.33705852653565166, 0.3610574119443524, 0.3850562973530532, 0.40905518276175395, 0.4330540681704547, 0.45705295357915554, 0.4810518389878563, 0.5050507243965571, 0.5290496098052578, 0.5530484952139586, 0.5770473806226594, 0.6010462660313601, 0.6250451514400609, 0.6490440368487617, 0.6730429222574625, 0.6970418076661633, 0.7210406930748641, 0.7450395784835648, 0.7690384638922656, 0.7930373493009664, 0.8170362347096671, 0.8410351201183679, 0.8650340055270687, 0.8890328909357695, 0.9130317763444703, 0.9370306617531711, 0.9610295471618718, 0.9850284325705726, 1.0090273179792735, 1.0330262033879742, 1.057025088796675, 1.0810239742053758, 1.1050228596140765, 1.1290217450227773, 1.153020630431478, 1.1770195158401788, 1.2010184012488796, 1.2250172866575804, 1.2490161720662811, 1.273015057474982, 1.2970139428836827, 1.3210128282923834, 1.3450117137010844, 1.3690105991097852, 1.393009484518486, 1.4170083699271867, 1.4410072553358875, 1.4650061407445882, 1.489005026153289, 1.5130039115619898, 1.5370027969706905, 1.5610016823793913, 1.585000567788092, 1.6089994531967928, 1.6329983386054936, 1.6569972240141944, 1.6809961094228951, 1.704994994831596, 1.7289938802402967, 1.7529927656489976, 1.7769916510576984, 1.8009905364663992, 1.8249894218751, 1.8489883072838007, 1.8729871926925015, 1.8969860781012022, 1.920984963509903, 1.9449838489186038, 1.9689827343273045, 1.9929816197360053, 2.0169805051447063, 2.040979390553407, 2.064978275962108, 2.0889771613708086, 2.1129760467795093, 2.13697493218821, 2.160973817596911, 2.1849727030056116, 2.2089715884143124, 2.232970473823013, 2.256969359231714, 2.2809682446404147, 2.3049671300491155, 2.3289660154578162, 2.352964900866517, 2.3769637862752178], \"y\": [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]}],\n",
       "                        {\"plot_bgcolor\": \"white\", \"template\": {\"data\": {\"bar\": [{\"error_x\": {\"color\": \"#2a3f5f\"}, \"error_y\": {\"color\": \"#2a3f5f\"}, \"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"bar\"}], \"barpolar\": [{\"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"barpolar\"}], \"carpet\": [{\"aaxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"baxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"type\": \"carpet\"}], \"choropleth\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"choropleth\"}], \"contour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"contour\"}], \"contourcarpet\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"contourcarpet\"}], \"heatmap\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmap\"}], \"heatmapgl\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmapgl\"}], \"histogram\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"histogram\"}], \"histogram2d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2d\"}], \"histogram2dcontour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2dcontour\"}], \"mesh3d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"mesh3d\"}], \"parcoords\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"parcoords\"}], \"pie\": [{\"automargin\": true, \"type\": \"pie\"}], \"scatter\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter\"}], \"scatter3d\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter3d\"}], \"scattercarpet\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattercarpet\"}], \"scattergeo\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergeo\"}], \"scattergl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergl\"}], \"scattermapbox\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattermapbox\"}], \"scatterpolar\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolar\"}], \"scatterpolargl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolargl\"}], \"scatterternary\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterternary\"}], \"surface\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"surface\"}], \"table\": [{\"cells\": {\"fill\": {\"color\": \"#EBF0F8\"}, \"line\": {\"color\": \"white\"}}, \"header\": {\"fill\": {\"color\": \"#C8D4E3\"}, \"line\": {\"color\": \"white\"}}, \"type\": \"table\"}]}, \"layout\": {\"annotationdefaults\": {\"arrowcolor\": \"#2a3f5f\", \"arrowhead\": 0, \"arrowwidth\": 1}, \"coloraxis\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"colorscale\": {\"diverging\": [[0, \"#8e0152\"], [0.1, \"#c51b7d\"], [0.2, \"#de77ae\"], [0.3, \"#f1b6da\"], [0.4, \"#fde0ef\"], [0.5, \"#f7f7f7\"], [0.6, \"#e6f5d0\"], [0.7, \"#b8e186\"], [0.8, \"#7fbc41\"], [0.9, \"#4d9221\"], [1, \"#276419\"]], \"sequential\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"sequentialminus\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]]}, \"colorway\": [\"#636efa\", \"#EF553B\", \"#00cc96\", \"#ab63fa\", \"#FFA15A\", \"#19d3f3\", \"#FF6692\", \"#B6E880\", \"#FF97FF\", \"#FECB52\"], \"font\": {\"color\": \"#2a3f5f\"}, \"geo\": {\"bgcolor\": \"white\", \"lakecolor\": \"white\", \"landcolor\": \"#E5ECF6\", \"showlakes\": true, \"showland\": true, \"subunitcolor\": \"white\"}, \"hoverlabel\": {\"align\": \"left\"}, \"hovermode\": \"closest\", \"mapbox\": {\"style\": \"light\"}, \"paper_bgcolor\": \"white\", \"plot_bgcolor\": \"#E5ECF6\", \"polar\": {\"angularaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"radialaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"scene\": {\"xaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"yaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"zaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}}, \"shapedefaults\": {\"line\": {\"color\": \"#2a3f5f\"}}, \"ternary\": {\"aaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"baxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"caxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"title\": {\"x\": 0.05}, \"xaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}, \"yaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}}}, \"title\": {\"text\": \"Persistence landscape for homology dimension 1\"}, \"xaxis\": {\"anchor\": \"y\", \"exponentformat\": \"e\", \"linecolor\": \"black\", \"linewidth\": 1, \"mirror\": false, \"showexponent\": \"all\", \"showline\": true, \"side\": \"bottom\", \"ticks\": \"outside\", \"type\": \"linear\", \"zeroline\": true}, \"yaxis\": {\"anchor\": \"x\", \"exponentformat\": \"e\", \"linecolor\": \"black\", \"linewidth\": 1, \"mirror\": false, \"showexponent\": \"all\", \"showline\": true, \"side\": \"left\", \"ticks\": \"outside\", \"type\": \"linear\", \"zeroline\": true}},\n",
       "                        {\"responsive\": true}\n",
       "                    ).then(function(){\n",
       "                            \n",
       "var gd = document.getElementById('fff19cf7-6f0e-462a-9f17-4181dfd78236');\n",
       "var x = new MutationObserver(function (mutations, observer) {{\n",
       "        var display = window.getComputedStyle(gd).display;\n",
       "        if (!display || display === 'none') {{\n",
       "            console.log([gd, 'removed!']);\n",
       "            Plotly.purge(gd);\n",
       "            observer.disconnect();\n",
       "        }}\n",
       "}});\n",
       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
       "if (notebookContainer) {{\n",
       "    x.observe(notebookContainer, {childList: true});\n",
       "}}\n",
       "\n",
       "// Listen for the clearing of the current output cell\n",
       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
       "}}\n",
       "\n",
       "                        })\n",
       "                };\n",
       "                });\n",
       "            </script>\n",
       "        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "persistence_landscape_extractor = PersistenceLandscape(n_layers=2, n_bins=100)\n",
    "sample_persistence_landscape = persistence_landscape_extractor.fit_transform([sample_pd])[0]\n",
    "persistence_landscape_extractor.plot([sample_persistence_landscape])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.4.3. Persistence Entropy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Persistence Entropy is the measure of entropy between points in PD. For PD $D = \\{ (b_i, d_i) \\}_{i \\in I}$ Persistence Entropy is defined by:\n",
    "\n",
    "$$\n",
    "E(D) = -\\sum_{i \\in I} {p_i \\log{p_i}},\n",
    "$$\n",
    "\n",
    "where $p_i = \\frac{d_i - b_i}{L_D}$ and $L_D = \\sum_{i \\in I}(d_i - b_i)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.04131086 0.04083675]\n"
     ]
    }
   ],
   "source": [
    "sample_persistence_entropy = PersistenceEntropy().fit_transform([sample_pd])[0]\n",
    "print(sample_persistence_entropy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.5. Topological Features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After introducing the Persistence Homology and it's derived representations, we can introduced features that we are going to use. Those features will be directly extracted from PD or related sturctures like Betti Curves and Persistence Landscape. First five features are proposed by Pereira in [2], rest of the features are proposed by us. All those topological features were implemented in package `src.TFE`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.5.1. Number of Holes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first feature (or set of features) is the number of holes for each homology dimension. This can be easily calculated with PD. Actually, in the 0th dimension, the holes actually indicate connected components, i.e., vertices that were connected along the filtration."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.5.2. Maximum Hole Lifetime"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maximum hole lifteime in each dimension helps to identify the most significant hole in each dimension, that is also the farthest point from the diagonal in PD. Note that the one hole that lasted the longest in the filtration indicates a prominent shape-based feature of the data set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.5.3. Number of Relevant Holes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The relevant holes for each dimension are the wholes whos lifetime is equal to the maximum hole lifetime with some ratio. In other words, they are the points that are at similar distance from the PD diagonal as the farthest point."