30_clustering.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# ICS 434: DATA SCIENCE FUNDAMENTALS\n",
    "\n",
    "## Clustering\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### What is Clustering\n",
    "\n",
    "* Clustering analysis, or clustering, is a computational approach to uncover structure in a dataset.\n",
    "\n",
    "    * Finding groups of points within a dataset that are grouped, or lumped, together.\n",
    "\n",
    "* It is a machine learning task.\n",
    "\n",
    "  * It is said to be unsupervised since the analyst does not describe or provide examples of things that should belong together in a cluster.\n",
    "  \n",
    "    * Supervised machine learning provides labeled data a response $y$ (e.g., instances of spam email vs. ham or legit email) and trains a model to recognize if an email is either spam or ham."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### What is a Cluster?\n",
    "\n",
    "* Descriptions such as “groups of points that are similar” or “close to each other”\n",
    "\n",
    "* The notion of a “cluster” is not well defined \n",
    "  * Clusters may be at times subjective\n",
    "    * The concept of boundary around  a set of similar points is subjective\n",
    "    \n",
    "* Once we see a cluster we \"kind of\" know what it is\n",
    "  \n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/f6v3hg574r9nmfr2xep1f/cluster_def.png?rlkey=g8ymnikayfepixxdh8gz5aevf&dl=1\" width=\"400\"/>\n",
    "<center>\n",
    "Data clustering: 50 years beyond K-means, Jain 2009\n",
    "</center> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Question\n",
    "\n",
    "* Is a cluster simply a group of points that are close?\n",
    "* How can you generate points that are distributed like in the figure below?\n",
    "\n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/0ytx0f70leabfoy3jvx01/random_points.png?rlkey=dlnnuj9b3y0c5snrl1kex0t1b&dl=1\" alt=\"drawing\" width=\"300\"/>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[71 64  9 63 65]\n",
      "[60 84 84 63 31]\n"
     ]
    }
   ],
   "source": [
    "x_axis = np.random.choice(np.arange(100), size=100)\n",
    "y_axis = np.random.choice(np.arange(100), size=100)\n",
    "\n",
    "print(x_axis[0:5])\n",
    "print(y_axis[0:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(4, 4))\n",
    "plt.scatter(x_axis, y_axis)\n",
    "\n",
    "# I used the code below to remove the x and y axis ticks ()\n",
    "_ = plt.xticks([], [])\n",
    "_ = plt.yticks([], [])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### What is a Cluster? -- Cont'd\n",
    "\n",
    "- We can define a cluster as a contiguous region of high data point density\n",
    "  - Points in the region are close to each other\n",
    "  - Areas contain more than just a few points that seem to occur randomly together\n",
    "- Regions are separated by areas of lower point density\n",
    "  - Points across regions are dissimilar\n",
    "  \n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/i3msfoclgxrtmtgk37r45/two_well_defined_clusters.png?rlkey=i862v028zp318txb4hgux9rug&dl=1\" alt=\"drawing\" width=\"300\"></center>\n",
    "    \n",
    "* How can we generate a dataset like the one above?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "mean_c1 = [8, 12]\n",
    "cov_c1 = [[1, 0], [0, 1]]\n",
    "c1 = np.random.multivariate_normal(mean_c1, cov_c1, 40)\n",
    "\n",
    "mean_c2 = [4, 4]\n",
    "cov_c2 = [[1, 0], [0, 1]]\n",
    "c2 = np.random.multivariate_normal(mean_c2, cov_c2, 29)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(4, 4))\n",
    "\n",
    "plt.scatter(c1[:, 0], c1[:, 1])\n",
    "plt.scatter(c2[:, 0], c2[:, 1])\n",
    "\n",
    "plt.xticks([], [])\n",
    "plt.yticks([], []);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### What is a Cluster? -- Cont'd\n",
    "\n",
    "- Contiguous regions of high data point density need not be highly dissimilar\n",
    "  - On average, points across regions are dissimilar\n",
    "  - Some points may be closer than others\n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/3kxvyghm6i5ua1fiyva5n/two_cluster_less_well_defined.png?rlkey=cdluozazgtjyhb9ulxj4hmcsz&dl=1\" alt=\"drawing\" width=\"300\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Data Shapes\n",
    "\n",
    "* Clusters may have complicated shapes\n",
    "  * While the clusters above are orderly but real clusters can be *very* messy\n",
    "  * Some clusters do not subscribe to the definitions above \n",
    "  * Such clusters may challenge simple solutions\n",
    "\n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/3gvzp550n3dt2afvrk5ld/data_moons.png?rlkey=c1w0kauppilsa8qs54n3k22zq&dl=1\" alt=\"drawing\" width=\"500\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Applications of Clustering\n",
    "\n",
    "* Clustering can be applied in a variety of contexts, from genetics and genomics to user input consolidation and investment\n",
    "* Definition of the clusters across domains is the same\n",
    "  * Regions of high-density points where points characterized by high similarity within regions and low similarity across regions  \n",
    "  * Naturally, the concept of similarity and distance between points is domain-specific\n",
    "    * Similarity between two Netflix users can be defined as the degree of agreement on ratings of movies they watched\n",
    "      * Or just the movies they watched\n",
    "    * The similarity between two stocks, say apple and qualcom\n",
    "        * Useful to the diversification of portfolios"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example: Data Reconciliation\n",
    "\n",
    "* Very useful for finding groups of different values that might be alternative representations of the same thing\n",
    "\n",
    "* This is called reconciliation and can be a massive problem for some industries\n",
    "\n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/phrvex55h060ayd380uey/Clustering_strings.png?rlkey=q64mqq1vi38nce2kzizuk33g0&dl=1\" alt=\"drawing\" width=\"500\"></center>\n",
    "\n",
    "* First Avenue, First Ave, 1st Ave, Furst Ave, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example: Stocks Clustering\n",
    "\n",
    "* Useful to derive a strategy for assets diversification\n",
    "\n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/wyio8h3u2wyzebgbu8d9f/stocks_clusters.png?rlkey=cm998ukemvuzzln9tutl07k6k&dl=1\" alt=\"drawing\" width=\"600\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example: Market Segmentation\n",
    "\n",
    "* Who are my potential customer groups?\n",
    "\n",
    "  * Who is buying my app and what features should be most appropriate?\n",
    "\n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/y8fzr44josf6req7jy3dn/market-segmentation.png?rlkey=lc8tjxddrwzf2rcvet7r453qk&dl=1\" alt=\"drawing\" width=\"500\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Distance and Similarity Measures \n",
    "  \n",
    "* Clustering  requires being able to compute a distance (or similarity) between the data points\n",
    "  * How similar are two stocks?\n",
    "\n",