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.5.4. Average Hole Lifetime"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Average hole lifetime for each dimensions shows whether the data consist of mosly short-lived holes, or vice versa, the long-lived holes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.5.5.  Sum of All Lifetimes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A sum of all hole lifetimes in each dimension can considered as an integral of PD graph. Actually, small sum for dimension shows that data has practically no holes in this dimension."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.5.6. Pesistence Entropy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Persistence Entropy actually is already a feature and can be informative."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.5.7. Average Number of Simultaneously Existing Holes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Average number of holes that exist simultaneously for each dimension in some sense can help to describe how sparse the holes are distributed for each dimension. If we represent the PD as set of sorted segments, which is also known as *Persistence Barcode*, this feature can be calculated as an average number of intersections of those segments."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.5.8. Average Value of Persistence Landscape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Average value of Persistence Landscape can help to handle the structure of Persistence Landscape diagram which can be informative. It's important to notice that in almost all of the studeid cases only Persistence Landscape for 1st homology dimension is informative, so we count this feature only for the 1st homology dimension."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.5.9. Sum of Betti Numbers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sum of Betti Numbers can be considered as an integral of Betti Curve for each dimension. This feature is introduced to handle the structure of Betti Curves."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.5.10. Radius at Maximum Betti Number"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This feature is inspired by work [5 Umeda]. It is actually the relative value of $s$ that corresponds to the maximum Betti number for each dimension."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Evaluation for Sample UCR Dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this part we are going to extract topological features for the dataset [GunPoint](http://www.timeseriesclassification.com/description.php?Dataset=GunPoint) from UCR collection of datasets. The same pipeline was applied to the rest of 1-dimensional time series datasets in UCR."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1. Topological Features Extraction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To extract Persistence Diagrams and corresponding features, we implemented own scikit-learn style transformers that we used for convenient feature extraction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 12.2 s, sys: 1.2 s, total: 13.4 s\n",
      "Wall time: 17.1 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "feature_extractor = TopologicalFeaturesExtractor(\n",
    "    persistence_diagram_extractor=PersistenceDiagramsExtractor(tokens_embedding_dim=2, \n",
    "                                                               tokens_embedding_delay=10,\n",
    "                                                               homology_dimensions=(0, 1),\n",
    "                                                               parallel=True),\n",
    "    persistence_diagram_features=[HolesNumberFeature(),\n",
    "                                  MaxHoleLifeTimeFeature(),\n",
    "                                  RelevantHolesNumber(),\n",
    "                                  AverageHoleLifetimeFeature(),\n",
    "                                  SumHoleLifetimeFeature(),\n",
    "                                  PersistenceEntropyFeature(),\n",
    "                                  SimultaneousAliveHolesFeatue(),\n",
    "                                  AveragePersistenceLandscapeFeature(),\n",
    "                                  BettiNumbersSumFeature(),\n",
    "                                  RadiusAtMaxBNFeature()])\n",
    "\n",
    "X_train_transformed = feature_extractor.fit_transform(X_train)\n",
    "X_test_transformed = feature_extractor.fit_transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_train_transformed shape:  (50, 19)\n",
      "X_test_transformed shape:   (150, 19)\n"
     ]
    }
   ],
   "source": [
    "print('X_train_transformed shape: ', X_train_transformed.shape)\n",
    "print('X_test_transformed shape:  ', X_test_transformed.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2. Model Selection in Extracted Features Space"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we are going to train different models and try to find the best parameters for them using cross-validation technique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [],
   "source": [
    "def evaluate_model(model, params, X_train, y_train, X_test, y_test):\n",
    "    clf_cv = GridSearchCV(model, \n",
    "                          param_grid=parameters,\n",
    "                          cv=StratifiedKFold(n_splits=2, shuffle=True, random_state=42),\n",
    "                          scoring='accuracy', \n",
    "                          n_jobs=-1)\n",
    "    clf_cv.fit(X_train, y_train)\n",
    "    acc_train = accuracy_score(y_train, clf_cv.best_estimator_.predict(X_train))\n",
    "    acc_test = accuracy_score(y_test, clf_cv.best_estimator_.predict(X_test))\n",
    "    print(clf_cv.best_estimator_.__class__.__name__)\n",
    "    print(clf_cv.best_params_)\n",
    "    print(\"Train accuracy: \", acc_train)\n",
    "    print(\"Test accuracy: \", acc_test)\n",
    "    return acc_train, acc_test, clf_cv.best_estimator_, clf_cv.best_params_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Support Vector Machine:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SVC\n",
      "{'C': 0.1, 'kernel': 'linear'}\n",
      "Train accuracy:  0.98\n",
      "Test accuracy:  0.86\n"
     ]
    }
   ],
   "source": [
    "parameters = {\"C\": [10**i for i in range(-2, 5)],\n",
    "              \"kernel\": [\"linear\", \"rbf\", \"sigmoid\", \"poly\"]}\n",
    "acc_train, acc_test, model, model_params = evaluate_model(SVC(random_state=42), parameters, X_train_transformed,\n",
    "                                                          y_train, X_test_transformed, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "XGBoost:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "XGBClassifier\n",
      "{'max_depth': 2, 'n_estimators': 20}\n",
      "Train accuracy:  1.0\n",
      "Test accuracy:  0.9\n"
     ]
    }
   ],
   "source": [
    "parameters = {\"max_depth\": [2, 10, 15, 20, 25, 30, 35, 40, 45, 50, 70, 100, 120, 150],\n",
    "              \"n_estimators\": [20, 50, 100, 150, 200, 250]}\n",
    "acc_train, acc_test, model, model_params = evaluate_model(XGBClassifier(n_jobs=-1, random_state=42), \n",
    "                                                          parameters, X_train_transformed,\n",
    "                                                          y_train, X_test_transformed, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "K Nearest Neighbours:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KNeighborsClassifier\n",
      "{'n_neighbors': 5}\n",
      "Train accuracy:  0.96\n",
      "Test accuracy:  0.8533333333333334\n"
     ]
    }
   ],
   "source": [
    "parameters = {\"n_neighbors\": [3, 5, 7, 11,]}\n",
    "acc_train, acc_test, model, model_params = evaluate_model(KNeighborsClassifier(n_jobs=-1), \n",
    "                                                          parameters, X_train_transformed,\n",
    "                                                          y_train, X_test_transformed, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CatBoost:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ubuntu/anaconda3/lib/python3.7/site-packages/joblib/externals/loky/process_executor.py:706: UserWarning:\n",
      "\n",
      "A worker stopped while some jobs were given to the executor. This can be caused by a too short worker timeout or by a memory leak.\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CatBoostClassifier\n",
      "{'early_stopping_rounds': 2, 'max_depth': 2, 'n_estimators': 50}\n",
      "Train accuracy:  0.98\n",
      "Test accuracy:  0.9\n"
     ]
    }
   ],
   "source": [
    "parameters = {\"max_depth\": [2, 10, 15, 20, 25, 30, 35, 40, 45, 50, 70, 100, 120, 150],\n",
    "              \"n_estimators\": [20, 50, 100, 150, 200, 250],\n",
    "              \"early_stopping_rounds\": [2, 5, 8, 10, 50, 200]}\n",
    "acc_train, acc_test, model, model_params = evaluate_model(CatBoostClassifier(random_state=42, verbose=False), \n",
    "                                                          parameters, X_train_transformed,\n",
    "                                                          y_train, X_test_transformed, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3 Dimensionality Reduction with Variational Autoencoder"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Variational Autoencoder (VAE) is a powerful dimensionality reduction technique. We are going to apply it to reduce the extracted topoligcal features space dimensionality."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "torch.manual_seed(0)\n",
    "torch.backends.cudnn.deterministic = True\n",
    "torch.backends.cudnn.benchmark = False\n",
    "np.random.seed(0)\n",
    "\n",
    "device = get_device()\n",
    "batch_size = 32\n",
    "latent_dim = num_classes * 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "scale = StandardScaler()\n",
    "scale.fit(X_train_transformed)\n",
    "\n",
    "X_train_transformed_dim = handle_dim(X_train_transformed, scale)\n",
    "X_test_transformed_dim = handle_dim(X_test_transformed, scale)\n",
    "\n",
    "y_hot_train = one_hot_encoding(y_train)\n",
    "y_hot_test = one_hot_encoding(y_test)\n",