    "* A distance is any function, `d`,  that takes two points (`x` and `y`) and returns a scalar value that is a measure for how different these points are\n",
    "  * The more dissimilar the points, the larger the distance \n",
    "  * It may be easier to make more sense to compute a similarity using a function `s`\n",
    "    * s(x, y) can be easily converted into d(x, y)\n",
    "    \n",
    "* While data points do not have to be embedded into a geometric space, it helps to think about their distance (or similarity) as if they were\n",
    "  * If we can transform data points to have properties of a vector space then we can develop more efficient algorithms that exploit these properties\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Distance to Similarity\n",
    "\n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/98dprxphhrq1aw8jdygq3/dist_sim.png?rlkey=v5u7uo7nue6iliulve8bhip65&dl=1\" alt=\"drawing\" width=\"700\"/>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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C\n",
      "text/plain": [
       "<Figure size 2200x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(22, 6))\n",
    "\n",
    "similairity = np.arange(0, 1.01, 0.01)\n",
    "\n",
    "method_1 = 1 - similairity\n",
    "\n",
    "plt.subplot(2,2,1)\n",
    "plt.plot(similairity, method_1)\n",
    "# plt.xlabel(\"Similarity\", fontsize=18)\n",
    "plt.ylabel(\"distance\", fontsize=18)\n",
    "_ = plt.xticks(fontsize=14)\n",
    "_ = plt.yticks(fontsize=14)\n",
    "\n",
    "\n",
    "method_2 =  -np.log(similairity + 0.0001)\n",
    "\n",
    "plt.subplot(2,2,2)\n",
    "plt.plot(similairity, method_2)\n",
    "plt.xlabel(\"Similarity\", fontsize=18)\n",
    "plt.ylabel(\"distance\", fontsize=18)\n",
    "_ = plt.xticks(fontsize=14)\n",
    "_ = plt.yticks(fontsize=14)\n",
    "\n",
    "\n",
    "method_3 =  np.sqrt(1 - similairity)\n",
    "\n",
    "plt.subplot(2,2,3)\n",
    "\n",
    "plt.plot(similairity, method_3)\n",
    "plt.xlabel(\"Similarity\", fontsize=18)\n",
    "plt.ylabel(\"distance\", fontsize=18)\n",
    "_ = plt.xticks(fontsize=14)\n",
    "_ = plt.yticks(fontsize=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Distance and Similarity Measures -- Cont'd\n",
    "\n",
    "* Sometimes, the concept of distance in geometric space is clear\n",
    "  * Ex. Use any measure that considers the locations of the points in such a space\n",
    "  * Most points are not just in 2-d but exist in higher-dimensional space\n",
    "  \n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/pbq6t0995wbv2xhehk20k/distnace_a_b.png?rlkey=kqqw02unt1zj0ad9s7n2703sl&dl=1\" alt=\"drawing\" style=\"width:250px\"/></center>\n",
    "    \n",
    "* Oher times, there is no obvious choice as to how to compute the distance between two points\n",
    "  * You are clustering music genres. How do you compute the distance between two songs?\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Clustering Music Genres\n",
    "\n",
    "* Example of an approach used to convert a song into features:\n",
    "  * Identify relevant dimensions\n",
    "    * For instance, beats per minute, the proportion of various instruments soloing, properties of the lyrics, or the presence/absence of certain words, etc.\n",
    "  * Consider the vectors as points in high-dimensional space and use a distance measure, e.g., Euclidean, to measure the distance between two songs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example: Distance Between Music Genres\n",
    "\n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/suwyu3psaotjw2mq9jrns/music_genres.png?rlkey=esp3kfrvemtz6cebi4dvmj90t&dl=1\" width=550/></center>\n",
    "\n",
    "<center>Genre Complexes in Popular Music. Silver et al., Plos One, 2016</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Common Distance Metrics \n",
    "\n",
    "* For simplicity, we'll classify the distances into two high-level categories\n",
    "\n",
    "* Euclidean and spherical geometry distances\n",
    "    * Use the location of the points in an Euclidean or spherical coordinate systems to estimate their distance\n",
    "\n",
    "* Other: Non-Euclidean and non-spherical geometry distances\n",
    "    * Use properties of points to estimate their distance\n",
    "\n",
    "* This is a coarse and somewhat subjective categorization, and other classifications are possible"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Euclidean and Spherical Distances\n",
    "\n",
    "* The Euclidean distance\n",
    "  * Most commonly used distance measure\n",
    "  * Distance between two points $P$ and $Q$ with coordinate $(p_1,p_2)$ and $(q_1,q_2)$ respectively is:\n",
    "\n",
    "$$\n",
    "d_{PQ} = \\sqrt{(p_1-q_1)^2 + (p_2-q_2)^2}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Euclidean and Spherical Distances -- Cont'd \n",
    "\n",
    "* The Manhattan (or taxicab or cityblock) distance\n",
    "* Geodesic distance\n",
    "  \n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/nrsyxbmoauydblxm3p51q/distances.png?rlkey=u5qbq3sgahmyw8sslzttcbhof&dl=1\" alt=\"drawing\" width=\"500\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Non-Euclidean Distance\n",
    "\n",
    "<br>\n",
    "Examples of non-euclidean distances are: \n",
    "\n",
    "* Edit distance or number of inserts and deletes to change one string into another\n",
    "  * Ex. what is the distance between `x = AGACGTAG` and  `y = GTTCAGA`\n",
    "\n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/few5r3nmoq2g1jzej0gly/edit_distance.png?rlkey=viso1y3hmxifz4tptw9gpl87x&dl=1\" alt=\"drawing\" width=\"600\"/></center>\n",
    "\n",
    "    Remove A, convert A to T, ... \n",
    "    The distance between `x` and `y` is 5\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Non-Euclidean Distance: Jaccard Distance\n",
    "\n",
    "* Jaccard distance is used with sets\n",
    "* It computes the number of items shared over all the items in the sets (Jaccard index)\n",
    "    \n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/licq7cze2gufusath1iw9/jaccard.png?rlkey=ia1sgqkmwm8j2465ztj52xte4&dl=1\" alt=\"drawing\" width=\"700\"/>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Sa5FmI', 'tiNdPp', 'Z4m9GU', 'XgHp7g', 'xs5rCQ', '7T6VFZ',\n",
       "       'Ns3uMt', 'OVYr8G', 'VeF3Ky', 'fxfGxX', 'Xl5GLH', 'Epnjrm',\n",
       "       'BzSBEV', 'Op4wXC', 'xJJEWG', 'zpQnUk', 'JQHCwB', 'HY4cTU',\n",
       "       '7EzU5A', 'wHOess'], dtype=object)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "symptoms = [\"Muscle Cramps\", \"Weight Gain\", \"Easy Bruising\", \"Metallic Taste\", \"Paranoia\",\n",
    "            \"Leg Pain\", \"Gas and Bloating\", \"Mouth Sores\", \"Nausea, Upset Stomach\", \n",
    "            \"Rectal Bleeding\", \"Shortness of Breath\", \"Muscle Cramps\", \"Urine Odor\",\n",
    "            \"Swollen Ankles and Feet\", \"Joint Cracking\", \"Eye Twitch\", \"Dry Skin\"]\n",
    "\n",
    "patient_ids = pd._testing.rands_array(6, 20)\n",
    "patient_ids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "patient_outcomes = np.random.choice([0, 1], size=(len(symptoms)))            \n",
    "patient_outcomes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0]),\n",
       " array([0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1]),\n",
       " array([1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0]),\n",
       " array([1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1]),\n",
       " array([1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1]),\n",
       " array([0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0]),\n",
       " array([0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0]),\n",
       " array([0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1]),\n",
       " array([1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1]),\n",
       " array([1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1]),\n",
       " array([0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1]),\n",
       " array([0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1]),\n",
       " array([1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1]),\n",
       " array([0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1]),\n",
       " array([0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0]),\n",
       " array([0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0]),\n",
       " array([0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0]),\n",
       " array([0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1]),\n",
       " array([0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1]),\n",
       " array([0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0])]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = [np.random.choice([0, 1], size=(len(symptoms))) for _ in range(len(patient_ids))]\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Muscle Cramps</th>\n",
       "      <th>Weight Gain</th>\n",
       "      <th>Easy Bruising</th>\n",
       "      <th>Metallic Taste</th>\n",
       "      <th>Paranoia</th>\n",
       "      <th>Leg Pain</th>\n",
       "      <th>Gas and Bloating</th>\n",
       "      <th>Mouth Sores</th>\n",
       "      <th>Nausea, Upset Stomach</th>\n",
       "      <th>Rectal Bleeding</th>\n",
       "      <th>Shortness of Breath</th>\n",
       "      <th>Muscle Cramps</th>\n",
       "      <th>Urine Odor</th>\n",
       "      <th>Swollen Ankles and Feet</th>\n",
       "      <th>Joint Cracking</th>\n",
       "      <th>Eye Twitch</th>\n",
       "      <th>Dry Skin</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Sa5FmI</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tiNdPp</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z4m9GU</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>XgHp7g</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>xs5rCQ</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Muscle Cramps  Weight Gain  Easy Bruising  Metallic Taste  Paranoia   \n",
       "Sa5FmI              1            0              1               1         1  \\\n",
       "tiNdPp              0            1              1               0         1   \n",
       "Z4m9GU              1            1              0               0         1   \n",
       "XgHp7g              1            1              1               0         1   \n",
       "xs5rCQ              1            1              1               0         1   \n",
       "\n",
       "        Leg Pain  Gas and Bloating  Mouth Sores  Nausea, Upset Stomach   \n",
       "Sa5FmI         0                 1            1                      1  \\\n",
       "tiNdPp         0                 0            1                      0   \n",
       "Z4m9GU         0                 0            1                      1   \n",
       "XgHp7g         1                 0            0                      1   \n",
       "xs5rCQ         1                 0            0                      1   \n",
       "\n",
       "        Rectal Bleeding  Shortness of Breath  Muscle Cramps  Urine Odor   \n",
       "Sa5FmI                0                    0              0           1  \\\n",
       "tiNdPp                0                    0              1           1   \n",
       "Z4m9GU                1                    0              0           1   \n",
       "XgHp7g                1                    0              0           0   \n",
       "xs5rCQ                1                    0              0           0   \n",
       "\n",
       "        Swollen Ankles and Feet  Joint Cracking  Eye Twitch  Dry Skin  \n",
       "Sa5FmI                        1               0           0         0  \n",
       "tiNdPp                        0               0           0         1  \n",
       "Z4m9GU                        1               1           1         0  \n",
       "XgHp7g                        0               0           1         1  \n",
       "xs5rCQ                        1               0           0         1  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "patients_data = pd.DataFrame(columns=symptoms, data=data, index=patient_ids)\n",
    "patients_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 17)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "patients_data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True, False,  True,  True])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vec_1 = np.array([1, 0, 1, 1, 1])\n",
    "vec_2 = np.array([1, 0, 0, 1, 1])\n",
    "\n",
    "(vec_1 == vec_2) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([True,  True,  False])\n",
    "y = np.array([True,  False, True])\n",
    "\n",
    "x & y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x == y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(x==y) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False,  True,  True,  True])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(vec_1 == 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vec_1 = np.array([1, 0, 1, 1, 1])\n",
    "vec_2 = np.array([1, 0, 0, 1, 1])\n",
    "\n",
    "sum((vec_1 == vec_2) & (vec_1 == 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vec_1 = np.array([1, 0, 1, 1, 1])\n",
    "vec_2 = np.array([1, 0, 0, 1, 1])\n",
    "\n",
    "sum((vec_1 == 1) | (vec_2 == 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def compute_Jaccard_distance(vec_1, vec_2):\n",
    "    \n",
    "    # All the symptoms shared by both\n",
    "    intersection = sum((vec_1 == vec_2) & (vec_1 == 1))\n",
    "    \n",
    "    # All the symptoms that either one has\n",
    "    union = sum((vec_1 == 1) | (vec_2 == 1))\n",
    "    \n",
    "    return 1 - intersection / union"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.25\n"
     ]
    }
   ],
   "source": [
    "vec_1 = np.array([1, 0, 1, 1, 1])\n",
    "vec_2 = np.array([1, 0, 0, 1, 1])\n",
    "\n",
    "print(compute_Jaccard_distance(vec_1, vec_2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Distance Matrix\n",
    "\n",
    "* It is common to store the pairwise distances between data points in a distance matrix $M$.\n",
    "\n",
    "* The matrix has dimensions $n \\times n$, where $n$ is the number of data points.\n",
    "\n",
    "* For any two points $p_i$ and $p_j$, it is typically assumed that:\n",