    "\n",
    "dataset_train = TimeSeriesDataLoader(X_train_transformed_dim, y_hot_train, batch_size)\n",
    "dataset_test = TimeSeriesDataLoader(X_test_transformed_dim, y_hot_test, batch_size)\n",
    "\n",
    "test_data = torch.zeros(dataset_train.dataset[:][0].shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of parameters: 13873\n"
     ]
    }
   ],
   "source": [
    "vae = VariationalAutoencoder(batch_size=batch_size, latent_dims=latent_dim, test_data=test_data)\n",
    "vae = vae.to(device)\n",
    "\n",
    "optimizer = torch.optim.Adam(params=vae.parameters(), lr=2e-3, weight_decay=1e-5)\n",
    "num_params = sum(p.numel() for p in vae.parameters() if p.requires_grad)\n",
    "print('Number of parameters: %d' % num_params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "VariationalAutoencoder(\n",
       "  (encoder): Encoder(\n",
       "    (conv1): Conv1d(1, 32, kernel_size=(4,), stride=(2,), padding=(1,))\n",
       "    (conv2): Conv1d(32, 64, kernel_size=(4,), stride=(2,), padding=(1,))\n",
       "    (fc_mu): Linear(in_features=256, out_features=8, bias=True)\n",
       "    (fc_logvar): Linear(in_features=256, out_features=8, bias=True)\n",
       "  )\n",
       "  (decoder): Decoder(\n",
       "    (fc): Linear(in_features=8, out_features=96, bias=True)\n",
       "    (conv2): ConvTranspose1d(32, 1, kernel_size=(15,), stride=(3,), padding=(1,))\n",
       "  )\n",
       ")"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_AE(1000, vae, dataset_train, dataset_test, optimizer, device, verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from_vae_loader2numpy = lambda model, x: model.transform(x.dataset[:][0]).cpu().detach().numpy()\n",
    "\n",
    "z_train = from_vae_loader2numpy(vae, dataset_train)\n",
    "z_test = from_vae_loader2numpy(vae, dataset_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reduced train size:  (50, 8)\n"
     ]
    }
   ],
   "source": [
    "print(\"Reduced train size: \", z_train.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's train our models on reduced dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Support Vector Machine:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SVC\n",
      "{'C': 10, 'kernel': 'sigmoid'}\n",
      "Train accuracy:  0.98\n",
      "Test accuracy:  0.9266666666666666\n"
     ]
    }
   ],
   "source": [
    "parameters = {\"C\": [10**i for i in range(-2, 5)],\n",
    "              \"kernel\": [\"linear\", \"rbf\", \"sigmoid\", \"poly\"]}\n",
    "acc_train, acc_test, model, model_params = evaluate_model(SVC(random_state=42), parameters, z_train,\n",
    "                                                          y_train, z_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "XGBoost:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "XGBClassifier\n",
      "{'max_depth': 2, 'n_estimators': 20}\n",
      "Train accuracy:  1.0\n",
      "Test accuracy:  0.8266666666666667\n"
     ]
    }
   ],
   "source": [
    "parameters = {\"max_depth\": [2, 10, 15, 20, 25, 30, 35, 40, 45, 50, 70, 100, 120, 150],\n",
    "              \"n_estimators\": [20, 50, 100, 150, 200, 250]}\n",
    "acc_train, acc_test, model, model_params = evaluate_model(XGBClassifier(n_jobs=-1, random_state=42), \n",
    "                                                          parameters, z_train,\n",
    "                                                          y_train, z_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "K Nearest Neighbours:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KNeighborsClassifier\n",
      "{'n_neighbors': 5}\n",
      "Train accuracy:  0.98\n",
      "Test accuracy:  0.8733333333333333\n"
     ]
    }
   ],
   "source": [
    "parameters = {\"n_neighbors\": [3, 5, 7, 11,]}\n",
    "acc_train, acc_test, model, model_params = evaluate_model(KNeighborsClassifier(n_jobs=-1), \n",
    "                                                          parameters, z_train,\n",
    "                                                          y_train, z_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CatBoost:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ubuntu/anaconda3/lib/python3.7/site-packages/joblib/externals/loky/process_executor.py:706: UserWarning:\n",
      "\n",
      "A worker stopped while some jobs were given to the executor. This can be caused by a too short worker timeout or by a memory leak.\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CatBoostClassifier\n",
      "{'early_stopping_rounds': 2, 'max_depth': 15, 'n_estimators': 200}\n",
      "Train accuracy:  1.0\n",
      "Test accuracy:  0.9066666666666666\n"
     ]
    }
   ],
   "source": [
    "parameters = {\"max_depth\": [2, 10, 15, 20, 25, 30, 35, 40, 45, 50, 70, 100, 120, 150],\n",
    "              \"n_estimators\": [20, 50, 100, 150, 200, 250],\n",
    "              \"early_stopping_rounds\": [2, 5, 8, 10, 50, 200]}\n",
    "acc_train, acc_test, model, model_params = evaluate_model(CatBoostClassifier(random_state=42, verbose=False), \n",
    "                                                          parameters, z_train,\n",
    "                                                          y_train, z_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, VAE helped to achieve best accuracy on test set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.4. ANN classifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's try to use an ANN as a classifier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ubuntu/anaconda3/lib/python3.7/site-packages/numpy/core/fromnumeric.py:3335: RuntimeWarning:\n",
      "\n",
      "Mean of empty slice.\n",
      "\n",
      "/home/ubuntu/anaconda3/lib/python3.7/site-packages/numpy/core/_methods.py:161: RuntimeWarning:\n",
      "\n",
      "invalid value encountered in double_scalars\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on train:  0.98\n",
      "Accuracy on test:  0.9266666666666666\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ubuntu/workspace/ml/project/Time-Series-Classification/src/utils.py:84: UserWarning:\n",
      "\n",
      "To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n",
      "\n"
     ]
    }
   ],
   "source": [
    "neural_net_params = {'in_features=latent_dim': latent_dim,\n",
    "                     'out_features': num_classes,\n",
    "                     'depth': 4}\n",
    "\n",
    "net = ANN(latent_dim, num_classes, device)\n",
    "net.fit(z_train, y_train)\n",
    "\n",
    "y_train_pred = net.predict(z_train)\n",
    "y_test_pred = net.predict(z_test)\n",
    "\n",
    "acc_train = accuracy_score(y_train, y_train_pred)\n",
    "acc_test = accuracy_score(y_test, y_test_pred)\n",
    "\n",
    "print(\"Accuracy on train: \", acc_train)\n",
    "print(\"Accuracy on test: \", acc_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Imputation Study"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's see how the combinations of proposed features influence the quality, and for which types of datasets they work worse or better."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1. Feature Importance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First let's ensure that our proposed features matter, for that, let's train classifier only with Pereira's features. For that, let's take a classifier that produced good accuracy on a test set, for example, XGBoost."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_extractor = TopologicalFeaturesExtractor(\n",
    "    persistence_diagram_extractor=PersistenceDiagramsExtractor(tokens_embedding_dim=2, \n",
    "                                                               tokens_embedding_delay=10,\n",
    "                                                               homology_dimensions=(0, 1),\n",
    "                                                               parallel=True),\n",
    "    persistence_diagram_features=[HolesNumberFeature(),\n",
    "                                  MaxHoleLifeTimeFeature(),\n",
    "                                  RelevantHolesNumber(),\n",
    "                                  AverageHoleLifetimeFeature(),\n",
    "                                  SumHoleLifetimeFeature()])\n",
    "\n",
    "X_train_transformed = feature_extractor.fit_transform(X_train)\n",
    "X_test_transformed = feature_extractor.fit_transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "XGBClassifier\n",
      "{'max_depth': 2, 'n_estimators': 100}\n",
      "Train accuracy:  1.0\n",
      "Test accuracy:  0.8666666666666667\n"
     ]
    }
   ],
   "source": [
    "parameters = {\"max_depth\": [2, 10, 15, 20, 25, 30, 35, 40, 45, 50, 70, 100, 120, 150],\n",
    "              \"n_estimators\": [20, 50, 100, 150, 200, 250]}\n",
    "acc_train, acc_test, model, model_params = evaluate_model(XGBClassifier(n_jobs=-1, random_state=42), \n",
    "                                                          parameters, X_train_transformed,\n",
    "                                                          y_train, X_test_transformed, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Still accuracy is not bad, but it decreased w.r.t. to initial accuracy. Now let's check the feature importance with Logistic Regression and XGBoost."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_extractor = TopologicalFeaturesExtractor(\n",
    "    persistence_diagram_extractor=PersistenceDiagramsExtractor(tokens_embedding_dim=2, \n",
    "                                                               tokens_embedding_delay=10,\n",
    "                                                               homology_dimensions=(0, 1),\n",
    "                                                               parallel=True),\n",
    "    persistence_diagram_features=[HolesNumberFeature(),\n",
    "                                  MaxHoleLifeTimeFeature(),\n",
    "                                  RelevantHolesNumber(),\n",
    "                                  AverageHoleLifetimeFeature(),\n",
    "                                  SumHoleLifetimeFeature(),\n",
    "                                  PersistenceEntropyFeature(),\n",
    "                                  SimultaneousAliveHolesFeatue(),\n",