    "\n",
    "$$ \n",
    "M[i, j] = d(p_i, p_j) \\\\\n",
    "M[j, i] = d(p_j, p_i)\n",
    "$$\n",
    "\n",
    "where $d(p_i, p_j)$ is the distance between points $p_i$ and $p_j$, and the matrix $M$ is symmetric.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0.],\n",
       "       [0., 0., 0.],\n",
       "       [0., 0., 0.]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(100)\n",
    "dist_patients = np.zeros([3, 3])\n",
    "dist_patients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 20)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute all pair-wise Jaccard coefficients\n",
    "dist_patients = np.zeros([len(patient_ids), len(patient_ids)])\n",
    "\n",
    "for i in range(patients_data.shape[0]):\n",
    "    for j in range(i, patients_data.shape[0]):\n",
    "        vec_1 = patients_data.iloc[i]\n",
    "        vec_2 = patients_data.iloc[j]\n",
    "\n",
    "        # compute distance and round to two decimal points\n",
    "        dist_patients[i, j] = round(compute_Jaccard_distance(vec_1, vec_2), 2)\n",
    "        dist_patients[j, i] = dist_patients[i, j]\n",
    "        \n",
    "dist_patients.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.  , 0.64, 0.5 , 0.69, 0.6 , 0.93, 0.92, 0.69, 0.79, 0.64, 0.67,\n",
       "        0.71, 0.71, 0.85, 0.73, 0.77, 0.77, 0.83, 0.69, 0.54],\n",
       "       [0.64, 0.  , 0.64, 0.5 , 0.75, 0.69, 0.73, 0.71, 0.5 , 0.46, 0.79,\n",
       "        0.73, 0.64, 0.77, 0.93, 0.58, 0.58, 0.64, 0.8 , 0.57],\n",
       "       [0.5 , 0.64, 0.  , 0.69, 0.62, 0.75, 0.79, 0.6 , 0.6 , 0.36, 0.46,\n",
       "        0.53, 0.53, 0.64, 0.62, 0.82, 0.75, 0.8 , 0.5 , 0.47],\n",
       "       [0.69, 0.5 , 0.69, 0.  , 0.69, 0.64, 0.67, 0.33, 0.33, 0.62, 0.73,\n",
       "        0.5 , 0.5 , 0.62, 0.79, 0.42, 0.27, 0.69, 0.67, 0.53],\n",
       "       [0.6 , 0.75, 0.62, 0.69, 0.  , 0.77, 0.7 , 0.79, 0.69, 0.54, 0.55,\n",
       "        0.71, 0.71, 0.85, 0.44, 0.77, 0.77, 0.92, 0.45, 0.64],\n",
       "       [0.93, 0.69, 0.75, 0.64, 0.77, 0.  , 0.75, 0.73, 0.64, 0.6 , 0.71,\n",
       "        0.46, 0.67, 0.69, 0.67, 0.5 , 0.5 , 0.67, 0.54, 0.6 ],\n",
       "       [0.92, 0.73, 0.79, 0.67, 0.7 , 0.75, 0.  , 0.67, 0.55, 0.62, 0.75,\n",
       "        0.69, 0.45, 0.73, 0.82, 0.75, 0.75, 0.7 , 0.67, 0.88],\n",
       "       [0.69, 0.71, 0.6 , 0.33, 0.79, 0.73, 0.67, 0.  , 0.46, 0.62, 0.64,\n",
       "        0.5 , 0.5 , 0.71, 0.69, 0.64, 0.54, 0.69, 0.57, 0.53],\n",
       "       [0.79, 0.5 , 0.6 , 0.33, 0.69, 0.64, 0.55, 0.46, 0.  , 0.53, 0.54,\n",
       "        0.69, 0.38, 0.5 , 0.79, 0.54, 0.54, 0.69, 0.67, 0.53],\n",
       "       [0.64, 0.46, 0.36, 0.62, 0.54, 0.6 , 0.62, 0.62, 0.53, 0.  , 0.5 ,\n",
       "        0.56, 0.47, 0.67, 0.73, 0.6 , 0.69, 0.64, 0.53, 0.4 ],\n",
       "       [0.67, 0.79, 0.46, 0.73, 0.55, 0.71, 0.75, 0.64, 0.54, 0.5 , 0.  ,\n",
       "        0.57, 0.57, 0.69, 0.55, 0.71, 0.71, 0.86, 0.54, 0.5 ],\n",
       "       [0.71, 0.73, 0.53, 0.5 , 0.71, 0.46, 0.69, 0.5 , 0.69, 0.56, 0.57,\n",
       "        0.  , 0.53, 0.73, 0.62, 0.57, 0.46, 0.71, 0.38, 0.56],\n",
       "       [0.71, 0.64, 0.53, 0.5 , 0.71, 0.67, 0.45, 0.5 , 0.38, 0.47, 0.57,\n",
       "        0.53, 0.  , 0.54, 0.71, 0.46, 0.57, 0.71, 0.6 , 0.56],\n",
       "       [0.85, 0.77, 0.64, 0.62, 0.85, 0.69, 0.73, 0.71, 0.5 , 0.67, 0.69,\n",
       "        0.73, 0.54, 0.  , 0.85, 0.58, 0.69, 0.5 , 0.8 , 0.57],\n",
       "       [0.73, 0.93, 0.62, 0.79, 0.44, 0.67, 0.82, 0.69, 0.79, 0.73, 0.55,\n",
       "        0.62, 0.71, 0.85, 0.  , 0.86, 0.77, 1.  , 0.45, 0.64],\n",
       "       [0.77, 0.58, 0.82, 0.42, 0.77, 0.5 , 0.75, 0.64, 0.54, 0.6 , 0.71,\n",
       "        0.57, 0.46, 0.58, 0.86, 0.  , 0.36, 0.55, 0.73, 0.5 ],\n",
       "       [0.77, 0.58, 0.75, 0.27, 0.77, 0.5 , 0.75, 0.54, 0.54, 0.69, 0.71,\n",
       "        0.46, 0.57, 0.69, 0.77, 0.36, 0.  , 0.77, 0.73, 0.69],\n",
       "       [0.83, 0.64, 0.8 , 0.69, 0.92, 0.67, 0.7 , 0.69, 0.69, 0.64, 0.86,\n",
       "        0.71, 0.71, 0.5 , 1.  , 0.55, 0.77, 0.  , 0.79, 0.64],\n",
       "       [0.69, 0.8 , 0.5 , 0.67, 0.45, 0.54, 0.67, 0.57, 0.67, 0.53, 0.54,\n",
       "        0.38, 0.6 , 0.8 , 0.45, 0.73, 0.73, 0.79, 0.  , 0.53],\n",
       "       [0.54, 0.57, 0.47, 0.53, 0.64, 0.6 , 0.88, 0.53, 0.53, 0.4 , 0.5 ,\n",
       "        0.56, 0.56, 0.57, 0.64, 0.5 , 0.69, 0.64, 0.53, 0.  ]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist_patients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.  , 0.64, 0.5 , 0.69, 0.6 ],\n",
       "       [0.64, 0.  , 0.64, 0.5 , 0.75],\n",
       "       [0.5 , 0.64, 0.  , 0.69, 0.62],\n",
       "       [0.69, 0.5 , 0.69, 0.  , 0.69],\n",
       "       [0.6 , 0.75, 0.62, 0.69, 0.  ]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist_patients[:5, :5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0 297 (14, 17)\n"
     ]
    },
    {
     "data": {
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Muscle Cramps</th>\n",
       "      <th>Weight Gain</th>\n",
       "      <th>Easy Bruising</th>\n",
       "      <th>Metallic Taste</th>\n",
       "      <th>Paranoia</th>\n",
       "      <th>Leg Pain</th>\n",
       "      <th>Gas and Bloating</th>\n",
       "      <th>Mouth Sores</th>\n",
       "      <th>Nausea, Upset Stomach</th>\n",
       "      <th>Rectal Bleeding</th>\n",
       "      <th>Shortness of Breath</th>\n",
       "      <th>Muscle Cramps</th>\n",
       "      <th>Urine Odor</th>\n",
       "      <th>Swollen Ankles and Feet</th>\n",
       "      <th>Joint Cracking</th>\n",
       "      <th>Eye Twitch</th>\n",
       "      <th>Dry Skin</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>X3q7w1</th>\n",
       "      <td>1</td>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>RLLgkV</th>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Muscle Cramps  Weight Gain  Easy Bruising  Metallic Taste  Paranoia  \\\n",
       "X3q7w1              1            1              0               0         1   \n",
       "RLLgkV              0            0              1               1         0   \n",
       "\n",
       "        Leg Pain  Gas and Bloating  Mouth Sores  Nausea, Upset Stomach  \\\n",
       "X3q7w1         1                 0            0                      1   \n",
       "RLLgkV         0                 1            0                      0   \n",
       "\n",
       "        Rectal Bleeding  Shortness of Breath  Muscle Cramps  Urine Odor  \\\n",
       "X3q7w1                0                    0              0           1   \n",
       "RLLgkV                1                    1              1           0   \n",
       "\n",
       "        Swollen Ankles and Feet  Joint Cracking  Eye Twitch  Dry Skin  \n",
       "X3q7w1                        0               1           0         0  \n",
       "RLLgkV                        0               0           0         1  "
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from numpy import unravel_index\n",
    "\n",
    "max_idx = unravel_index(np.argmax(dist_patients), dist_patients.shape)\n",
    "\n",
    "print(np.nanmax(dist_patients), np.nanargmax(dist_patients), max_idx)\n",
    "\n",
    "patients_data.iloc[[max_idx[0], max_idx[1]]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 2)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# What is the index in a 3x3 matrix of element at position 5 in an unraveled matrix?\n",
    "\n",
    "array_shape = (3, 3)\n",
    "\n",
    "flat_index = 5\n",
    "\n",
    "# Convert the flat index to a 2D index\n",
    "coords = np.unravel_index(flat_index, array_shape)\n",
    "coords"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.27 76 (3, 16)\n"
     ]
    },
    {
     "data": {
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       "<div>\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Muscle Cramps</th>\n",
       "      <th>Weight Gain</th>\n",
       "      <th>Easy Bruising</th>\n",
       "      <th>Metallic Taste</th>\n",
       "      <th>Paranoia</th>\n",
       "      <th>Leg Pain</th>\n",
       "      <th>Gas and Bloating</th>\n",
       "      <th>Mouth Sores</th>\n",
       "      <th>Nausea, Upset Stomach</th>\n",
       "      <th>Rectal Bleeding</th>\n",
       "      <th>Shortness of Breath</th>\n",
       "      <th>Muscle Cramps</th>\n",
       "      <th>Urine Odor</th>\n",
       "      <th>Swollen Ankles and Feet</th>\n",
       "      <th>Joint Cracking</th>\n",
       "      <th>Eye Twitch</th>\n",
       "      <th>Dry Skin</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>POsi8h</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>So27VP</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Muscle Cramps  Weight Gain  Easy Bruising  Metallic Taste  Paranoia  \\\n",
       "POsi8h              0            0              1               0         1   \n",
       "So27VP              0            1              1               0         1   \n",
       "\n",
       "        Leg Pain  Gas and Bloating  Mouth Sores  Nausea, Upset Stomach  \\\n",
       "POsi8h         0                 0            1                      0   \n",
       "So27VP         0                 0            1                      0   \n",
       "\n",
       "        Rectal Bleeding  Shortness of Breath  Muscle Cramps  Urine Odor  \\\n",
       "POsi8h                1                    1              1           1   \n",
       "So27VP                1                    1              0           1   \n",
       "\n",
       "        Swollen Ankles and Feet  Joint Cracking  Eye Twitch  Dry Skin  \n",
       "POsi8h                        1               1           1         0  \n",
       "So27VP                        1               0           1         0  "
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "dist_patients_temp = dist_patients.copy()\n",
    "\n",
    "for i in range(patients_data.shape[0]):\n",
    "    dist_patients_temp[i, i] = 1000\n",
    "\n",
    "min_idx = np.unravel_index(np.argmin(dist_patients_temp), dist_patients_temp.shape)\n",
    "\n",
    "print(np.nanmin(dist_patients_temp), np.nanargmin(dist_patients_temp), min_idx)\n",
    "\n",
    "patients_data.iloc[[min_idx[0], min_idx[1]]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "###  Devising Your Own Distance\n",
    "\n",
    "* There are certain properties that a distance (or similarity) function should have\n",
    "  * A distance in a mathematical sense must have at least the following properties (properties of a metric)\n",
    "    * Non-negativity rule $d(x, y) \\ge 0$\n",
    "    * Symmetry rule $d(x, y) = d(y, x)$\n",
    "    * Triangle Inequality rule $d(x, y) + d(y, z) \\ge d(x, z)$ \n",
    "\n",
    "* In practice, it may be hard to identify a distance that guarantees all these properties\n",
    "  * Some metrics are not symmetric\n",
    "     * E.g., length of the shortest clockwise path between $p$ and $q$ \n",
    "       * Navigation on a one-way road: If \n",
    "$p$ and  $q$ are locations on a circular track or road that allows only clockwise movement, then the distance from \n",
    "$p$ to $q$ along this path might be shorter than the distance from  $q$ to $p$.\n",
    "  * For technical reasons, the symmetry property is usually highly desirable\n",
    "    * You can always construct a symmetric distance function from an asymmetric one\n",
    "$$\n",
    "    dS(x,y)= \\frac{d(x,y)+d(y,x)}{2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Smooth Functions are Better than Non-Smooth Ones\n",
    "\n",
    "* Naive distance\n",
    "\n",
    "$$\n",
    "d(x,y) = \\sum{d_i(x_i, y_i)}\n",
    "$$\n",
    "\n",
    "$\\hspace{0.6in}$ where\n",
    "\n",
    "$$\n",
    "d_i(x_i, y_i)= \\left\\{\n",
    "    \\begin{array}{ll}\n",
    "        1 & \\mbox{if } x_i=y_i \\\\\n",
    "        0 & \\mbox{otherwise}\n",
    "    \\end{array}\n",
    "\\right.\n",
    "$$\n",
    "\n",
    "* This function is not smooth\n",
    "  * Difference between `[1, 2]` and `[2, 3]` is the same as the difference between `[1, 2]` and `[100, 200]`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Clustering Approaches\n",
    "\n",
    "In this section we will cover two approaches to clustering a set of points into  clusters\n",
    "\n",
    "* Hierarchical \n",
    "  * Each point is a cluster\n",
    "  * Repeatedly combine the two “closest” clusters into one\n",
    "  * Stop when only one cluster remains\n",
    "  * This is also known as \"agglomerative hierarchical clustering\"\n",
    "  \n",
    "* Point-to-cluster Assignment\n",
    "  * Maintain a set of `k` clusters (ex. `k = 3`)\n",
    "  * Place points into “closest” cluster\n",
    "    * Iteratively repeat the process until the solution is stable\n",
    "    \n",
    "* There are more advanced/complex approaches\n",
    "  * Difficult to combine into categories because of the diversity of approaches and overlaps\n",
    "  * Probabilistic methods increasingly popular\n",
    "  * Will briefly cover other methods to visualize cluster\n",
    "     * PCA, T-SNE and UMAP\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Clustering Approaches\n",
    "\n",
    "In this section we will cover two approaches to clustering a set of points into  clusters\n",
    "\n",
    "* Hierarchical \n",
    "  * Each point is a cluster\n",
    "  * Repeatedly combine the two “closest” clusters into one\n",
    "  * Stop when only one cluster remains\n",
    "  * This is also known as \"agglomerative hierarchical clustering\"\n",
    "  \n",
    "* Point-to-cluster Assignment\n",
    "  * Maintain a set of `k` clusters (ex. `k = 3`)\n",
    "  * Place points into “closest” cluster\n",
    "    * Iteratively repeat the process until the solution is stable\n",
    "    \n",
    "* There are more advanced/complex approaches\n",
    "  * Difficult to combine into categories because of the diversity of approaches and overlaps\n",
    "  * Probabilistic methods increasingly popular\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Hierarchical Clustering\n",
    "\n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/ozfaisljkehldbm9fxirr/hierarchical_clustering.png?rlkey=c5owo2jv7r2mn30w4xi4u06ul&dl=1\" alt=\"drawing\" width=\"650\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Hierarchical Clustering Dendogram Representation\n",