    "                                  AveragePersistenceLandscapeFeature(),\n",
    "                                  BettiNumbersSumFeature(),\n",
    "                                  RadiusAtMaxBNFeature()])\n",
    "\n",
    "X_train_transformed = feature_extractor.fit_transform(X_train)\n",
    "X_test_transformed = feature_extractor.fit_transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_feature_importances(feature_importances, feature_names, model_name):\n",
    "    plt.figure(figsize=(7, 5))\n",
    "    features = np.sort(feature_importances)\n",
    "    names = [feature_names[i] for i in np.argsort(feature_importances)]\n",
    "    plt.barh(range(len(features)), features, align='center')\n",
    "    plt.title(model_name + \" Feature Importance\")\n",
    "    plt.yticks(np.arange(0, len(names) + 1, 1), names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_names = [\"Hole_num_0\", \"Hole_num_1\", \"Max_lifetime_0\", \"Max_lifetime_1\", \"Relevant_num_0\", \n",
    "                 \"Relevant_num_1\", \"Average_lifetime_0\", \"Average_lifetime_1\", \"Sum_lifetime_0\", \n",
    "                 \"Sum_lifetime_1\", \"Entropy_0\", \"Entropy_1\", \"Sim_alive_0\", \"Sim_alive_1\", \"Average_landscape_1\",\n",
    "                 \"Betti_num_sum_0\", \"Betti_num_sum_1\", \"Rad_max_bn_0\", \"Rad_max_bn_1\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LogisticRegression\n",
      "{'C': 1}\n",
      "Train accuracy:  0.98\n",
      "Test accuracy:  0.8533333333333334\n"
     ]
    }
   ],
   "source": [
    "parameters = {\"C\": [10 ** i for i in range(-3, 5)]}\n",
    "acc_train, acc_test, model, model_params = evaluate_model(LogisticRegression(), \n",
    "                                                          parameters, X_train_transformed,\n",
    "                                                          y_train, X_test_transformed, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_feature_importances(abs(model.coef_[0]), feature_names, \"LogisticRegression\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "XGBClassifier\n",
      "{'max_depth': 2, 'n_estimators': 20}\n",
      "Train accuracy:  1.0\n",
      "Test accuracy:  0.9\n"
     ]
    }
   ],
   "source": [
    "parameters = {\"max_depth\": [2, 10, 15, 20, 25, 30, 35, 40, 45, 50, 70, 100, 120, 150],\n",
    "              \"n_estimators\": [20, 50, 100, 150, 200, 250]}\n",
    "acc_train, acc_test, model, model_params = evaluate_model(XGBClassifier(n_jobs=-1, random_state=42), \n",
    "                                                          parameters, X_train_transformed,\n",
    "                                                          y_train, X_test_transformed, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_feature_importances(model.feature_importances_, feature_names, \"XGBoost\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that here our proposed features have quite high importance in both cases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2. Studying Multiclass Dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we got a binary classification problem. Now let's check how these features will perform on multiclass problem. Let's take a [Trace](http://www.timeseriesclassification.com/description.php?Dataset=Trace) dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset:  Trace\n",
      "X_train shape:  (100, 275)\n",
      "y_train shape:  (100,)\n",
      "X_test shape:   (100, 275)\n",
      "y_test shape:   (100,)\n",
      "num. of class:  4\n"
     ]
    }
   ],
   "source": [
    "directory_list = get_files_directory_list()\n",
    "directory_list = sorted(directory_list)\n",
    "\n",
    "random_index =  115\n",
    "random_path = directory_list[random_index]\n",
    "\n",
    "X_train, X_test, y_train, y_test = get_data_from_directory(random_path)\n",
    "X_train = X_train.squeeze()\n",
    "y_train = y_train.squeeze()\n",
    "X_test = X_test.squeeze()\n",
    "y_test = y_test.squeeze()\n",
    "num_classes = np.unique(y_train).shape[0]\n",
    "\n",
    "print('Dataset: ', random_path)\n",
    "print('X_train shape: ', X_train.shape)\n",
    "print('y_train shape: ', y_train.shape)\n",
    "print('X_test shape:  ', X_test.shape)\n",
    "print('y_test shape:  ', y_test.shape)\n",
    "print('num. of class: ', num_classes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at sample embedding for all classes from this dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_embedding(X_train[0], 3, int(y_train[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_embedding(X_train[7], 3, int(y_train[7]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_embedding(X_train[1], 3, int(y_train[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_embedding(X_train[17], 3, int(y_train[17]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA1gAAAFgCAYAAACmKdhBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAgAElEQVR4nOzdd3gc5bn38e+tYhXLllxlS264IGPjRkwJJZhqSELgkEZIQk4C6SQn5xCfhNQTkmASn7wJOaTRAiEJEBJiSgBTBTZg4yJ3I3dZltzUe3/eP2YkS/Ku+mpX0u9zXb68mpmdvZ/Z3Zm953nmHnPOISIiIiIiIr0XFe4AREREREREBgslWCIiIiIiIn1ECZaIiIiIiEgfUYIlIiIiIiLSR5RgiYiIiIiI9BElWCIiIiIiIn1ECZaIiIiIiEgfUYIlIiIiIiLSR5RgScQzs+fN7DMdzP+9mX2/i+vKNLNb+uq1I1F3tkd/M7N/N7M14Y5DRPqXmR00s8vDHUdf6Mu2mNlDZvaTrs43sx1mtqQvXrvd62SYWZaZlZvZ1/t6/YNRZ+/dQDKYvp+RQgmWhEV3vszOuaudcw/7zzvlB7pz7kvOuR/3QUz/Y2Z/DvbaA0VfbY/BxMxmmVlN+/dXRLrOzCpa/Wsys+pWf38y3PF1xD/mVLdrwz3hjqu7nHNznXOZIVj1fwOZzrkRzrlfh2D9IWFmcWb2gJnl+MlhlpldHe64QsnM/mxmR8yszMx2d+ekcSQZ7MflmHAHICJ9x8yinXON4Y4jAv0GWB/uIEQGMudcUvNjMzsI3OKcezl8EXXbNQMs3v40FXisJ080sxjnXEMfx9NVMUAucDFwCHg/8Dczm+ecOximmEJtOXCzc67WzGYDmWaW5ZzbGO7AumlQH5fVgyVh19wrZWb/a2bFZnag9Rmo5mF9ZnYG8Hvgvf7ZxxJ/fks3vZmNMrNnzeyEv65nzWxSF2K4CvgO8HF/3Vtav3arON80s1+aWYmZ7Tez8/3puWZ2vPVwQv/M2v+a2SEzO+YP3UsI8vozzex1Mys1swIze7zVvNlm9pKZFZlZtpl9rNW8h8zsd2b2nJlVApcEGFLyQTPb7Mf8lpnNbzXvW2aW55/5yzazy/zp/2NmT/hnysrNbJuZnW5mt/vtzDWzKzvYnpPN7En/fSgMdqbYzO7211VmZhvN7KJW884xsw3+vGNm9v/86fF+XIV+m9abWWoHsdwAlACvBFtGRHrPzL5tZvv8fcZOM/u3IMvN9vfzN/h/p5nZP/z9xQFrN0TNvN6nb5rZVn8f+biZxfvzAu7DehD7QTNb5r9GpXm9IqnmDRMvN7OXzWxUq6ec7bex2Mz+2BxPZ+0xs0Vmtslf5+NAfLs4OpvfMvqjo+3izz/LTg77e8Kff8qQNjN7FbgEuMe849/pZnaGece/EvOGJX4oQBzfMrOtQKWZxbSbf4uZrfKPT8Xm9bTMMbP/MO+YWGBm13f9HQrMOVfpnPsf59xB51yTc+5Z4ADwnkDLd/YZ7eSz1uF7E+C1dvnbs87/19xzekYv27zDOVfb/Kf/b0ZXnmtdPzYH3U7BvnPd+S7aEDguK8GSSHEukA2MBX4OPGBm1noB59wu4EvA2865JOdcSoD1RAF/xDsbNwWoBjodBuKcewG4E3jcX/eCDuLcCowB/op3xu9sYCbwKbwDVPNZ3p8BpwML/fnpwA+CrPfHwIvAKGAS8H8AZjYceMl/rfHAJ4DfmtncVs+9EfgpMAJoM3zSzM4CHgS+6Mf8B+Bp85K/DOBW4Gzn3AhgKXCw1dOvAR7xY8oCVuFt33TgDn9dpzCzaOBZIAeY5i8f7MzoerztM9pv4xOtfiDcDdztnBuJd/D4mz/9M0AyMNlv05fw3udAsYz0Y70tyOuLSN/ZB1yE9/38EfBnM5vYegF/n/Qi8DXn3GNmFgU8A2zB21dcBnzDzJa2W/fHgKuA04D5wL93YR/WXR8GrsDbb18DPI934m0s3r6vdeL3Sf/1ZvjLf89vX9D2mNkwYCXefnU08IT/ms3bpsP5QZyyXVqt65/AQ/66HgUCJrzOuUuB1cCtfi/lAb8NL+Idd74G/MXf3q19AvgAkBKgB2s+sBj4O97224a3PcHbZj/G32atmXdStCTIv2c72RaYd7LtdGBHkEU6/YwS+LPW7ffGOXeGvz0fAX7k/7ZI8n/L9Kq9ZvZbM6sC3gWOAM91FIv/nO4cmwNup2Dfue58F4fKcVkJlkSKHOfcff7wtoeBiUDQXolgnHOFzrl/OOeqnHPleInHxX0Y5wHn3B/9OB/H+5F/h3Ou1jn3IlAHzPSTw88D/+mcK/JjuRO4Ich66/GSwjTnXI1zrjlR+iBw0H/NBufcJuAfwEdaPfcp59yb/tm7mnbr/TzwB+fcOudco389WS1wHtAIxAFzzCzWPwO4r9VzVzvnVvkHzieAccBdzrl6vJ3yNDMLlOSeA6QBy/yzi63b04Zz7s/+e9bgnPuFH0/zQbze35ZjnXMVzrm1raaPAWb6bdronCsLsl1/DDzgnMsNMl9E+ohz7gnnXL6/L3oc2IO3P2h2EfA08Bm/pwG8E1TjnHN3OOfqnHP7gfs4dV/5a3/dRXg//hfS+T6svZXtfsB+vt38/3POHXPO5eElHOucc1l+b8E/gUWtlr3HOZfrx/NTvGSjs/acB8QCv3LO1Tvn/k7bIVKdzQ8k0HZpXleMP7/eOfck8E4n62odRxLe/r7OOfcq3g/zT7Rb7tf+Ngh0gmsBsNw594p/vNwJbHPO3e0fQ7YT4DIV59wHnXMpQf59sKOgzSwW+AvwsHPu3UDLdOEz2tyu9tu0J+9Ns/l+ewPF06P2Oue+gndS9SLgSbzjeme6c2wOtp2Cfee6810cEsdlJVgSKY42P3DOVfkPk4IsG5SZJZrZH8y74LUMeANI8c/c9IVjrR5XAzjn2k9LwktGEoGNzQdz4AV/eiD/DRjwjj8c43P+9KnAua1/FOCdOZ3Q6rkd7aSmAre1e/5kvERuL/AN4H+A42b2mJmlddDWAnfy+q7mA2qg92gyXsLc6Zh8M7vNH0ZR6seWjHe2E+BmvDOR75o3DLD5YPMIXm/aY2aWb2Y/9w+s7de9ELgc+GVncYhI75nZTXZyOHIJcCYnv8/g9Ta/5Zx7rdW0qUBau33Udzj1BNvRVo+rgKQu7MPau67dD9j72s1vv88LtG9v1nq/m4P3w7Wz9qQBec451+65zTqbH8gp26WDdXX1B20akOuca2oXR3q75Tpa33y8pKzZnAB/B0yCesLvOXwE7yTnrR0s19lnFAJv0568N81xzSFIgtUb/gnGNXijXr7chad059gccDsF+8519bs4lI7LSrBkoHGdzL8NrwfkXOcNLXufP92CP6XL6+6OArwD8txWB/Nk1+oi8TYv7NxR59znnXNpeMP5fmtmM/EOYK+3+1GQ5JxrvTPtKO5c4Kftnp/onHvUf92/OucuxPtR4PCGNfZWLjDF2o3Jb8+8662+hTccY5TzhnyW4r9Xzrk9zrlP4A1R+RnwdzMb7p89/JFzbg5wPl4v300BXmIJ3jCIQ2Z2FPgm8GEz29QHbRSRVsxsKl5Pza3AGP/7vJ22+94v4e0bWv+4ysUbGdB6HzXCOff+rrxuiPZhXTG51eMpQL7/uKP2HAHS2w1/n9LqcWfzuyPQuiYHW7idfGCynxy0jiOv3XIBjz3+Z2EYsLvV5IXA5lZ/z2/3d/Nzn7e2lR5b/3u+/fL+cwx4AC+J/bDfQxYsrs4+o8H09L2Zgvdbe3+QmLrd3gBi6No1WF09Nne4nYJ957r4XVzCEDkuK8GSgeYYMMkfDx3ICLzEpsTMRgM/7Oa6p7U7qPSIf+bvPuCXZjYewMzS7dTrCvDnfdROFuMoxts5NeKd8TvdzD5tZrH+v7Ot6xfJ3gd8yczONc9wM/uAmY0w774nl5pZHFCDt936ogLhO3gHo7v814s3swsCLDcCaABOADFm9gNgZPNMM/uUmY3zt2WJP7nRzC4xs3l+r2QZ3pDBQHHfi3fQWej/+z3wL7yx4SLSt4bj7bdOAJjZZ/HOerdWjndty/vM7C5/2jtAmXkXyCeYWbSZnWlmZ3f2giHch3XFV81skn+c+Q7ekHHouD1v4+3zvm5mMeYVeWg9PK2z+d3xNt62uNVf17XdWNc6oBL4b/+YswTvmrSuVhlcgDccsAlarrmZinf9cutltrR/ovNujZIU5F+w8uu/A87AqxIZ8HpcX1c+o8H09L0ZibctA/5m6W57zWy8md1gZkn+Z2sp3tDNV/35D5nZQ0Fi6eqxOeh2Cvad68Z3ccgcl5VgyUDzKt7Fq0fNrCDA/F8BCXg9SGvxhuV11RP+/4V9dDblW8BeYK15wxVf5uT1Re2dDawzswq8axT+wzl3wHnXbl2JN34/H2/ows/wxjp3yjm3Ae86rHvwEre9+BdB++u4C29bHcXrKfpO95oY8DUb8Q7GM/HK5h4GPh5g0VV4Fz3vxhtqUUPbISdXATv8bXI3cIPzrjGbgHfhdBmwC3gdOOU+Gs67Du9o8z+gAqhxzp3obRtFpC3n3E7gF3g/RI8B84A3AyxXgldI4moz+3Gr/cVCvOIKBcD9eMOFO9Pdfdgz7XoI/tnV9gXwV7wiEPv9fz+BNvu/U9rjnKsDrsfbBxfj7RefbF5hZ/O7o9W6bsY7QfUpvBN2nV6r4z/3Q8DVfvy/BW5yQa5rCmABp/ZW7W0e/u+fxDyTAD1Y3eX3tnwRb3sftQ7uy9bVz2ggvXhvduElksXmlVTvLYc3HPCwH8f/At9wzj3lz59MkDZ19djcyXYK9p3r0ndxKB2Xre1wUhEREREZbMxsHfB759wfwx2L9D1/ZM8WYH6wYZLSf9SDJSIiIjLImNnFZjbBH9L2GbyepO6M6pABxHkVH89QchUZOrzQTUREREQGpAy8+wcm4d3X6CPOuSPhDUlkaNAQQRERERERkT6iIYIiIiIiIiJ9ZFAOERw7dqybNm1aj59fWVnJ8OHD+y6gAWIotlttHjqGYrsHaps3btxY4JwLdlPuQaO3x6qeGKifid4aiu1Wm4eGodhmiJx2BzteDcoEa9q0aWzYsKHHz8/MzGTJkiV9F9AAMRTbrTYPHUOx3QO1zWaWE+4Y+kNvj1U9MVA/E701FNutNg8NQ7HNEDntDna80hBBERERERGRPqIES0REREREpI8owRIREREREekjSrBERERERET6iBIsERERERGRPqIES0REREREpI8owRIREREREekjSrBERERERET6iBIsERERERGRPqIES0REREREpI/EhDsAERn8DhRUkp6SwLAYndMRERGRvrUyK48Vq7LJK6km2oxG50hPSWDZ0gyuW5Te7/EowRKRkCqpqmPpL9/gW1fP5uYLTwt3ON1WXdfI3a/s4auXzGBEfGy4wxERERnySqrrueCuV8kvqSYlMZaKmgbqmxwAjc77P6+kmm88vplvPL4ZAAM+ed4UfnLdvJDHpwRLJII0Njl+//o+Jo1K4NqFPTvjUtfQRJRBTHT/9Bb9eW0OucVV3H71GQHnb88ro66xiU2HirmZUxOs42U11DY0MXl0Yp/GtWrHUfYer+Crl8zs1Xre3l/A71/fx4xxw/no4sl9FF3fWv78LoZFR3HblRnhDkVERKTPNfdQNSdUN8+oIa8kGoDiqvourcMBf157iD+vPQQQ0h4ujdeRIcM5R21DY5+sa0d+aZ+tq5lzjq/+ZRMrVmXz29f2BVympKqOZ7bk4/yzM4HccO/bfG/l9k5f7x8bD5NfUt3jeAHW7i/kB09t56/+zso5x1f+spF/bT3Sssz2/FIAduR5/9fUN/LG7hMtbfjyXzZxy8MbehVHIPe+sZ/fvra3w23VFYcKqwDYmFPco+eX19Tz4JoDNDQ29SqO1rbnlfL/Xsxuaduq7Ud5+K2DffoaHalraOJnL7zLpb/IpLiyrl9eU0REhqaVWXks+/sW8kqqcXgJlaN3x3bwerhuf3IbK7Pyeh9kO0qwZMj4x6Y8zvj+C3zxkQ2UVJ38UVjb0EhOYWWX13O8vIYP3fMmD6w5cMq8mvpGmpoCf+n3Hq/g2a35p0w/WlrD4+sPsed4BS/sOMrYpDj2naigruHkj+XteaXklVTzxIbDfO3RLNbsLWjzmrlFXhKQX1LNpkMlvLTzWNA4mmO57Ykt/PjZnQHnv7D9KPev3h9wXmOT49V3j3GsrIb/eCyLJgfltQ2UVtezv6CS57Yd5fENuW1iBzhYWEV5TT33r97PTQ++w+o9Bew9Xs7GnGKyj5VTWlWPc44/vnmAZ7bkdzlZWLXjKC/tPNZmWnVdI1sPl1BZ10hBRecJgHMuaCJ2qMhLQjcESbCWPbGFv6zLCbruu1/ewx3P7mTdgaJO4+iKfScq+PQD6/j1q3vZd6IS5xxHSmsoq2kgK7ekT16jM794MZvfZe5j/4nKlgRaREQkFH70zA7qG3ufUAVSXd/IilXZfb5eJVgyYDjnKO1iNzB4icfXHs1iz7FyALIOFRMbHcVLO4/x20yvhyjreANn3fESF6/IZPWeEx2ur6Cilrf2FbAlt5TGJscbu9suX13XyKX/m8mvX91DU5OjorYBgJ35ZeQUVvKZB9/h1r9m8cuXdrM5t4RGPwH61cu7+dY/tvHzF7wv+C0XnUZDkyP7aDkrs/JoaGzipgff4c7ndrG/oAKA32We7OH65Uu7ufKXb1BZ28DrfkyFlXWsP1jEExtyAyYOL2z3ephW7Tja0kPTzDnHXc/v4if/2sVbrRK5Zs9uzedzD23g4hWvUVxVz9cu9YbgHS6uYs0eb/mNB4taEqQd+WWMjI9pedycfP3+9X08seFwy3o3Hy7hWFktP3pmJ197NIsfPL2jw/ejOdYfPLWd5c/tajN906Hilp1x++S5obGpTYL92rvHuewXr3P13asDbqvcYm/77D1ecUpvTUVtA3/fdJhntpyaOIOX8P5prZd8ZR8t77Q9nTlWVsNND7zT0rZNOcUUV9VT6yfjmdnHAz7vcHEV5975MlmHitmeV8qDaw6c8vntjpd2HmNu2kgA9p/o+skJERGR7liZldflIYA91dvRPIEowZIB46nN+Zxz58scKe3aF2HXkTKe2ZLPr17eA8DBwkpmTxzJdQvT+dPbBymoqOW1Qw0kJ8QyZXQiP3pmJ/Ud9Jrc/uQ2PnX/Ol591+st2ZRTQnXdyWGCj68/RH5pDW/vK+Shtw5y3p2v8ML2I3zg/1Zz8YpMjpbVcP6MMdz9yh6u+82bPLjmANV1jTzrD6d7eZf3o/Xi08cB3hmbbzy+md9l7qOoso7dR8s5WOD92H9rXyGbDhXT1OR4eks+1fWNrDtQSGb28ZZk5guPbGTZ37ey68ipP+yf23aUmeOTiI4y7l29j/Kaep7bdoTGJseuI+UcLKwiOsr47srtbdrotbuYuJgoUhKGcceH5nLFnFQA8oqrW5LUyrpGfvPaPr74yAYOFFS2jG++f/V+couqOWtKCm/tK+T+NQe4YOYYzLwEeJvf2zUxOZ639xUCXhK1es+JloS17XtczrGyWvYXVLYkP8451u0vbFnmYGEVzjn+vLOWzOzj3Lt6Pxf97LWWZP07/9zG4eJq3j1aTm5zb9XBopYdbm5RFaOHDwNOHSa47XApznnJU/vkrLiyji//ZRM4SIqLYbef6D+1OY872yWEXdHU5Pj8n7ze10c/fx4pibFszCluiTMmyvjX1iPsPV5xynNf3nmMY2W1/HntIb74yEbueHYnn3toPTX13R/meri4iv0FlVx/1iSS4mLYf+Lk6+06Usadz+2irCa0B0MRERn8VmblcfuT20L+OmkpCX2+TiVYMmC8uPMotQ1NQc+8t/+Bm+P3zLyw4yj5JdUcOFHJ9LHDufXSmdQ1NPHwWwfZU9LIxRnj+f4H57D3eAXf+vvWgNdWbc8r9YbdOXhiw2Fiooy6xiY25HjDvuobm7hvtTdkcGd+Ga/v9hKCL/15E6MTh3HTe6fy0+vO5E+fO4fHvnAe500fze9e38ffN+ZSUdvAwskpAFw2ezzTxw0nOspahqQ197YdKKhk74kKls5NZWxSHD/91y6ycos5UloDwKrtx3hzbyEfmJ/G1DGJlFZ7P3K35bUdNna0somdR8q44ezJ3HD2FP667hCffuAdvvKXTTy56TDPbTtClMGvPr6QAwWVpyQDm3NLWDQlhbXfuYwbzplCur9jyimsYu3+Ii4/w0u4fvnyblbt8JLRSzLGM25EHC/vOs7o4cO476bFXLswjS9fPIO7b1hERuoIsg6VsC2vlCiDaxakkVNY6V2vtaeATz/wDl9/NOuUYY+vteqxycotprS6nrN/+jK/e30fsyeMIDrKyCmsZM3eAl4+1MDvMvexavtRymsbeHprPifKazlSWsO/+Qng2gOFFFTUcuP96/jCIxtobHIcKqriqjMnMCwmijf8BHJjTjFn/fglntrsjdsurqrnREVtSyxPb8nn6rtXs+tIGffcuIgz00eS7SdYv8vcx/2r93eYhJTX1J/yeX5x5zG2Hi7lx9edybxJybxnyig25BRx1H//b7loOvmlNVz+/17ncw+tb9Mz2Tyk9Mmsw+SVVLN0bioNTa7lO9IR51yb4arNvZQXzRrL9HHD2deqB2v58+/y2DuHOhyeKiIi0hUrVmVT3YMTgd2REBvNsqV9XyBKCZYMCI1Njjf3er0Sb+w5ddja1sMlXPiz13jsnUMt05p/PDrneHDNAfJLa5g2ZjjTxyXx3hljeOjNg1Q3wOKpo7j8jPH85+Wn82RWHj959tTehd+9vo+R8TGkjoyjocnxgfkTiYkyVvuxrNtfRF5JNUsyxlFe28CbewsYm+T1etx2ZQZ3XHsmN5wzhZjoKM6bPoZvXTWboso6vv/UDqaPHc7dNyxkbtpIrl2UTlxMNKeNHQ54vRLNO5eGJseJ8lrmpiXzzStPZ2NOMf/1ty0Mi47irCkpPL7BS9Y+8p5JXDY7lfSUBEbEx7DlcGnLNnprXwEv5tQTG21csyCNby7NYExSHJtzS0hOiOUXL+7msfW5nDd9DNcsSOOWC0/jkbU5ZB3ykr3ahkZ2Hilj4eRRLdtm9PBhJMRG8+zWfCpqG/jwWelMG5NIdJTx0GfP5qf/diYXzRrLT647k++8fzZPffUCxiTFcfcNi/jm0gzGJsWxaEoKWYeK2ZxbwszxScyflEyT84af/fa1vQyLieLVd4/zu9f38eg7h7jo56/yp7cP8vz2I8wYN5yYKGNjTjGZ2ccpqKjjvOlj+MolM0lPSeBgYVXLkMr1B4vY6veS/X3j4Zbrw/7trHRGDx/Guv1F/GXtIeoamtieV8Y9r+6lqq6RWeOTWDp3Ak9vyae2oZG1+wspqqzjsfW5mHnboXkI4F/W5fD1R7NIHRnH3774Xq6cO4GM1BHsPlpOfonXU9bkvF6yQKrqGjj/rlf5wxsnr4FzzvGb1/YydUwiH1qQBsBZU0ex70Qlu46UAfC5C6bx1rcv5T8vP531B4v4xH1rOVHVRH1jE2v3FzF97HCcg/Ej4vjyEm9Y5/a8Us5f/gr/zDrcJoaa+kZ+/OxO1uwp4IE1B3jv8ldaEsLVewpIHRnHrPFJTB87vKUHa/WeE7yx+wRfu3QWKYnDArZNRESkq/JCMHSvveXXzwtJFUGVaZcBYXteKaXV9YwePow39xZQUdvAW3sLeGXXcbbllXKgoJLq+kaWP/8uV505gZTEYeQUVpKWHM+0scN5bL133c+0sV4p8A/OT2tJ2M6eNhoz4z8un8XBwkqe2pzH9z54BmXVDdz04Dus+Mh83sg+wQcXpBEXE8VDbx3kvdPHUFXXyCNv53DjOVNYvecEsdHGly6eQWb2CRqaHN+6ajbzJiWTkTrilPYsmjKKZUszqGto4hPnTGFCcjz/+vpFLfMzUkew93gFX14yg/97dS8LJqewxS9gMHVMIh+cn8Y7B4t450ARN547hUmjEth0qITrz0rnPVNHsWBSMsuWZnDLn9az7XApWw+X8PE/rKW2oZEo4COLJ5M6Mh6A333yLDbkFDMvPZlP3r+OKaMTW0qu/8fls/jjWwd5edcxFk0Zxc78MuobHQsnJ7fEamakj0pgy2Gv9+n8GWO57coMKmsbWJIxvmW5pXMnBH1/L5udyqPv5PLG7hNcf1Y6s8Z72+xvG3JZd6CI733gDLbllbJiVTbRUcbwYdH84CnvGq3/uuJ0Xtp5jE05JeQUVjE2KY6HP3sOUVHGExu8dZZW13PexGjWHvGS1WsXpvHU5nye2OglSGemJ3POtNGs2XuCxibHJRnjqKlv4u5XdgMweVQi08cl8cyWfF7eebzN9VQXzhzL6j0FZB8tJ9qM763czqWzx/OHT7+HWL9UfsaEkVTWNbYUwzCDtfuLuHR2aks7V2blMWFkPB8/ezLlNQ3cv/oAn71gGnEx0Ww9XMq2vFJ++m9ntpTfXzzVS3Kf2ZpPTJQxJimO6Cjvc3zp7PHceN9avrOmgVUnNlJR28Cd18/j/17Zw8fPnsys8UkA/DMrj/zSGn750h6umZ9GTHQU1XWNfOGRDazeU8CLO4/S2OgorKzjn5vy+Mz509iYU8y5p43BzJg+LomVm73E+s7n3mXSqARuOn9q0PdZRESkq6IMQj0gIlQ3IVaCJQNC8xCnWy+ZyR3P7mTRHS9S3+gYERfDWVNHMTdtJO+fP5GbH1rPHc/sZMVHF3CwsJKpY4azJGMcb/nX8zT3DF01dwLfX7md4bEwefTJsbcfWpjGP7PyWL27gNqGJnYdKeN7K7dTXtvABTPHMGV0Ik9vyef8GWO5OGMcV/7yDW57YgsVNQ0snjqaRVNSiIkyGpoci6eNbnm9QDq6P9M1CyaCwVeWzGR7Ximff990brxvXUsboqOM//exhS3LHy+rYUd+WUtiFBMdRUw0zJ+Uwv2r93PLwxsYPXwY40bEsfVwCV+8eEbLcxdPG83iaaMBeObWC5kxfjiJw7xdw4j4WBZOTmHNngKWLYU3dnvvwwJ/SGOz9JQE9h6vYN6kFJITY7nG72XpqsvOGImAw/QAACAASURBVM97po5io5/oNbfxkbU5JMXF8IlzpvDpaKOoso6jpTX8/Uvnk1NUSXxsNDPHJVFUWcdf3zlETJRxzfw0oqK8bqWpYxJZvaeACSPj+ezcKHKqmqhtaOKH18zlpZ3HeG7bUaaPG05SXAznTR/NCzuOkhQXw9cvm0VSXAxX372aJueYMiaRGeOSmJgczz+zDnO4uJq05HhvSN4Zqew6Usa6A0U8uOYAp40Zzm9uPKsluQLImOAlNI+8nUN6SgLpKQms9a8TK6up545ndmLAW7WFLbEXVNTy0JsH+dyFp/HSzmNERxnvP3NiyzoXTRlF4rBodh+rID0lgWj/eQDzJiXz7Ncv5Lt/XcOGnGJGxsdw8axxLb1fABNGxvPmPu/9PFRUxfPbj3LZGeP53EPrWXegiA+fNYl/bPJ6tkbExfDI2hyunjeBo2U1zJ/kJdjTx3mf71+8mM2uI2X8+hOLiIuJ7tZ7LyIi0t7KrLyQJ1dmnS/TU2FNsMzsKuBuIBq43zl3V7v5/w6sAJoL1N/jnLu/X4OUsHPOsTIrj4WTU/jI4kms3nOCaWOHc/kZqZw9bTTDYk7+kL310ln8+pU9OLwfjZefkcolGeO587l3AZjmJzyjhg/jhnMmU3zsCNbqG3bhzLGkJMbyzNZ8Jo3yEq/Nfs/RedPHMDYpjk3fv6Jl+Tuunct/Pr4FgP++KoO4mGhOTx3BsbIapo3p+Y1zrzpzIlf5P6b/+NlzAJg0KoHDxdVMHXNq0jZ+ZDy//PjCU6bPT0+mvtFRVlPPyq9ewNTRw/nni68HTfzmTUo+ZdqFM8fy61f38MOntvPw2zmce9poJvi9X82at9X7Zo3tXkN9Zsb3PnAGn31oPRfMHMuwmCimjUlk34lKrlkwkeFx3q7qT587h8YmR0x0FPMTTyZ5X7lkBm/vKyT7WDmXnXGy12yav63++6oM4sr28sNr5lLb0Mjo4cP41HlTufeN/cxL99p8wzlTSB0Zz4WzxjIiPhaAL148nYffymHyKG/I45VzUnl8Qy5NTfDZC6Zx+ZxU5qUn8+JOr1R8TJTxxJfeS8KwtklGxoSRjIiPoaa+iS9ePIXahibueXUPy5/bRV1jExW1Ddx302I+/6cNrMzKY2JyPBOS41n+/Lte1UXn9ViNGn5y6N2wmCjOnzGGl3cdZ2Jy2/cDYOqY4dwyL46LL764ZZu1Nn3ccI76n9MoM37/+j6yj5az7kARv/r4Qq6Zn8b2vFIqahv42qUz+faT23j4rYOA1+MHMGOclzj+8c2DLJiUzDXzJyIiItJboSid3l4vb5PZobAlWGYWDfwGuAI4DKw3s6edc+1vzPO4c+7Wfg9QIsa6A0XsOV7Bio/MZ2R8bEvCEch/XXE6DY1NLYUhpo4ZzszxSaSnJFDb0MhI/4czwE+um0dmZmGb58dGR3HV3Ak8u/UIi6ac/AE/e8IIxibFnfJ61y1MZ9X2Y7yw4yjvm+VV/7v10pmU19S3Sdz6wqzxSVTVNZKcENv5wr7F00YzNimO73/wDGZP8MpqpyV179LLi2aN5e5X9vDw2zl84pwp/M+H5pzStnQ/wbpwZs8SLPB6ZLK+f0XLuk9PHcG+E5V8bPHklmXMjJjoU7fr+BHxPP7F88jMPtFSZAPg+rMmMTI+lusWpvPGG3u56syTwxRvufA0Hn3nEOfPGANAfGw0V89rmyB888oMvnDRjJaEaUnGeB5+O6clvrP9nr+vXjKT90wZxTUL0pgVYEhoUlwM6797ObHRUURHGSfKa9mZX8oDaw7Q0OQ4f8YYrpiTygy/aMT8ScncfcMiVu04ym1/20JDk+PGc6ecst73nT7OS7A6qIAUbJvNGJfEW/sKOWvqKM6ZNppvP7mN3cfKuWruBK5d6A2ZeOhzZ1Pf4BidNIwfPL2DB9ccBGCOX6J99oQRfP+Dc3DO8aGFaX3+mY8kOiEoItJ/QlE6vb30EFQPbBbOHqxzgL3Ouf0AZvYYcC0Q+M6nMmQ98nYOyQldH3b2pSUz+NPbOVTUNjB1TCJmxlcumcGJ8trOnwxcOns8j63PZc3eAq6Yk8pbewu4OGNcwGXNjBUfnc91i9Jbzuq/f15ozuJ//bJZLRUDu2rciDjWf/eyXv3wXTA5hdNTkzh/xlh+eM2pyRXAB+ZNpLiyjvdMHRVgDV3Xet3XLUpnRHxMS4XFzqQkDjtlLPXo4cP42NmTAy4/fmQ86797OXExwRNOMyM58WRCe970McTFRFHb0MTprRKp82eM5fwZHSeX8bEne7XGjYjj/s+cTWFFLa/sOs65071E7cKZY/0EK4X42GiuXZhOUWUdy59/N+A1bM0l/QP1YHWmeXjfoimj+Lez0vnFS7s5UV7Ll5ecHD46Mfnkwefi08fx0s5jTBuT2HKiwsy4+cLTuv3aA41OCIqIhMbKrDxWrMomv6SatJQEli3N4LpF6aSlJIS8yMUlswP/tusL4Uyw0oHcVn8fBs4NsNyHzex9wG7gP51zuQGWwcy+AHwBIDU1lczMzB4HVlFR0avnD1SR0u5DZY1kFzVxxbRYjlY28dy2aq46LZa1b67u8joumACrcuDEgZ1kFmaTDqTHQGZm2xvCBmpzU4Mj2qDRwejGYn703mGMGHaUzMxjQV8vHsjMfLcbreyZRCAzs3fd5j15n29f6DA7weuvvx50mQuGw5rVgW902xNxwPvH0uFrdkdffb5PTzG2F0B+9iYK9/a+x2Y8cGDbPg4Ao/x7fUUX55CZ6V3/dBpwzyXx7Nv6DvsCPP8Ts4cxrelIwM9nR2220kZioyC2cB9vrznAR2fAobJYivZuJnPvqctPi/aqCI6PrY2I/UQ/0wlBEZE+1nyfq+ZqyXkl1S33vVq2NKPNvFD4x8Y8Fk8dHZJCF9b+Xiv9xcw+Cix1zt3i//1p4Bzn3NdaLTMGqHDO1ZrZl4CPOecu7Wzdixcvdhs2bOhxbJmZmSxZsqTHzx+oIqHdTU2OD/zfGnYdKePpWy/gT2/n8MyWfNZ861LGjTh1iF4wpVX1PLM1n0+eO6XD3ptgbf7U/etYs7eAR24+h4tmhe4MRzhEwvscDn3V7vUHi9hwsLhNT09fcc6x9XAp8ycl98lwu87a3NTkWopqdKa0up73/fw1li3N4FPnhbZSoJltdM4tDumLdIOZfQS4qt3x6tzWvVX+EMHlwAk6OCHY7mTgex577LHQN6CViooKkpKS+vU1I8FQbLfaPDQM5DZnHy2nrrHplOnDoqPImDCC/JJqiirrcZyaq6QmwLE+6OBqfq2euuSSSwIer8LZg3UYaD12ZxLQpnvBOdf6Apn7gJ/1Q1wSRk9vyWfXkTLM4Lv/3M7OI2V85r3TupVcASQnxvbqR+BVZ05g/cEi5qadWvRBhrazp41uufaqr5nZKRUaQ6mryRVAckIsb99+KfFDs0pgoA3V/oj/DPBoqxOCDwOnnBB0zt0L3AveycD+PtmhEyxDh9o8NAzkNv/7t/9FsFvy/urjs/jxK9uorg98zLltXgO/2Nb7NMaAA3ct6fV62gvnjYbXA7PM7DQzGwbcADzdegEza30xy4eAU+8AK4PKQ28dZPaEEXzmvdPYlldKRuoI/vOKWf0ex43nTGH1f1/C6OG6YapIs8RhMd1KygaRLp0QdM41X+h5H/CefopNRGRACnY0MbwqgqEcHtgsLUSFLsLWg+WcazCzW4FVeFWZHnTO7TCzO4ANzrmnga+b2YeABqAI+PdwxSuhV1PfyI78Uj534WnccuF0osz40pLpLSWz+1NUlDF+ZPcLB4jIoNRyQhCvSuANwI2tFzCzic65I/6fOiEoItKJYBcpOfq+iuCoxFgqahqob3VzrYTYaJYtzejT12kW1vtgOeeeA55rN+0HrR7fDtze33FJeOw8UkZ9o2PR5FGMGxHHD66ZE+6QRER0QlBEpJ8FqyKY7lcaPJa9CYBoMxqdY1RiLDX1jVTXt72mKyE2muXXz+O6RelBKxaGQlgTLJHWNh/ybujb+v5TIiKRQCcERUT61qjEWIqr6gNOD1RFsLnH6bpF6WSW7uFggGunOkqirluUHrKEqj0lWBIxsnJLmJgcT6qG5omIiIgMKK2Tm+SEWMygpKq+zePWSc8Pr5nLsr9vob7x5LC92Gjjh9fMbUmEutvj1J9JVEeUYElYrT9YxPLndnHFnAm8va+Qs6f17ka1IiIiItK/2t/TqqT6ZM9U68et73XVWRIVKclSTyjBkrB6Zks+mw6VsOlQCSPiYrjhnCnhDklEREREuqE7Vf+q6xtZsSq7JYEaqElUR5RgSVhtzi3hvOmjWfGRBUxIjic2Opx3DhARERGR7upu1b++rhIYafRrVsKmpr6RXUfKWDh5FJNHJyq5EhERERmAuns/qVDdfypSqAdLwqa5LPvCyaoaKCIiIjKQtC9qERttbQpWBBPK+09FCiVYEjZbcr2y7EqwRERERAaOQEUtYqOMUYmxp1QODFZFcDBTgiVh8/ruE0wYGc+EZJVlFxERERkoAhW1qG9yJA6LIesHV4YpqsihBEvC4p0DRWRmnxj0XcQiIiIig0HrIYHBBgIO9uIVXaUES/qdc447n9vFhJHxfO6C08IdjoiIiIh0oP2QwGAGe/GKrlLZNul3z28/yubcEv7rytNJGBYd7nBEREREJIiVWXnc9rctnSZXQ6F4RVepB0v6VX1jEz9/4V0