    "\n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/tyw58dsbxciez0sbf9wya/hierarchical_clustering_dendo.png?rlkey=iilfgn0hrp92bkwzbdyc9otkm&dl=1\" alt=\"drawing\" width=\"750\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Hierarchical Clustering -- Cont'd\n",
    "\n",
    "* Repeatedly combine the two “closest” clusters into one\n",
    "\n",
    "* How do you know which pair of clusters is the closest?\n",
    "  * We can only compute the distances between two points\n",
    "\n",
    "* One possible solution: \n",
    "  * Represent the location of each cluster using a single measure:\n",
    "    * E.g., centroid, or the average of all points in a cluster\n",
    "\n",
    "  * Take all centroids and find the closest pair      "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Question\n",
    "\n",
    "* Does the centroid approach work for all types of data?\n",
    "\n",
    "    * How do you compute the centroid for the DNA sequences from before?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Hierarchical Clustering with Non-Euclidean Distances\n",
    "\n",
    "* There is no “average” of two points\n",
    "\n",
    "* We can compute the distance between two clusters using other approaches. For example:\n",
    "    \n",
    "  * Minimum of the distances between any two points, one from each cluster\n",
    "    * Minimum Linkage (or Single Linkage)\n",
    "  * Maximum of the distances between any two points, one from each cluster\n",
    "    * Maximum Linkage (or Complete Linkage)\n",
    "  * Average of the distances between any two points, one from each cluster\n",
    "    * Average Linkage\n",
    "\n",
    "* Pick a notion of “cohesion” of clusters, e.g., the maximum distance from the clusteroid \n",
    "\n",
    "  * A clusteroid is simply the center of the cluster based on, for example, the average of intra-cluster distances\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Question\n",
    "\n",
    "* Given $n$ data points, what is the complexity of clustering in the worst-case scenario?\n",
    "* Recall we need to:\n",
    "\n",
    "  1- Build the distance matrix\n",
    "  \n",
    "  2- Merge $n$ points iteratively until we end up with a single cluster\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "heading_collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Hierarchical Clustering Results\n",
    "\n",
    "* Easy to implement and understand (plus)\n",
    "\n",
    "* Method is computationally intensive (minus)\n",
    "\n",
    "* Extracting clusters can be tricky! (minus)\n",
    "\n",
    "   * Data points are leaves \n",
    "   * Distance in the tree between the leaves is representative of the distance between the data points\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "heading_collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Hierarchical Clustering Results\n",
    "\n",
    "* Easy to implement and understand (plus)\n",
    "  * Provides an interpretable visualization of the algorithm and data\n",
    "\n",
    "* Useful summarization tool giving a holistic view (plus)\n",
    "\n",
    "* Method is computationally intensive (minus)\n",
    "\n",
    "* Extracting clusters can be tricky! (minus)\n",
    "\n",
    "   * Data points are leaves \n",
    "   * Distance in the tree between the leaves is representative of the distance between the data points\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Second Category: Assigning Points to Clusters\n",
    "\n",
    "* A popular clustering algorithm\n",
    "\n",
    "* Two steps:\n",
    "  * Define the number of clusters \n",
    "  * Initializing cluster representatives\n",
    "  * Assignment of points to each cluster\n",
    "  * Recalculating the centroids\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Second Category: Assigning Points to Clusters\n",
    "\n",
    "* A popular clustering algorithm\n",
    "\n",
    "* Steps:\n",
    "  * Define the number of clusters \n",
    "  * Initialize cluster representatives (centroids)\n",
    "  * Assign points to each cluster\n",
    "  * Recalculate the centroids\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### k-Means Clustering Steps\n",
    "\n",
    "* Assumes Euclidean space\n",
    "  * Cannot handle categorical data\n",
    "\n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/sdgfey9wkl2zwzlgf3hr8/kmeans_a.png?rlkey=sm8q7m7friituorf349sksycb&dl=1\" width=\"350\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "### k-Means Clustering: Initialization\n",
    "\n",
    "* Initialize clusters by $k$ points; one per cluster\n",
    "  * Those are the cluster representatives; the cluster centroids\n",
    "     * For instance, take $k$ points in space at random\n",
    "  \n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/fpoysasv2caspmox4glu1/kmeans_b.png?rlkey=d9uiefg0g88nwshg2g59wrcka&dl=1\" width=\"350\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### k-Means Clustering: Assign Points to Clusters\n",
    "\n",
    "* Place each point in the cluster identified by the closest centroid\n",
    "\n",
    "  * Here, we \"paint\" the examples with the same color as the cluster centroid to which it was assigned\n",
    "  \n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/li1cg4pmxsq7pv39kxib2/kmeans_c.png?rlkey=0jbj1ev6aoi16bmdh5m2bx8p3&dl=1\" width=\"350\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "8quv8Db0ivBx",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### k-Means Clustering: Recalculate the Centroids\n",
    "\n",
    "* After all points are assigned, recompute the centroids of the $k$ clusters\n",
    "\n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/r5lx77betbor2tw6umzil/kmeans_d.png?rlkey=kembglyyxpa40z2yg6y6tvtbg&dl=1\" width=\"350\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "poKo7tYIivB1",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### k-Means Clustering: Assign and Recalculate Centroids \n",
    "\n",
    "* Repeat these two steps until convergence\n",
    "\n",
    "  * The clustering is stable, and nothing changes\n",
    "      * I.e., assigning the points to the closest centroid and recomputing the centroids does not change the centroids or the assignments\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### k-Means Clustering Results\n",
    "\n",
    "* Algorithm is non-deterministic (minus)\n",
    "  * A different choice of starting values may result in a different assignment of points to clusters\n",
    "    * Customary to run the k-means algorithm several times and compare results or compute a consensus\n",
    "\n",
    "* Cannot be used with categorical data (non-Euclidean space) (minus)\n",
    "  * Difficult, or sometimes impossible, to construct centroids from categorical data\n",
    "  \n",
    "* Can use k-medoid, the smallest average distance to all other points in the cluster (plus)\n",
    "    * A medoid is the point in the cluster with the smallest distance to all the other points in the cluster\n",
    "        * Less affected by outliers\n",