yUkfw4bMmhTscEREREQmiueeq0QWvDmgwZIpXdJUSLOlXr+w6zsHCKv7w6fcQHWXhDkdEREREgghUzKK19JQE3vz2pf0Y0cCgBEv61WPrDzFhZDyXzR4f7lBEREREhqTWBSs66n3qqGiFhgQGp2uwpN8cLq7i9d0n+NjiScRE66MnIiIi0t+ah/3l+dUA80qquf3JbazMyjtl2WBFK6LNWH79PA0JDEK/cqXf/G3DYQA+dvbkMEciIiIiMjQFGvZXXd/IilXZpyy7bGkGCbFtC5IlxEbzi48tUHLVAQ0RlH7R2OR4YkMu75s1jkmjEsMdjoiIiMig1Nnwv2DD/gJNb35eV4YTyklKsKRfvL77OEdKa/jhNXPCHYqIiIjIoNT+flXNw//gZLKUlpJAXoBkKthwwOsWpSuh6iYNEZSQq2to4ucvZHvFLc5IDXc4IiIiIgPayqw8LrjrVbbllXLBXa+2XD/VleF/wYb9qWBF31EPloTcb17by7tHy7n/psXEqriFiIiISI+16aWa3LaXqivD/zTsL/SUYEnIPbs1n/edPo7L56j3SkRERKQ3Ouql6urwPw37Cy11J0hINTY5couqmTNxZLhDERERERnwOuql0vC/yKAES0LqSGk1dY1NTBujyoEiIiIivRWsGEVaSgLXLUpn+fXzSE9JwID0lATdryoMNERQQiqnsAqAqWOGhzkSERERkYFv2dKMNpUCoW0vlYb/hZ8SLAmpg4WVAEwbqx4sERERkd5qXaQCyklXkYqIowRLQiqnsIq4mChSR8SHOxQRERGRQaG5lyozM5OvfXJJuMORdnQNloTUwYJKpo5JJCrKwh2KiIiIiEjIqQdLQiqnsErXX4mIiIh008qsPN2raoBSD5aETFOTI6eokqmjdf2ViIiISFc130w4r6Qax8mbCa/Mygt3aNIFSrAkZPYXVFBT38Rs3QNLREREpMs6upmwRD4lWBIym3NLAVg4OTnMkYiIiIgMHB3dTFginxIsCZnNucUkxcUwfWxSuEMRERERGTA6upmwRD4lWBIyW3JLmT8pWRUERURERLph2dIMEmKj20xrfTNhiWyqIighUVPfyK4jZXz+fdPDHYqIiIhIRApWKbD1zYRVRXDgUYIlIbHzSBkNTY6Fk1PCHYqIiIhIxGmuFNhczKK5UiCcvJGwEqqBSUMEJSS25JYAKMESERERCUCVAgcvJVgSEptzS5gwMp7UkfHhDkVEREQk4qhS4OClBEtCYktuCQtUnl1EREQkIFUKHLzCmmCZ2VVmlm1me83s2wHmx5nZ4/78dWY2rf+jlO4qqarjYGEVCzQ8UEQGCR2vRKSvqVLg4BW2IhdmFg38BrgCOAysN7OnnXM7Wy12M1DsnJtpZjcAPwM+3v/RSndsOdx8g2ElWCIy8Ol4JSK9oUqBQ084qwieA+x1zu0HMLPHgGuB1gesa4H/8R//HbjHzMw55/ozUOmeLbklmMG8dA0RFJFBQccrEekRVQocmsKZYKUDua3+PgycG2wZ51yDmZUCY4CC9iszsy8AXwBITU0lMzOzx4FVVFT06vkDVV+1+5XNNUwcbmxc+2bvgwqxofheD8U2w9Bs91Bsc4j06fFKRIaOjioFKrEavMKZYFmAae3P9HVlGW+ic/cC9wIsXrzYLVmypMeBZWZm0pvnD1R90W7nHLetfplLZk9kyZIFfRNYCA3F93oothmGZruHYptDpM+OV315MrAnhmrSPRTbrTZHhhsml8PkQHPK+yTWSGxzf4j0doczwTpM24/cJCA/yDKHzSwGSAaK+ic86YnDxdUUVtapwIWIDCZ9drzqy5OBPTFUk+6h2G61OTJ8965XyQtQdj09JYGvfXJJr9cfiW3uD5He7nBWEVwPzDKz08xsGHAD8HS7ZZ4GPuM//gjwqsazR7Yth/0bDE9SgiUig4aOVyIS1MqsPC6461VO+/a/uOCuV1mZldcyT5UCh6aw9WD5Y9RvBVYB0cCDzrkdZnYHsME59zTwAPCIme3FOxN4Q7jila7ZklvCsJgoZk8cEe5QRET6hI5XIhJMV4pYgCoFDjXhHCKIc+454Ll2037Q6nEN8NH+jkt6bnNuCWemjSQ2WvewFpHBQ8crEQmkK0UsVClw6NGvYOkzDY1NbMsr1fVXIiIiMiTkB7i+qqPpMjQowZI+s/tYBTX1TbrBsIiIiAwJaSkJ3ZouQ4MSLOkzzQUuFqjAhYiIiAwBKmIhgYT1GiwZXLbklpCSGMvUMYnhDkVERESkS1Zm5fW4CIWKWEggSrCkz2zOLWHBpBTMAt1vU0RERCSydFYFsCtUxELa0xBB6ROVtQ3sPlauAhciIiIyYHRUBVCkp5RgSZ/YnldKk4OFk5PDHYqIiIhIl6gKoISCEizpE80FLuarwIWIiIgMEKoCKKGga7CkT2zJLWXSqATGJsWFOxQREREZ5AIVpujJKd5lSzPaXIMFqgIovaceLOkTm3NLdP8rERERCbnmwhR5JdU4ThamKKmu7/a6rluUzvLr55GekoAB6SkJLL9+nopWSK+oB0t67UR5LXkl1fz7+dPCHYqIiIgMcsEKUxwr7X6CBaoCKH1PPVjSa9vzSwGYN0kFLkRERCS0ghWgqGts6udIRAJTgiW9tjO/DIA5aSPDHImIiIgMdsEKUAyL1s9aiQz6JEqv7cwvY/LoBEbGx4Y7FBERERnkli3NICE2us20hNhoUpPjwxSRSFu6Bkt6bUd+KXMnanigiIiIhF7z9VKnVBEs3RPmyEQ8SrCkVypqGzhYWMWHz5oU7lBERERkEAhUgr19EYpAhSkyM5VgSWRQgiW9suuIrr8SERGRvtFcgr25SmBzCXZAlf5kwNA1WNIr+45XAHB66ogwRyIiIiIDXbAS7CtWZYcpIpHuU4IlvXKsrBaA1JG6sFRERER6J1gJ9mDTRSKREizplePlNYwePoxhMfooiYiISO8EK8EebLpIJNKvYumVY2W1jB8RF+4wREREZBAIVoJ92dKMMEUk0n0qciG9cqK8hvEaHigiIiJ9IFgJdhW4kIFECZb0yrGyWhW4EBERkT4TqAS7yECiIYLSY01NjhMVtYwfqSGCIiIiIiKgBEt6obCyjsYmpwqCIiIiIiI+JVjSY8fLawBU5EJERERExKcES3rsuH8PLBW5EBERERHxqMiF9Jh6sERERKS1lVl5qgAoQ54SLOmxY34P1jglWCIiIkPeyqw8bn9yG9X1jQDklVRz+5PbAJRkyZCiIYLSYyfKa0lJjCUuJrrzhUVERGRQW7EquyW5alZd38iKVdlhikgkPJRgSY8VVtYyZviwcIchIiIiESC/pLpb00UGKyVY0mNFlXWMGa7hgSIiIgJpKQndmi4yWCnBkh4rqqxjtHqwREREBFi2NIOE2LaXDSTERrNsaUaYIhIJDyVY0mNFlXWMUoIlIiIieIUsll8/j/SUBAxIT0lg+fXzVOBChhxVEZQeaWpyFFfV6xosERERaXHdonQlVDLkqQdLeqSspp7GJqceLBERERGRVpRgSY8UVtYBqAdLRERERKQVJVjSI8V+gqUiFyIiIiIiJynBkh4pVIIlIiIiInKKsCRYZjbazF4ysz3+/6OCLNdoZpv9f0/3d5wSnHqwRGQo0PFKRES6K1w9WN8GXnHOzQJe8f8OpNo5t9D/96H+C086ox4sERkidLwSEZFuCVeCdS3wsP/4YeC6MMUhPVRUWUfisGji291QUERkkNHxSkREusWcc/3/omYlzrmUVn8XO+dOGXZhZg3AZqABuMs5t7KDdX4B+AJAamrqex577LEex1dRUUFSUlKPnz9Qdafd926tJbuokV8sSQxxVKE1FN/rodhmGJrtHqhtvuSSSzY65xaHOw7o++NVXx6remKgfiZ6ayi2u6M2l1TXc6y0hrrGJoZFR5GaHE9KQmw/R9j39D4PHZHS7mDHq5DdaNjMXgYmBJj13W6sZopzLt/MpgOvmtk259y+QAs65+4F7gVYvHixW7JkSXdDbpGZmUlvnj9Qdafdf9z/DulRdSxZcmFogwqxofheD8U2w9Bs91Bsc0/05/GqL49VPTFUPxNDsd3B2rwyK4/bX9lGdX0UzQOZEmIbWX79nAF/g2C9z0NHpLc7ZAmWc+7yYPPM7JiZTXTOHTGzicDxIOvI9//fb2aZwCIgYIIl/auosk7XX4nIoKDjlQwlK1ZlU13f2GZadX0jK1ZlD/gESyRShOsarKeBz/iPPwM81X4BMxtlZnH+47HABcDOfotQgmpqcuw/UcHUMQN7eKCISBfoeCWDSn5Jdbemi0j3hSvBugu4wsz2AFf4f2Nmi83sfn+ZM4ANZrYFeA1vTLsOWBHgUFEVlXWNzE0bGe5QRERCTccrGVTSUhK6NV1Eui9kQwQ74pwrBC4LMH0DcIv/+C1gXj+HJl2wI78MgDkTk8MciYhIaOl4JYPNsqUZ3P7ktjbDBBNio1m2NCOMUYkMLmFJsGRg23mklJgoY1Zq+Ku3iIiISNc1X2e1YlU2+SXVpKUksGxphq6/EulDSrCk23bmlzFzfJLugSUiIhLBVmblBUykmv+JSGgowZJu23mkjAtmjA13GCIiIhJESXW9X47dGwqYV1LN7U9uA1ByJRJi4SpyIQNUeU09x8pqOX3CiHCHIiIiIkEcK60JWo5dREJLCZZ0y4nyWgBSR8aFORIREREJpq6xKeB0lWMXCb1OEywzSzWzB8zsef/vOWZ2c+hDk0hUUFEHwNgkJVgiIiKRalh04J94KscuEnpd6cF6CFgFpPl/7wa+EaqAJLIVVHg9WEqwREREIldqcjwJ7YpRqRy7SP/oSoI11jn3N6AJwDnXADR2/BQZrAr9BGtM0rAwRyIiciozmxTuGEQiQUpCLMuvn0d6SgIGpKcksPz6eSpwIdIPulJFsNLMxgAOwMzOA0pDGpVErBMVdZjB6EQlWCISke4Ebgp3ECKRQOXYRcKjKwnWfwFPAzPM7E1gHPCRkEYlEaugopbRicOICTK2W0QkzC4wsx8B24CPOuc+Hu6ARERkaOk0wXLObTKzi4EMwIBs51x9yCOTiFRYUavhgSISyd7Cu3Z4HnBPeEMREZGhqNMEy8zaD7U4y8xwzv0pRDFJBCuoqFOBCxGJZPc45w4AB8IdiIiIDE1dGSJ4dqvH8cBlwCZACdYQVFBRy4JJKeEOQ0QkIOfcunDHICIiQ1tXhgh+rfXfZpYMPBKyiCSiFZRriKCIRDYzG+ecOxHuOEREZGjqSg9We1XArL4ORCJfdV0jlXWNGiIoIpHuR8BXwh2ESE+szMpjxaps8kuqSUtJYNnSDFUCFBlgunIN1jP4Jdrx7ps1B/hbKIOSyNR8k+FxSrBEJAL598CaAaSZ2fsAnHNvhDcqka5bmZXH7U9uo7reu91oXkk1tz+5DUBJlsgA0pUerP9t9bgByHHOHQ5RPBLBmhOssSM0RFBEIlIKMA0Y4f8PoARLBowVq7Jbkqtm1fWNrFiVrQRLZADpyjVYr/dHIBL5iqvqABilmwyLSARyzm0HtpvZeap0KwNRfkl1t6aLSGQKmmCZWTknhwa2mQU459zIkEUlEamkyrv9WYoSLBGJbL8OdwAiPZGWkkBegGQqLSUhDNGISE9FBZvhnBvhnBsZ4N8IJVdDU0uClRAb5khERIJzzu0KdwwiPbFsaQYJsdFtpiXERrNsaUaYIhKRngiaYLVnZuPNbErzv1AGJZGptNpLsEYqwRKRCGVm/9XqsX6VyoBy3aJ0ll8/j/SUBAxIT0lg+fXzdP2VyADTlSqCHwJ+AaQBx4GpwC5gbmhDk0hTWl3PiPgYoqMs3KGIiLRhZinAL4EMM6sBtgI3A58Na2Ai3XTdonQlVCIDXFeqCP4YOA942Tm3yMwuAT4R2rAkEpVW15OSqN4rEYk8zrkS4LNmthQoAOYDT4Y3KhERGYq6MkSw3jlXCESZWZRz7jVgYYjjkghUUlVHsoYHikiEMbNfmZkBOOdWOec2Ouf+6Jx7JtyxiYjI0NOVBKvEzJKA1cBfzOxuvPthyRBTWl1PSoIqCIpIxKkAnjaz4QBmdqWZvRnmmEREZIjqqEz7PcCjwLVANfAN4JNAMnBHv0QnEaWkup6JySoVKyKRxTn3PTO7Ecg0s1qgEvh2mMMSEZEhqqNrsPYA/wtMBB4HHnXOPdwvUUlEKquuJ1nXYIlIhDGzy4DP4yVWE4GbaA53LgAAIABJREFUnXPZ4Y1KRESGqo7ug3W3c+69wMVAEfBHM9tlZt83s9P7LUKJCM45SqrqdQ2WiESi7wLfd84tAT4CPG5ml4Y3JBERGao6vQbLOZfjnPuZc24RcCNwPV6ZdhlCquoaaWhyusmwiEQc59ylzrk1/uNtwNXAT8IblYiIDFWdJlhmFmtm15jZX4Dngd3Ah0MemUSUEv8mw+rBEpFI55w7AlwW7jhERGRo6qjIxRV497v6APAO8BjwBedcZT/FJhGktMpLsHQfLBEZCJxz1eGOQUREhqaOilx8B/gr8E3nXFE/xSMRqqS6DoCR6sESEREREQkqaILlnLukPwORyNbSg6X7YImIiPSplVl5rFiVTX5JNWkpCSxbmsF1i9LDHZaI9FBHPVgiLUqrNURQRESkr63MyuP2J7dRXd8IQF5JNbc/uQ1ASZbIANVpkQsRUJELERGRUFixKrsluWpWXd/IilW6lZvIQKUES7pk99FyRg8fRuKw6HCHIiIiMmjklwSuxxJsuohEPiVY0innHGv2FnDBzLGYWbjDERERGTTSUhK6NV1EIp+uwZJO7TlewfHyWi6cOSbcoYiIiAwKzYUt8kqqMcC1mpcQG82ypRnhCk1EekkJlnRqzZ4CAC6YOTbMkYiIiAx87QtbOGhJstJVRVBkwAvLEEEz+6iZ7TCzJjNb3MFyV5lZtpntNbNv92eMctK6A4VMHZPIpFGJ4Q5FRKRf6XgloRCosEVzcvXmty9VciUywIXrGqztwPXAG8EWMLNo4DfA1cAc4BNmNqd/wpPWjpTWMG3M8HCHISISDjpeSZ9TYQuRwS0sCZZzbpdzrrP6o+cAe51z+51zdcBjwLWhj07aK/z/7d19eJT1ne/xzzdDAiE8hMeQRFQQCKKgaOrztlHRWHQrUrvH3Z7WXrtdj+cc+3DWsgvruVqvutdiy257bU972mrtttvaWk+L2K7UoIWU+oBVGzEiBAURSQQCJEiSIZlMfuePmYSEzIRJMjP3zNzv13XNxcw9dybfb34TfvnO7+Fu69K0Ii4wDMB/6K+QCmxsAeS2TF6DVS7pvX6PD0i6PN7JZnaXpLskqaSkRLW1tSP+xm1tbaP6+mwVL+/mE0G1txzKyZ+JH9vajzlL/szbjzl7JOH+Kpl91Uj49T2RaXmvuiisxpawetyprS3yzFQ+JZy0ODMt53QgZ//I9LxTVmCZ2bOSZsV46j7n3JOJvESMYy7GscgTzj0k6SFJqqysdFVVVYmEGVNtba1G8/XZKlbewa6wup5+WhctPE9VVfO8CSyF/NjWfsxZ8mfefsx5JNLZXyWzrxoJv74nMjHv3l0Em1qDKkvBxhaZmHOqkbN/ZHreKSuwnHPLRvkSByTN7vf4LElNo3xNDNPR9k5JYooggJxFfwUvrFhazmYWQI7K5AsNvyxpvpnNMbMCSXdI+rXHMfnOsfYuSdLUorEeRwIAGYv+CgDQx6tt2m8zswOSrpT0lJnVRI+XmdlGSXLOdUu6R1KNpJ2SHnfO7fAiXj872ldg5XscCQCkH/0VAGC4PNnkwjn3hKQnYhxvkrS83+ONkjamMTSc5lgbI1gA/Iv+CgAwXJk8RRAZ4NQUQdZgAQAAAGdCgYUhHevoUn7ANGlcJu/oDwAAAGQGCiwM6Vhbl6aML5BZrF2IAQAAAPTHsASGdLS9i+mBAADfS/V1qwDkDgosDOlYe6emTaDAAgD414a6Rq1ZX69gKCxJamwNas36ekmiyAIwCFMEMaRj7V3sIAgA8LV1NQ19xVWvYCisdTUNHkUEIJNRYCGuYFdYhz7o1DSmCAIAfGhDXaOufnCzGluDMZ9vinMcgL8xRRBx/WTbPgVDYS1fXOp1KAAApNXp0wJjKSsuTGNEALIFBRZiOnEypO/W7tGHF8zQZXOmeh0OAABDSvYmFLGmBfZXmB/QquqKEb8+gNxFgYWY/v35fWrpCOneGxZ4HQoAAENKxSYUQ03/K2cXQQBDYA0WBmnt6NLDW/fqhkUlumh2sdfhAAAwpFRsQhFv+l95caGeX30dxRWAuCiwMMjTbxzUic5ufeH6+V6HAgDAGcUbbRrNJhSrqitUmB8YcIxpgQASQYGFQQ6f6JQkLSiZ6HEkAACcWbzRptFsQrFiabnWrlys8uJCmSIjV2tXLmbkCsAZsQYLg7R0dGni2DEqGEP9DQDIfKuqKwbt+JeM0aYVS8spqAAMGwUWBmlp79IUrn0FAMgSvUVQMncRBICRosDCIMc6QhRYAICswmgTgEzBHDAM0tLepanj870OAwAAAMg6FFgY5Fh7l6aMZwQLAAAAGC4KLAzS0sEaLAAAAGAkKLAwwMlQWB1dYU2lwAIAAACGjQILA7R2hCSJKYIAAADACFBgYYBj7V2SpKlFbHIBAAAADBcFFgZo6YgUWIxgAQAAAMNHgYUBTo1gUWABAAAAw8WFhjFA3wgWBRYAIEtsqGvUupoGNbUGVVZcqFXVFVx0GIBnKLAwQEt7ZJOL4kLWYAEAMt+GukatWV+vYCgsSWpsDWrN+npJosgC4AkKLAzQ0tGlSePGaEyA2aMAgNQb7ejTupqGvuKqVzAU1rqaBgosAJ6gwEKfrrDT5l2HNWfGBK9DAQD4QDJGn5pag8M6DgCpxjAF+mzaF9L+Yx1adWOF16EAAHxgqNGnRJUVFw7rOACkGgUW+vyhsVvXzJuua+ZP9zoUAIAPJGP0aVV1hQrzAwOOFeYHtKqaDwsBeIMCC30+6HKaX8L0QABAeiRj9GnF0nKtXblY5cWFMknlxYVau3Ix668AeIY1WJAkhcI9CnZzgWEAQPqsqq4YsAZLGtno04ql5RRUADIGBRYk9bv+1Xi2ZwcApEdvUcQ1rADkEgosSJJaO6LXv2IECwCQRow+Acg1rMGCJKmlPTKCNbWIAgsAAAAYKQosSJJa+kawmCIIAAAAjBQFFiT1X4PFCBYAAAAwUhRYkESBBQAAACQDBRYkRTa5yM+TCgsCZz4ZAHzCzD5hZjvMrMfMKoc4b5+Z1ZvZa2b2SjpjBABkFk8KLDqszHOsvUsTC8zrMAAg07whaaWkrQmce61z7mLnXNx+DQCQ+7zapr23w/p+Aude65w7kuJ4fK+1o0tF+RRYANCfc26nJJnx/yMAIDGejGA553Y65xq8+N6IraUjpAlsIAgAI+UkbTKzV83sLq+DAQB4x5xz3n1zs1pJX3LOxZz+Z2bvSGpRpOP6vnPuoSFe6y5Jd0lSSUnJpY899tiI42pra9OECRNG/PXZaPXWDpWO79EXKv2Vtx/b2o85S/7MO1tzvvbaa19N5zQ7M3tW0qwYT93nnHsyek6thu6vypxzTWY2U9Izkj7nnBs0rTCZfdVIpPs90RoM6dDxk+oK96ggkKeSyeNUXJj+T/Oy9XdhNMjZH/yYs5Q5ecfrr1I2RTCRDisBV/fvsMxsV6wOS5KixddDklRZWemqqqpGErYkqba2VqP5+mzUuXWTphQ63+Xtx7b2Y86SP/P2Y84j4ZxbloTXaIr+e9jMnpB0mWKs20pmXzUSqXxPbKhr1LqaBjW1BlVWXKhrF87Qr15tVDCUp94JM4X5Ya1duUgrlpanJIZ4/Pi7QM7+4MecpczPO2UFVjo7LIxOuMfpeDCkogLmCALAcJlZkaQ859yJ6P0bJX3V47DSakNdo9asr1cwFJYkNbYG9ei2/Tp9jkwwFNa6moa0F1gAkE4Zu027mRWZ2cTe+4p0WG94G1XuCfc4fe3pXepxUvFYFnEDQH9mdpuZHZB0paSnzKwmerzMzDZGTyuR9JyZbZf0R0lPOeee9iZib6yraegrrnrFW4DQ1BpMfUAA4CFPdhE0s9sk/R9JMxTpsF5zzlWbWZmkHzjnlivSYT0R3blpjKSf+a3DSoctuw7roa17ddvScl0zrcXrcAAgozjnnpD0RIzjTZKWR+/vlXRRmkPLKMMpmsqKC1MYCQB4z5MCiw4rc7x/PNIp/uPy87Xj1Rc9jgYAkI3KigvVGKPIMg0cySrMD2hVdUXa4gIAL2TsFEGkR/OJTuWZNLWowOtQAABZalV1hQrzAwOOFeYH9MkrzlZ5caFMUnlxodauXMz6KwA5z6sLDSNDNLd1atqEsQrksf4KADAyvUVT/10EV1VXUEwB8CUKLJ9rPtGp6RPGeh0GACDLrVhaTkEFAGKKoO81n+jUjIkUWAAAAEAyUGD5XPOJTs1gBAsAAABICgosH3POqbmNESwAAAAgWSiwfOx4MKRQ2FFgAQAAAElCgeVjzSc6JYkCCwAAAEgSdhH0sb4CizVYAIBR2FDXyBbtABBFgeVjzW2MYAEARmdDXaPWrK9XMBSWJDW2BrVmfb0kUWQB8CWmCPoYUwQBAKO1rqahr7jqFQyFta6mwaOIAMBbFFg+dvD4SY0dk6dJ4xjIBACMTFNrcFjHASDXUWD52O7DbZo3c4LMzOtQAABZqqy4cFjHASDXUWD5WMPBD1Qxa6LXYQAAstiq6goV5gcGHCvMD2hVdYVHEQGAt5gb5lOtHV069EGnKkoosAAAI9e7kQW7CAJABAWWTzUcPCFJjGABABIy1FbsK5aWU1ABQBQFlk/tPkSBBQBIDFuxA0DiWIPlU7sOntCkcWM0a9I4r0MBAGQ4tmIHgMRRYPlUfeNxLZw1iR0EAQBnxFbsAJA4pgj60MHjJ/X6gePs8AQAiOn09VbF4/PV0hEadB5bsQPAYBRYPrTpzYOSpOoLSjyOBACQCfoXVJML89Xe1a1Q2EmKrLfKzzPlB6zvmMRW7AAQDwWWD23acUhzZxRp3kw2uAAAvzt9A4vW4OCRqlCPU3FhvorGjmErdgA4Awosn9my67Ce33NE91w7z+tQAAAZINYGFrEcD4b02lduTENEAJDd2OTCRw5/cFKf/3mdFpVO0n+vOs/rcAAAGSDRjSpYbwUAiaHA8pHa3c060dmtr9++ROMLGLwEACRWOLHeCgASx1/ZPrJt71FNKyrQotJJXocCAPBY78YWja1BmSTX77n8PNOEcWPU2hFivRUADBMFlk845/TS3mO6Yu40rn0FAD53+sYWTuorssopqABgVCiwfOJAS1CNrUHd/ZG5XocCAPBYrI0teour51df501QAJAjWIPlEy/sOSJJumLuNI8jAQB4Ld7GFolueAEAiI8RLJ/43c7DKp08TvNmTvA6FACAx8qKC9UYo5gqHp+vqx/czLWuAGAUGMHygZOhsP7w1hEtO7+E9VcAAK2qrlBhfmDAsfyAqe1ktxpbg3KSGluDWrO+XhvqGr0JEgCyFAWWD7yw54iCobCWLSrxOhQAgAc21DXq6gc3q77xuK5+cLMkae3KxSovLpQpsvaqqGCMQj1uwNcFQ2Gtq2nwIGIAyF5MEfSBTTsOacLYMbpi7lSvQwEApNn/3lCvR7ftj2zDPvvUyNTalYsHbGgxZ/VTMb+edVkAMDyMYOW4k6Gwnqp/XzcsKtHYMYEzfwEAIGdsqGs8VVz1E2tkKt4FhxO5EDEA4BQKrBz09uE2/dXD29Ta0aVNbx7SiZPd+sSlZ3kdFgAgzdbVNAwqrnqdPjIVa11WYX5Aq6orUhQdAOQmpgjmoK27m/XCnqN6qv591ew4pPLiQrZnBwAfirVTYK/TR6Z6dwtcV9PALoIAMAoUWDnonSPtkqRH/vCO9h5p1/9atkB5eeweCAB+sqGuUSbFHMEyKebI1Iql5RRUADBKFFg5aN/RSIG190i7igoCuvOqczyOCACQbBvqGgeMNl27cIa27Grue9zR1R13euAnrzibQgoAUoQ1WDnonSPtWlASuaDwp648V8XjCzyOCACyk5mtM7NdZva6mT1hZsVxzrvJzBrM7G0zW53quDbUNWrN+voB16z66bb9Ax63dITifv0/rVic6hABwLc8KbAytcPKBZ3dYTW2BvXRC0v1s7+9XF9cNt/rkAAgmz0j6ULn3BJJuyWtOf0EMwtI+o6kj0paJOkvzWxRKoNaV9OgYCg8oq+dMj4/ydEAAPrzagQrIzuseN471qFHX3o35d/n4a179e3Nb43qNfYf7ZBz0pzpRbrqvOkal8/W7AAwUs65Tc657ujDbZJibcl6maS3nXN7nXNdkh6TdGsq4xrNtalaOkI6d/VTuvrBzdpQ15jEqAAAkkdrsJxzm/o93Cbp9hin9XVYkmRmvR3Wm6mPcKDvbHlbj738npadX6KSSeMGPBfucfrmM7u1Ymm55s2ckNDrOee0sf6gQuGeAXPgf/ziPplJ91w39KjT/b/eofNmFOlTV5474DXNrG+Di3OnFyWWHAAgUX8t6RcxjpdLeq/f4wOSLo/1AmZ2l6S7JKmkpES1tbUjCmT1xT3qCvcM++tKCqV7F/fWiyfUuPNVbTj4pooLc3tUq62tbcQ/62xFzv7gx5ylzM87Eza5GHWHJSWv05IGNppzTk+/Hvmk8Bc1z2lswDR7Yp7G50d25dt3PKxvv3hSP3lhj9ZcNk6zioYeFOxxTo/Ud+n5pm4VBKSJLbsVyDN90Ol0oCUok/TM5i3KzzMdDfZoyjhTnp3aAfDdD8L60QsnJUnb39ytW84rUHvI6f4Xgjp/WkATonE17qpT657h7RyY6W/WVCBn//Bj3n7MeSTM7FlJs2I8dZ9z7snoOfdJ6pb0aKyXiHEs5v4SzrmHJD0kSZWVla6qqmokIas1ugZruNME713crX+tH9j1lxcH9PzqkcWRLWprazXSn3W2Imd/8GPOUubnnbICK50dlpS8Tksa2Gg7mo6rteY5SdLRgln6j23v6jNXnauv3HCBJOlXrx6QtF0nw6Znj0zUD27+UNzXPRkK61u/e0vPN+3R5XOm6qV3jqmk4hJdWD5Zm3cdkvSKnKRzL6jUu0c79KWfvKIvXD9fX1y2QO8d69Ajz72jlo4uFYw5qKoFM/TErsO6+8+v1FOvH1RzcLeaD0Q+lZwzvUg33zD8/DP9zZoK5OwffszbjzmPhHNu2VDPm9mdkm6RdL1zLlY/dEDS7H6Pz5LUlLwIB+ud/XDv49sVjhlS4kYz3RAAMFjK1mA555Y55y6Mcestrno7rE9mSocVy5ZdhyVJU4sK9NjL78k5aWP9++rpiYT81uE25QdMf3nZ2aptaFZLe1fM19n+XqsueeAZ/d/aPbr90rP0L5+4SJJUt79FkvTae8f7zv397mZ9/rE6OSf9dNu76uyOFGY/emGfnnytSdUXzNLalYs1viCgv3t8ux55bq9uWFSin332cv3bHRfrN5+7JpU/EgDwDTO7SdI/SPqYc64jzmkvS5pvZnPMrEDSHZJ+nerYViwtH3VxJUnFbHoBAEnl1S6CGdthNZ/o1ItN3eqt+bY0NGtx+WRdPmeqOrsj890PfdCpV6OF0VuHTmju9Am6/dKz1N3j9Ns3Dso5p7cPt6l/3fjjF/cpYKZH7qzU1z6+RGdNKdSMiWP1p/2tkiIFWHlxoSTpe7/fq46usNauXKwjbV366bb9+s3rTfqz+dNVec4U/bcPz9W0CWP19zct1I6mD1Q0dozuvXGBrpo3XbdeXK4JYzNh5icA5IRvS5oo6Rkze83MvidJZlZmZhslKboJxj2SaiTtlPS4c25HqgNL1gYVSajRAAD9ePWX+LcljVWkw5Kkbc65u82sTNIPnHPLnXPdZtbbYQUk/TAdHdazOw/p+6936vbr2zR9wljV7W/RPdfNV36e6bdvHNTNS0r17JuH9I1Nu3Xfzedr9+ETuuisYl1QNklzZxTpB3/Yq1f2HdP6ukbd/ZHztPqjC9Xe2a2n3zioWy8u0/Xnl/R9r0vOLtaf9rco3OO0/UCrqhfN0u92HdKRtk5dWD5J/6Vytn70/D498J+RfT1Wf3ShLiib3Pf1n7riHP3Xy8+W2fDWWgEAEuOcmxfneJOk5f0eb5S0MV1x9V4HKxmOB+NfLwsAMHxe7SKYkR2WJF0zb7okaetbRzStqEA9Trpu4Uy1dESm/t2yuFQXlk3Wt373lj7+3RfU2d2jT1w6W2amL9+ySPc+vl3r6xq1qHSSvvf7PaqYNUHdYaeOrrBWXjJwd99Lz5mimh2H9Ns33ldrR0hXzZumvUfadKStS1ULZiovz/Szv71c39+6V6Fwz4DiqhfFFQD4z2iug3W6sujsCQBAcjCX7DSzp47XrPGmP7zVrMmF+ZpWVKAl5ZHC5uFPV+r6hZHC57al5Vr2jd+rs7tHC0oi27NXVczUllVV2nO4TYvLJ+uvHn5JX35yhwoCeTq/dJIqz5ky4HvddEGp/nnjLn35yR0K5JmqFszU828f0cv7WlRVMUOSNG3CWP3j8vPT+0MAAGS0ZG1MUZgf0KrqiqS8FgAgwqsLDWe0C6cH9OKeo3rmzUOqqogUVHl5phsWlSgvLzJiNGvyOP39TRUK5JkuLD81sjRpXL6Wnj1FYwJ5+vrtSxQK96i9q1vfuuPiQaNNZ08br6vOm6Zj7V360LlTNHl8vj6yYKYqz5mii2cXpzVnAED2SMaoU3FhvtauXDzgeowAgNFjBCuGC6cH9Oz+bpVOHqd7b1wQ97xPX3mubllSpqlFBTGfP3d6kf79M5dpTMA0v2RizHP+onK2XthzVMuia7NuXlKqm5eUjj4JAEDOWlVdMaLrYPX32lduTGJEAIBeFFgxXDA9oP957Xm6belZZ/yUMF5x1evK86YN+fzNS0p1pK1Tf/Gh2UOeBwBAr95Rp3U1DWpqDap4fL7aTnYr1HNqS8DC/IDyTGrvGlyETWFrdgBIGQqsGPLzTKuqF6bnewXy9Nk/m5uW7wUAyB0rlpYPmN63oa6xr+AqKy7sW1u16pfbFQqfKrzyA6av/PkFaY8XAPyCAgsAgBxwesHVX2/hVRDI07rbL2LdFQCkEAUWAAA5rH/hVVtbqyqKKwBIKXYRBAAAAIAkocACAAAAgCShwAIAAACAJKHAAgAAAIAkocACAAAAgCShwAIAAACAJKHAAgAAAIAkocACAAAAgCShwAIAAACAJDHnnNcxJJ2ZNUt6dxQvMV3SkSSFk038mDc5+4cf887WnM9xzs3wOohUS0JfNRLZ+p4YLT/mTc7+4MecpczJO2Z/lZMF1miZ2SvOuUqv40g3P+ZNzv7hx7z9mDOG5tf3hB/zJmd/8GPOUubnzRRBAAAAAEgSCiwAAAAASBIKrNge8joAj/gxb3L2Dz/m7cecMTS/vif8mDc5+4Mfc5YyPG/WYAEAAABAkjCCBQAAAABJQoEFAAAAAElCgXUaM7vJzBrM7G0zW+11PKliZvvMrN7MXjOzV6LHpprZM2b2VvTfKV7HOVpm9kMzO2xmb/Q7FjNPi/hWtO1fN7NLvIt85OLkfL+ZNUbb+zUzW97vuTXRnBvMrNqbqEfHzGab2RYz22lmO8zsC9HjOdvWQ+Sc022N4TGzdWa2K/o+f8LMiuOclzN9n5l9Ivo70WNmcbdxjtUPZrNh5J1LbZ3Q3y1mFu73f+Kv0x1nMpyp3cxsrJn9Ivr8S2Z2bvqjTK4Ecv6MmTX3a9vPehFnTM45btGbpICkPZLmSiqQtF3SIq/jSlGu+yRNP+3Y1yWtjt5fLelrXseZhDw/LOkSSW+cKU9JyyX9VpJJukLSS17Hn8Sc75f0pRjnLoq+z8dKmhN9/we8zmEEOZdKuiR6f6Kk3dHccrath8g5p9ua27DfJzdKGhO9/7VY/6/nWt8n6XxJFZJqJVUOcd6gfjCbb4nknYNtndDfLZLavI51lHmesd0k/Q9J34vev0PSL7yOOw05f0bSt72ONdaNEayBLpP0tnNur3OuS9Jjkm71OKZ0ulXSj6P3fyxphYexJIVzbqukY6cdjpfnrZL+w0Vsk1RsZqXpiTR54uQcz62SHnPOdTrn3pH0tiK/B1nFOfe+c+5P0fsnJO2UVK4cbushco4nJ9oaw+Oc2+Sc644+3CbprBin5VTf55zb6Zxr8DqOdEsw75xqa+Xg3y1xJNJu/X8Wv5R0vZlZGmNMtqx+r1JgDVQu6b1+jw9o6D9YspmTtMnMXjWzu6LHSpxz70uRP94kzfQsutSKl2eut/890WlCP+w3jSLnco5Oi1gq6SX5pK1Py1nySVtj2P5akZHb0/n1vRGrH8x1udbWif7dMs7MXjGzbWaWjUVYIu3Wd070Q5XjkqalJbrUSPS9+vFof/dLM5udntDObIzXAWSYWJV+ru5jf7VzrsnMZkp6xsx2eR1QBsjl9v+upAcUyecBSf+qyB9bOZWzmU2Q9CtJX3TOfTDEh3c5k3eMnH3R1jjFzJ6VNCvGU/c5556MnnOfpG5Jj8Z6iRjHMvq9kUjOCRjUD0ZnAGSsJOSdU209jJc5O9rWcyVtNrN659ye5ESYFom0W9a17Rkkks9vJP3cOddpZncrMoJ3XcojSwAF1kAHJPWvfs+S1ORRLCnlnGuK/nvYzJ5QZCj2kJmVOufej06XOuxpkKkTL8+cbX/n3KHe+2b2sKT/jD7MmZzNLF+RQuNR59z66OGcbutYOfuhrTGQc27ZUM+b2Z2SbpF0vYsuXDhN1r03zpRzgq8Rqx/M6AIrCXnnVFubWUJ/t/Rr671mVqvIiH82FViJtFvvOQfMbIykyUp8uUAmOmPOzrmj/R4+rMg604zAFMGBXpY038zmmFmBIosEs3K3maGYWZGZTey9r8gi6DcUyfXO6Gl3Skr0U8BsEy/PX0v6tEVcIel479SDbHfa+qLbFGlvKZLzHdHdh+ZImi/pj+mOb7Si88wfkbTTOfeNfk/lbFvHyznX2xrDY2Y3SfoHSR9zznXEOc0XfV9/Q/SDuS7X2vqMf7eY2RQzGxu9P13S1ZLeTFuEyZFIu/X/WdwuaXOcD1SyxRlzPq2/+5gia5Ezg9e7bGTaTZHdxXYr8snGfV7Hk6Ic5yqyG8t2STt681Rkru7vJL0V/Xeq17EmIdefS3pfby+GAAACzElEQVRfUkiRT0P+Jl6eigxHfyfa9vUaYvepTL7Fyfkn0ZxeV+Q/qNJ+598XzblB0ke9jn+EOV+jyNSB1yW9Fr0tz+W2HiLnnG5rbsN+n7ytyDqG3vdI7y5jZZI29jsvZ/o+RT5YOCCpU9IhSTWn5xyvH8zmWyJ552Bbx/s/vlLSD6L3r4r+n7g9+u/feB33CHMd1G6SvqrIhyeSNE7S/4v+zv9R0lyvY05Dzmujv7/bJW2RtNDrmHtvFg0QAAAAADBKTBEEAAAAgCShwAIAAACAJKHAAgAAAIAkocACAAAAgCShwAIAAACAJOFCw4DHzKx3m1kpcrX6sKTm6OMO59xVngQGAACAYWObdiCDmNn9ktqcc//idSwAAAAYPqYIAhnMzNqi/1aZ2e/N7HEz221mD5rZJ83sj2ZWb2bnRc+bYWa/MrOXo7ervc0AAOAXZrbFzG6I3v8nM/uW1zEBXmCKIJA9LpJ0vqRjkvYqcpX6y8zsC5I+J+mLkv5N0jedc8+Z2dmSaqJfAwBAqn1F0lfNbKakpZI+JklmNsU51+JpZEAaUWAB2eNl59z7kmRmeyRtih6vl3Rt9P4ySYvMrPdrJpnZROfcibRGCgDwHefcVot0QH8nqco5F44+9U1Jn/EsMCDNKLCA7NHZ735Pv8c9OvW7nCfpSudcMJ2BAQBgZosllUo60vvBnpndJGmhmX2J9cXwC9ZgAbllk6R7eh+Y2cUexgIA8AkzK5X0qKRbJbWbWXX0qSOSfkpxBT+hwAJyy+clVZrZ62b2pqS7vQ4IAJDbzGy8pPWS7nXO7ZT0gKT7o08vkbTdo9AAT7BNOwAAAFLCzD4m6eOSHowWX0DOo8ACAAAAgCRhiiAAAAAAJAkFFgAAAAAkCQUWAAAAACQJBRYAAAAAJAkFFgAAAAAkCQUWAAAAACQJBRYAAAAAJAkFFgAAAAAkyf8HHf5Z0edbqtcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_embedding(X_train[2], 3, int(y_train[2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_embedding(X_train[10], 3, int(y_train[10]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_embedding(X_train[3], 3, int(y_train[3]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_embedding(X_train[13], 3, int(y_train[13]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It seems that embeddings of different classes produce quite distinguishable embeddings (point clouds). So, here topological features can produce good results. Let's check it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_extractor = TopologicalFeaturesExtractor(\n",
    "    persistence_diagram_extractor=PersistenceDiagramsExtractor(tokens_embedding_dim=2, \n",
    "                                                               tokens_embedding_delay=3,\n",
    "                                                               homology_dimensions=(0, 1),\n",
    "                                                               parallel=True),\n",
    "    persistence_diagram_features=[HolesNumberFeature(),\n",
    "                                  MaxHoleLifeTimeFeature(),\n",
    "                                  RelevantHolesNumber(),\n",
    "                                  AverageHoleLifetimeFeature(),\n",
    "                                  SumHoleLifetimeFeature(),\n",
    "                                  PersistenceEntropyFeature(),\n",
    "                                  SimultaneousAliveHolesFeatue(),\n",
    "                                  AveragePersistenceLandscapeFeature(),\n",
    "                                  BettiNumbersSumFeature(),\n",
    "                                  RadiusAtMaxBNFeature()])\n",
    "\n",
    "X_train_transformed = feature_extractor.fit_transform(X_train)\n",
    "X_test_transformed = feature_extractor.fit_transform(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Support Vector Machine:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SVC\n",
      "{'C': 1, 'kernel': 'linear'}\n",
      "Train accuracy:  1.0\n",
      "Test accuracy:  0.98\n"
     ]
    }
   ],
   "source": [
    "parameters = {\"C\": [10**i for i in range(-2, 5)],\n",
    "              \"kernel\": [\"linear\", \"rbf\", \"sigmoid\", \"poly\"]}\n",
    "acc_train, acc_test, model, model_params = evaluate_model(SVC(random_state=42), parameters, X_train_transformed,\n",
    "                                                          y_train, X_test_transformed, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "XGBoost:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "XGBClassifier\n",
      "{'max_depth': 2, 'n_estimators': 20}\n",
      "Train accuracy:  1.0\n",
      "Test accuracy:  0.99\n"
     ]
    }
   ],
   "source": [
    "parameters = {\"max_depth\": [2, 10, 15, 20, 25, 30, 35, 40, 45, 50, 70, 100, 120, 150],\n",
    "              \"n_estimators\": [20, 50, 100, 150, 200, 250]}\n",
    "acc_train, acc_test, model, model_params = evaluate_model(XGBClassifier(n_jobs=-1, random_state=42), \n",
    "                                                          parameters, X_train_transformed,\n",
    "                                                          y_train, X_test_transformed, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And again let's check the feature importance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ubuntu/anaconda3/lib/python3.7/site-packages/sklearn/linear_model/_logistic.py:940: ConvergenceWarning:\n",
      "\n",
      "lbfgs failed to converge (status=1):\n",
      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
      "\n",
      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
      "Please also refer to the documentation for alternative solver options:\n",
      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LogisticRegression\n",
      "{'C': 1}\n",
      "Train accuracy:  0.99\n",
      "Test accuracy:  0.98\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "parameters = {\"C\": [10 ** i for i in range(-3, 5)]}\n",
    "acc_train, acc_test, model, model_params = evaluate_model(LogisticRegression(max_iter=1000), \n",
    "                                                          parameters, X_train_transformed,\n",
    "                                                          y_train, X_test_transformed, y_test)\n",
    "plot_feature_importances(abs(model.coef_[0]), feature_names, \"LogisticRegression\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "XGBClassifier\n",
      "{'max_depth': 2, 'n_estimators': 20}\n",
      "Train accuracy:  1.0\n",
      "Test accuracy:  0.99\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "parameters = {\"max_depth\": [2, 10, 15, 20, 25, 30, 35, 40, 45, 50, 70, 100, 120, 150],\n",
    "              \"n_estimators\": [20, 50, 100, 150, 200, 250]}\n",
    "acc_train, acc_test, model, model_params = evaluate_model(XGBClassifier(n_jobs=-1, random_state=42), \n",
    "                                                          parameters, X_train_transformed,\n",
    "                                                          y_train, X_test_transformed, y_test)\n",
    "plot_feature_importances(model.feature_importances_, feature_names, \"XGBoost\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3. Dataset Where TDA Fails"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's study dataset where topological features can potentially fail. Consider the [ECGFiveDays](http://www.timeseriesclassification.com/description.php?Dataset=ECGFiveDays) dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset:  ECGFiveDays\n",
      "X_train shape:  (23, 136)\n",
      "y_train shape:  (23,)\n",
      "X_test shape:   (861, 136)\n",
      "y_test shape:   (861,)\n",
      "num. of class:  2\n"
     ]
    }
   ],
   "source": [
    "directory_list = get_files_directory_list()\n",
    "directory_list = sorted(directory_list)\n",
    "\n",
    "random_index =  30\n",
    "random_path = directory_list[random_index]\n",
    "\n",
    "X_train, X_test, y_train, y_test = get_data_from_directory(random_path)\n",
    "X_train = X_train.squeeze()\n",
    "y_train = y_train.squeeze()\n",
    "X_test = X_test.squeeze()\n",
    "y_test = y_test.squeeze()\n",
    "num_classes = np.unique(y_train).shape[0]\n",
    "\n",
    "print('Dataset: ', random_path)\n",
    "print('X_train shape: ', X_train.shape)\n",
    "print('y_train shape: ', y_train.shape)\n",
    "print('X_test shape:  ', X_test.shape)\n",
    "print('y_test shape:  ', y_test.shape)\n",
    "print('num. of class: ', num_classes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a look at embeddings:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_embedding(X_train[1], 3, int(y_train[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_embedding(X_train[10], 3, int(y_train[10]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_embedding(X_train[2], 3, int(y_train[2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_embedding(X_train[5], 3, int(y_train[5]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can notice that for this dataset we produced embeddings that are less distinguishable than in previous cases. The main difference here is the \"scale\" of this loop, and for topology it is much harder to handle difference in scale rather than distinguishable difference in core form. Thus, results can be poor for this dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_extractor = TopologicalFeaturesExtractor(\n",
    "    persistence_diagram_extractor=PersistenceDiagramsExtractor(tokens_embedding_dim=2, \n",
    "                                                               tokens_embedding_delay=3,\n",
    "                                                               homology_dimensions=(0, 1),\n",
    "                                                               parallel=True),\n",
    "    persistence_diagram_features=[HolesNumberFeature(),\n",
    "                                  MaxHoleLifeTimeFeature(),\n",
    "                                  RelevantHolesNumber(),\n",
    "                                  AverageHoleLifetimeFeature(),\n",
    "                                  SumHoleLifetimeFeature(),\n",
    "                                  PersistenceEntropyFeature(),\n",
    "                                  SimultaneousAliveHolesFeatue(),\n",
    "                                  AveragePersistenceLandscapeFeature(),\n",
    "                                  BettiNumbersSumFeature(),\n",
    "                                  RadiusAtMaxBNFeature()])\n",
    "\n",
    "X_train_transformed = feature_extractor.fit_transform(X_train)\n",
    "X_test_transformed = feature_extractor.fit_transform(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Support Vector Machine:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SVC\n",
      "{'C': 1000, 'kernel': 'poly'}\n",
      "Train accuracy:  0.7391304347826086\n",
      "Test accuracy:  0.6596980255516841\n"
     ]
    }
   ],
   "source": [
    "parameters = {\"C\": [10**i for i in range(-2, 5)],\n",
    "              \"kernel\": [\"linear\", \"rbf\", \"sigmoid\", \"poly\"]}\n",
    "acc_train, acc_test, model, model_params = evaluate_model(SVC(random_state=42), parameters, X_train_transformed,\n",
    "                                                          y_train, X_test_transformed, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "XGBoost:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "XGBClassifier\n",
      "{'max_depth': 2, 'n_estimators': 50}\n",
      "Train accuracy:  1.0\n",
      "Test accuracy:  0.6771196283391405\n"
     ]
    }
   ],
   "source": [
    "parameters = {\"max_depth\": [2, 10, 15, 20, 25, 30, 35, 40, 45, 50, 70, 100, 120, 150],\n",
    "              \"n_estimators\": [20, 50, 100, 150, 200, 250]}\n",
    "acc_train, acc_test, model, model_params = evaluate_model(XGBClassifier(n_jobs=-1, random_state=42), \n",
    "                                                          parameters, X_train_transformed,\n",
    "                                                          y_train, X_test_transformed, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, results are not so satisfiable. But still they potentially can be improved with tuning Takens embeddings parameters and more complicated classifiers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Conclusions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this work we studied the potential of Topological Data Analysis and topological features for time series classification problem. This notebook shows the part of the whole pipeline and analysis for different datasets, for the rest of the work please refer the report.\n",
    "\n",
    "To sum up, we can figure out following highlits:\n",
    "\n",
    "* Persistence Homology and Persistence Diagrams are powerful tools for describing data from topology point of view\n",
    "\n",
    "* Features that are extracted from PD shows the topological and geometrical behaviour of the data\n",
    "\n",
    "* Features extracted from constructions above the PD like Betti Curves, Persistence Landscape and Persistence Entropy showed good performance\n",
    "\n",
    "* Techniques like Dimensionality Reduction still can be applied for topological features and can improve the performance\n",
    "\n",
    "* Topological features seem to work well for data that has distinguishable difference in geometry and topology for different classes. If the difference is not very distinguishable, topology features can fail in this case.\n",
    "\n",
    "* Computing Persistence Diagram can take a lot of time, so it can be hard to tune parameters to achieve good results for those datasets\n",
    "\n",
    "In future work other properties and applications of TDA and topological features can be studied to improve the performance for different UCR datasets along with more accurate parameters tuning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. F. Takens, *Detecting strange attractors in turbulence*, Dynamical systems and turbulence, Warwick, pp. 366–381, Springer, 1980\n",
    "\n",
    "2. C. M. M. Pereira and R. F. de Mello, *Persistent homology for time series and spatial data clustering*, Expert Syst. Appl. 42, 6026–6038, 2015\n",
    "\n",
    "3. S. Agami, *Vietoris-Rips Persistent Homology*, arXiv:1905.06071, 2019\n",
    "\n",
    "4. Y. Umeda, *Time series classification via topological data analysis*, Transactions of the Japanese Society for Artificial Intelligence, 32(3):D–G72_1, 2017"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}