    "        * More stable\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### k-Means Clustering Results -- Cont'd\n",
    "\n",
    "* Can take a long time to converge with some poor initializations  (minus)  \n",
    "  * Very rare, but a possibility, nevertheless \n",
    "\n",
    "* Computationally efficient $O(k \\cdot t \\cdot n)$ (plus)\n",
    "  * Linear in the number of points!\n",
    "  * Small number of iterations to converge (10–50 iterations are typical)\n",
    "\n",
    "* Works relatively well in real life"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### How Do We Evaluate the Results of Clustering\n",
    "\n",
    "* What distinguishes a good clustering solution from a bad one?\n",
    "\n",
    "* Recall that what we want is:\n",
    "  1. Points within the same cluster to be very similar; \n",
    "     * The average distance between points in the same cluster should be small\n",
    "     * This is called *cohesion* and it should be relatively small\n",
    "  2. Points across clusters to be highly dissimilar; \n",
    "      * Distance between points from distinct clusters should be large\n",
    "      * This is called *separation* and it should be relatively large\n",
    "  \n",
    "* A criteria to evaluate a clustering solution:\n",
    "$$\n",
    "    \\frac{separation}{cohesion}\n",
    "$$ \n",
    "$\\hspace{0.6in} -$ Large separation compared to low cohesion<br>\n",
    "$\\hspace{0.6in} -$ Large values are indicative of a good separation \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### The Silhouette Coefficient\n",
    "\n",
    "* A good \"score\" to estimate the ratio of separation to cohesion\n",
    "  * *Silhouette Score*: the mean silhouette coefficient over all data instances\n",
    "\n",
    "* For each cluster we denote:\n",
    "  * $a_i$ is the average distance that point $i$ has from all points in the same cluster (i.e., the mean intra-cluster distance)\n",
    "    * Represents the cohesion; we want it to be as small as possible   \n",
    "  * $b_i$ be the smallest distance between point $i$ and a point not in the same cluster as point $i$\n",
    "    * Represents separation; we want it to be as large as possible "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### The Silhouette Coefficient -- Cont'd\n",
    "\n",
    "* We measure the Silhouette Coefficient of a point $i$ as \n",
    "\n",
    "$$\n",
    "S_i = \\frac{b_i - a_i}{max(a_i, b_i)}\n",
    "$$\n",
    "\n",
    "* Silhouette coefficient ranges from −1 to 1\n",
    "  * Negative values indicate $a_i$ is larger than $b_i$\n",
    "    * Low cohesion or small separation or both\n",
    "    * This suggests poor clustering\n",
    "  * Positive values indicate $b_i$ is larger than $a_i$\n",
    "    * High cohesion or high separation or both\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean_c1 = [8, 12]\n",
    "cov_c1 = [[1, 0], [0, 1]]\n",
    "c1 = np.random.multivariate_normal(mean_c1, cov_c1, 40)\n",
    "\n",
    "mean_c2 = [4, 4]\n",
    "cov_c2 = [[1, 0], [0, 1]]\n",
    "c2 = np.random.multivariate_normal(mean_c2, cov_c2, 29)\n",
    "\n",
    "plt.figure(figsize=(4, 4))\n",
    "plt.scatter(c1[:, 0], c1[:, 1])\n",
    "plt.scatter(c2[:, 0], c2[:, 1])\n",
    "\n",
    "plt.xticks([], [])\n",
    "plt.yticks([], []);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.spatial import distance\n",
    "\n",
    "def compute_b(pt_cl1, c2):\n",
    "    # Closest points across cluster distant points\n",
    "    min_dist = np.inf\n",
    "    hit_pt_c2 = None\n",
    "    \n",
    "    for j, pt2 in enumerate(c2):\n",
    "        d = distance.euclidean(pt_cl1, pt2)\n",
    "        if d < min_dist:\n",
    "            min_dist = d\n",
    "            hit_pt_c2 = pt2\n",
    "            \n",
    "    return hit_pt_c2, min_dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pt_c2 = c2[10]\n",
    "\n",
    "plt.figure(figsize=(5, 5))\n",
    "plt.scatter(c1[:, 0], c1[:, 1], c=\"blue\", alpha=0.3)\n",
    "plt.scatter(c2[:, 0], c2[:, 1], c='black', alpha=0.3)\n",
    "\n",
    "for other_pt in c1:\n",
    "    plt.plot([pt_c2[0], other_pt[0]], [pt_c2[1], other_pt[1]], 'r-', alpha=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 6.64360095, 10.76756549]), 9.020962811698482)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compute_b(pt_c2, c1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tPfawXRFQMAIHCLof/1i67f3dOZctM/1RgBAicIAg27RJmjHDHM+eHb27yCgrBA4QVKmUdPbZ0uuvS0cfLd1+u+2KgJIQOEBQ3XyzmTs7erS0cqU0cqTtioCSEDhAEP3qV2aBhiTdd590+OF26wFcQOAAQfPaa2YryL4+6bzzzLAaEAEEDhAkfX3SueeayQJHHiktXmy7IsA1BA4QJHfeaaZBjxxp7tuMHm27IsA1BA4QFE8/LV1zjTlubJQ+/nGr5QBuI3CAIHj7benMM6XeXum006QLL7RdEeA6AgewzXGkCy4wzTkPOkh64IHCd+kCQoDAAWy77z6ppcX0R1u5Uho3znZFgCcIHMCm55+XLr3UHN96q/T3f2+3HsBDBA5gyzvvmK2i33tP+spXdgcPEFEEDmDL7NnSSy+Z/YYfeoj7Nog8Agew4ZFHzFdFhdnfZsIE2xUBniNwAL+9+KL0jW+Y4+uuM/sJA2WAwAH8tG2buW/z7rvS5z8vfetbtisCfEPgAH66/HLphRekiROl5cvNZvZAmSBwAL+0tEj33muOH31Uqqy0Ww/gMwIH8ENHh3T++eb4qqukL33Jbj2ABQQO4LUdO0yftO5u6XOfk2680XZFgBUEDuC1+fOlZ56R9t3XTIHeYw/bFQFWEDiAl/7rv6TbbzfHDz4oHXig3XoAiwgcwCudndKMGeZ4zhxp6lSr5QC2ETiAF1Ip6ayzpDfekD75SWnhQtsVAdYROIAXbrxR+tWvpH32MVsOjBxpuyLAOgIHcFtrq3TDDeb4vvukww6zWw8QEAQO4KbNm81QmuNIM2eaYwCSCBzAPX190rnnSl1d0lFHSXffbbsiIFAIHMAtd9wh/eQn5n7NqlXS6NG2KwIChcAB3PDUU7s7Py9aJH3sY3brAQKIwAFK9dZbpnVNb6/ZemDWLNsVAYFE4AClcBzpggukv/xFOvhgaelStooGsiBwgFLce6+UTJr+aCtXSmPH2q4ICCwCByjWc89Jl15qjm+7TTrmGKvlAEFH4ADFeOcdc79mxw7pq1+V5s61XREQeAQOUCjHkS6+WHr5ZSmRMF2guW8D5ETgAIV6+GFp+XKpokJqapLGj7ddERAKBA5QiP/7P2n2bHN8ww1STY3deoAQIXCAfG3bZu7bbN0qnXCCdPXVtisCQoXAAfJ12WXSH/4g7befGVKLx21XBIQKgQPkY/Vqs9VALGbC5kMfsl0REDoEDpDLn/9suglIZhjtC1+wWw8QUgQOMJwdO0yftJ4e6bjjdm+sBqBgBA4wnGuukf77v6UPfEBasUIaMcJ2RUBoEThANo8/Lt15pzl+8EHpwx+2Ww8QcgQOkMnGjWb3Tkn65jel2lq79QARQOAAg/X2StOnS2+8IX3qU6YxJ4CSETjAYDfcILW3S2PGmC0H9trLdkVAJBA4QH+//KV0003m+P77pUMPtVsPECEEDpC2ebN01lmmG/T550vTptmuCIgUAgeQpL4+6ZxzpFdflT7yEenuu21XBEQOgQNI0sKF0s9+Jo0aJa1aJe29t+2KgMghcIAnn5TmzzfHd98tffSjdusBIorAQXl76y3TuiaVMt/PP992RUBkETgoX44jzZwp/fWv0iGHmFlpbBUNeIbAQfm65x7pscekPfYw623GjrVdERBpBA7K0//8j3T55eZ44ULp05+2Ww9QBggclJ8tW6TTTzdbD3zta6ZXGgDPETgoL44jXXyxtG6dVFVlukBz3wbwBYGD8vLQQ9L3vy/F42Z/mw9+0HZFQNkgcFA+/vQnac4cc3zDDdI//IPdeoAyQ+CgPGzbJp1xhrR1q/SFL0hXX227IqDsEDgoD/PmSX/8o7T//tKjj0oV/NMH/Mb/dYi+lSulpUvN5IDly03oAPAdgYNoe+UVadYsc/ytb0knnmi3HqCMETiIrh07TH+0LVuk44+XrrvOdkVAWSNwEF1XXy39/vdm6nNTkzRihO2KgLJG4CCa/uM/pLvuMscPPmgWeQKwisBB9GzYIJ13njmeN8+0rwFgHYGDaOntlaZPl9580zTkvPVW2xUBeB+Bg2i5/nrpN7+Rxowx06H32st2RQDeR+AgOp54Qrr5ZnO8dKnZVA1AYBA4iIa//U06+2zTDXrWLDMdGkCgEDgIv74+6ZxzTOh89KNSY6PtigBkQOAg/L77XennP5dGjZJWrZL23tt2RQAyIHAQbr/9rXTtteZ48WLpIx+xWw+ArAgchNebb0rTpkmplJkK/fWv264IwDAIHIST40gzZ5pFnoceKt13H1tFAwFH4CCc/u3fpDVrpD33NOttxoyxXRGAHAgchM+zz0oNDeb49tulT33Kbj0A8kLgIFx6esxW0Tt2SFOnSnPm2K4IQJ4IHISH40gXXSStWyd9+MPSsmXctwFChMBBePz7v0srVkjxuPn+wQ/arghAAQgchMP//q90ySXm+KabpOOOs1sPgIIROAi+rVvNfZtt26QvflG68krbFQEoAoGD4Js711zhfOhD0iOPSBX8swXCiP9zEWw/+IH0ve+ZyQHLl0v772+7IgBFInAQXOvWSRdeaI7nz5dOOMFuPQBKQuAgmN57z9y32bJFqqmRFiywXRGAEhE4CKarrjIdBcaPl5qapBEjbFcEoEQEDoLnRz+SFi0yxw89JCUSVssB4A4CB8Hy179K551nji+9VPrnf7ZaDgD3EDgIjt5es6/NW29Jxxwj3Xqr7YoAuIjAQXAsWGB28Bw71mw5sOeetisC4CICB8Hw859L3/mOOX7gAengg+3WA8B1BA7se/VV6eyzTTfoCy+UTj/ddkUAPEDgwK6+Pumcc6TNm6WPfUxqbLRdEQCPEDiw69ZbpSeekPbeW1q1Sho1ynZFADxC4MCe3/xG+va3zfHixdJRR9mtB4CnCBzY8cYb0rRpUipl7t+k194AiCwCB/5zHGnmTGnjRumww6QlS9gqGigDBA78d/fdpn3Nnnua+zZjxtiuCIAPCBz46/e/lxoazPEdd0hHH221HAD+IXDgn54e6cwzpZ07pVNOkWbPtl0RAB8ROPCH40j/8i/SK69IBx4oLVvGfRugzBA48MeyZWa76HhcWrFC+sAHbFcEwGcEDrz3xz9Kl1xijm+5Rfrc5+zWA8AKAgfe2rrVbBW9fbv0pS9JV1xhuyIAlrBvr4dSqZTa29vV1dWlyspK1dTUKB6P2y7LX9/8pvSnP0mVldIjj0gVnOMA5YrA8UgymdTcuXO1cePGXY8lEgktWrRIdXV1FivzUVPT7skBy5dL++1nuyIAFnG66YFkMqn6+voBYSNJnZ2dqq+vVzKZtFSZj9auNbPSJOnaa6XPf95uPQCsizmO4xTzH/b09GjcuHHq7u7W2LFj3a4rtFKplKqrq4eETVosFlMikVBHR0d0h9fee0867jjp2Welf/xH6Re/kEZwMQ1EUSFZwBWOy9rb27OGjSQ5jqMNGzaovb3dx6p8duWVJmzGjzfDaoQNABE4ruvq6nL1eaHz2GOmV5okPfywNGmS1XIABAeB47LKykpXnxcqf/2r6QItSZdfLn3lK3brARAoBI7LampqlEgkFMvStiUWi6mqqko1NTU+V+axnTvN/jZvvSUde6xZ4AkA/RA4LovH41q0aJEkDQmd9K8bGxujN2Hg29+Wfvc7adw408Jmzz1tVwQgYAgcD9TV1am5uVmTBt2/SCQSam5ujt46nJ/9TLr1VnP8ve9JBx1ktx4AgcS0aA+VRaeBV1+VPvEJafNm6aKLpHvvtV0RAB8VkgXMV/VQPB7X5MmTbZfhnVRKOussEzYf/7h05522KwIQYAypoXjf+Y70y19Ke+8trVwpjRpluyIAAUbgoDjt7dKCBeZ4yRLpyCPt1gMg8AgcFO71180U6L4+6ZxzpHPPtV0RgBAgcFAYx5G+/nWps1M6/HBzdQMAeSBwUJjGRuk//1Paay9p1Sppn31sVwQgJAgc5O/3v5euusoc33mnmQ4NAHkicJCf7m6zVfTOndKpp0oXX2y7IgAhQ+AgN8eRLrxQ+vOfpepq000gS684AMiGwEFuDzxg7teMGGH6pO27r+2KAIQQgYPh/eEP0ty55viWW6TPfMZuPQBCi8BBdu++K51+urR9u3TyyWaPGwAoEoGD7C65RHrxRemAA8zunRX8cwFQPD5BkNny5dKDD5qQ+f73pYkTbVcEIOQIHAz18stmqwFJuvZaKcodrwH4hsDBQNu3m/U2775rgubaa21XBCAiCBwM1NAgPfecNGGCGUqL2oZxAKwhcLDbD38oLV5sjh95xEwWAACXEDgw1q+XZs40xw0NZho0ALiIwIHpjzZtmvT222Zh5803264IQAQRODATA556Sho3zrSu2WMP2xUBiKARtguAZT/5ifTd75rjZctMc84yl0ql1N7erq6uLlVWVqqmpkZxJk8AJSNwPBCaD6xNm6QZM8zxN75hth0oc8lkUnPnztXGjRt3PZZIJLRo0SLV1dVZrAwIP4bUXJZMJlVdXa0pU6Zo+vTpmjJliqqrq5VMJm2XNlAqJZ19tvTaa2YjtTvusF2RdclkUvX19QPCRpI6OztVX18fvL9DIGQIHBeF6gPrlluk1lZp9Ghp5Upp5EjbFVmVSqU0d+5cOY4z5PfSj82bN0+pVMrv0oDIIHBcEqoPrF/9SrruOnN8773SEUdYLScI2tvbh5wo9Oc4jjZs2KD29nYfqwKihcBxSWg+sF5/XZo+Xerrk849VzrnHLv1eCSVSqmtrU0rVqxQW1tbzqDv6urK63XzfR6AoZg04JJQfGD19UnnnWcmCxxxxO6uAhFTzI3/ysrKvF473+cBGIrAcUkoPrDuukt6/HFpr73MltH77GOvlhJlmwmYvo82eGgzfR+tubk5Y+jU1NQokUios7Mz47BoLBZTIpFQTU1N3rUAGMQpUnd3tyPJ6e7uLvYlIqW3t9dJJBJOLBZzJA35isViTlVVldPb22unwKefdpwRIxxHcpx777VTg0taWlqcRCIx4M83kUg4q1atGvJ4IX8HLS0tTiwWG/J3mH6spaUl71oyPReIokKygMBxUTEfWL54+23HOeggEzb19Y7T12enDhek/4wzhUm2oBn81draOuzrDw6QqqqqrGGTrRarf9+Ajwgciwr5wPJFX58JGclxqqsd56237NThgvRVZL7Bku2rqakp5/u0trY6TU1NTmtra8Yroly1WL+iBXxSSBZwD8dldXV1qq2tDc6Y/v33S83N0ogRZr3NvvvaqcMFuWYC5ivXfbR4PK7JOXY5LWRWYq7XAsoFgeOBfD6wfPHCC9K8eeb41lulY4+1Wk6pSp3hN9yNf69qYRo1sBvrcKLqnXfMVtHvvSd9+cvSpZfarqhkhczwi8ViGX/d2NjoytVmKGYlAgFD4ETVnDnSiy+aXTsffliqCP9fdXrq8uAwSYvFYqqqqtLq1as1adKkAb+XSCSyTon2shY3rqaAqAj/pxCGevTR3SHT1CRNmGC7IlfE43EtWrRI0tArGMncN7ngggt0yimnaP369WptbVVTU5NaW1vV0dHharfn4Wpx+2oKiAw/ZibARy++6DijR5tZaddfb7saT2SaCdj/y891MIGblQj4rJAsiDlOhmXVeejp6dG4cePU3d2tsWPHuhJ+YRSoVebbt0uf/az0/PPSlCnSz38uRfQMO5VK6eabb9aCBQuG/F76CsPNIbRctQTm3wDgs0KygMApQeA265o9W1qyRJo4UXruOXP/JqJSqZSqq6uzTk1Oz0jr6Ojgwx/wUCFZwD2cIgVu75uWFhM2kvTII5EOGylE3bkB7ELgFCFwe990dEjnn2+Or7xSOukkf97XItbBAOFD4BQhUGfXO3dK06ZJ3d3m/s1NN3n/ngHAOhggfAicIgTq7Hr+fOnpp03LmhUrpD328P49A4B1MED4EDhFCMzZ9Y9/LC1caI6XLZOqq719vwBhHQwQPgROEQo5uy50q+O8bdokzZhhjmfPlmzMirOsrq5Ozc3NnncVAOAOpkUXKT1LTdKAyQP914BIyjltuqg1HKmUdOKJUlubdPTR0pNPSiNHuvfDhQzrYAB7QrEOJwofEpnW4VRVVamxsVGSMm51XGggZXT99dJ110mjR0vPPisdfrg7P5DLovB3DGB4BWWBH+0MBovStryZNuvKZ3Ou8ePHZ/29YXeLbG11nIoK07rm0Ud9/VkzybZZWaa/4wkTJjirVq2yXLEd+WzqBoRRoHf8LIdteVtbW0vakTLrbpGbNztOZaUJm/POs/PD9ZPtxKGhoWHYLZ8bGhp8qzEIH/RROsECBgts4JTLtrxNTU0lb4MsyWltbd39oqmU45x8sgmbI490nHfesfbzOc7wJw75/GyrV6/2pUbbH/TlcIKF8hbYwMn3zH/AB20IlXqFk/5qamra/aILF5qwGTnScV54wd4P5+Q+ccjna+LEiZ6eWAThg75cTrBQ3grJAl+nRQdqwWQOpUxnzjVtOl+71vE8/bR0zTXmuLFR+ru/K+l1S5Wr00I+XnvtNc86MQSl9VCgOlIAAeBr4ARmwWQOyWRS1dXVmjJliqZPn64pU6aouro674acuRYlxmIxjR8/fthAmjhxoo477jjp7belM8+Uenul00+XLryw6J/LLW6dEHh1YhGUD/ownWABfvA1cMLQjsStLtC5FiUuXbpUUuadKyVzBXDIwQer8+STpfXrpYMPlpYulUq8anKDWycEXp1YBOWDPiwnWIBv/Bi36y89tj54fD0IN1G9GHMfbpZUrp0rL5YcR3JSI0Y4zjPPePEjFyX955TvBIFMX17euwjKvcJcf07cw0EUBHbSQFpQt+W18UH13nvvORMnThzyHp+QnG3vB851++4buA+lXCcOtbW1wwa3l3/XQfqgD/IJFuCGwAeO4wRjfcRg+U5nHjB7rESZQm605Lz4ftj8yKez8WLkOnFYvXr1kDD168QiSB/0QT3BAtxQSBaMyDzQ5r14PK7JkyfbevuMbIy5Z7qPcI+kIyRtlPT1YZ5nW11dnWpra7O2r6mvr9cpp5xipb1N+h5aptZBjY2Nvjb2zPXnBJQLmnf2k0qlVF1drc7OzoxTamOxmBKJhDo6Olz7sGhra9OUKVN2/XqGpIclpSRNlvSb9x9vbW0NXECHQdD6uQWtHqBUge+lFmR+D8X0v99whOS88/5Q2nxuLEdOEDofAG4L7MLPMPB7j5X0mp2RjqOVkkZL+oWk7yg4G4l5tqdPGXFruj0QZgypZeH30MefTzpJB//0p9os6ROSXtXurQ5sbiSWaQuGvLZQwC7podpsi1G9GKoF/BKK/XDQz+rVpouApOdvu01/SiQCMb6fPisf/E+k/54+hE5ug+/TZcN9OoRRIVlgbZYa3tfRIV1wgTm++mp9oqFBn7BbkaTc/chisZjmzZun2tpazspzCErnA8A27uHYtGOH6ZPW0yN97nPSDTfYrmiXoPQjiwJa3AAGgWPT/PnSM89I++4rrVgh7bGH7Yp24azcPWHoIQj4gcCx5fHHpdtvN8cPPigdeKDdegbhrNw9ubqHS/ZnIgJ+IHBs6OyUzj3XHF9yiTR1qtVyMuGs3F1+T7cHgohZan7r7ZVOOEH69a+lT35SevJJaa+9bFeVUXqWmqQBkweYpVY8Og0gapilFmQ33mjCZp99pJUrAxs2kvf9yMrxwzeIPQQBv3CF46fWVnN14zjS978vTZ9uu6K8eBEMLCgFooGFn0G0ebN09NFSV5c0c6a0bJntiqxhQSkQHYVkAZMG/NDXJ82YYcLmqKOku++2XZE1uRaUStK8efPo1wZEEIHjh9tvl376U2nkSGnVKmn0aNsVWcOCUqB8EThee+ops8BTMlc2H/uY3XosY0EpUL4IHC+99ZZpXdPbK51xxu6eaWWMBaVA+SJwvOI40vnnS3/5i3TIIdLSpVKWRZTlhAWlQPkicLyyZIn0wx+a/mg/+IHETD5JtHkByhmB44XnnpMuu8wc33abdMwxVssJGtq8AOWJdThu27JF+vSnpbVrpa9+VVqzZsBQWjmurs+GPwsg/Ght46PUtm3qaGhQ39q1qjj0UB385puqWLtWSiRMF+h+YcPq+oFo8wKUF65wSvDS1Kk6dM0aDT4ndyTF2tul44/f9Rir6wFEEZ0GfPDS1Kk6fM2arH+AL72/100qldIvfvELzZo1KxCr61OplNra2rRixQq1tbXtes9sjwOAa5widXd3O5Kc7u7uYl8itHq3bnV6JafPTH4e8tUnOTslZ3VTk5NIJByZi56cX62trZ7W3dLSMqSeRCLhNDQ0ZHy8paXF03oAhF8hWcAVThE6GhoUl5RtVU1M5ubYb6ZPH7aNy2Berq5PD+kNrmfjxo1auHBhxsdPPfVUrV692rOaAJQXAqcIfWvX5vW8Qwp8Xa9W1w/XMDOXadOmqbm52YOqAJQbAqcIFYcdltfzXsnz9bxeXZ+rYeZwUqmUTjvtNCWTSZerAlBuCJwiHLRwoVIyNzsycST1Sronj9fyY3W9G0N1bBkAoFQEThHio0ZpXW2tpKGhk/71HTKhk4sfq+vdGKpjywAApSJwinTEY4/p5dpa9Q16PCXppa99TYuHaVApSePHj9cTTzyhjo4Oz9ff5GqYma+WlhamTAMoGoFTgiMee0zaulXrZs/Wy1/8otbNnq3Y1q06cs2aYRtUxmIxLV26VCeccIIvrVyGa5hZiMWLF2vKlCmqrq7mng6Awvkx97pcZVr3UlVVZW19S7Z6Lr/8cicej+e9XigWizmxWIx1OgAKygJa23gsaA0qs9XT3Nys0047Le/XicViSiQS6ujooOEmUMYKyQICB7tkai6aS2trKw04gTJGLzUUpa6uTuvXr1dra6vmzJmT13/jZXcEANFC4GCA9JYBp556al7P96o7AoDoIXCQUa6p1F53RwAQPQQOMhpuKrUf3REARA+Bg6zq6urU3NysSZMmDXjcj+4IAKKHWWrIKWhTuwEERyFZMMKnmhBi6YkEAFAKhtQAAL4gcAAAviBwAAC+IHAAAL4gcAAAviBwAAC+IHAAAL4gcAAAviBwAAC+IHAAAL4gcAAAviBwAAC+IHAAAL4gcAAAviBwAAC+IHAAAL4gcAAAviBwAAC+IHAAAL4YYbsAhEsqlVJ7e7u6urpUWVmpmpoaxeNx22UBCAECB3lLJpOaO3euNm7cuOuxRCKhRYsWqa6uzmJlAMKAITXkJZlMqr6+fkDYSFJnZ6fq6+uVTCYtVQYgLAgc5JRKpTR37lw5jjPk99KPzZs3T6lUyu/SAIQIgYOc2tvbh1zZ9Oc4jjZs2KD29nYfqwIQNgQOcurq6nL1eQDKE4GDnCorK119HoDyROAgp5qaGiUSCcVisYy/H4vFVFVVpZqaGp8rAxAmBA5yisfjWrRokSQNCZ30rxsbG1mPA2BYBA7yUldXp+bmZk2aNGnA44lEQs3NzazDAZBTzMk01zUPPT09GjdunLq7uzV27Fi360JA0WkAQH+FZAGdBlCQeDyuyZMn2y4DQAgxpAYA8AWBAwDwBYEDAPAFgQMA8AWBAwDwBYEDAPAFgQMA8AWBAwDwBYEDAPBF0Z0G0h1xenp6XCsGABAu6QzIp0ta0YGzZcsWSVJVVVWxLwEAiIgtW7Zo3Lhxwz6n6OadfX192rRpk8aMGZN1nxQAQLQ5jqMtW7bogAMOUEXF8Hdpig4cAAAKwaQBAIAvCBwAgC8IHACALwgcAIAvCBwAgC8IHACALwgcAIAvCBwAgC8IHACALwgcAIAvCBwAgC8IHACAL/4fi5e9YK9/v5YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "closest_pt, _ = compute_b(pt_c2, c1)\n",
    "\n",
    "plt.figure(figsize=(5, 5))\n",
    "plt.scatter(c1[:, 0], c1[:, 1], c=\"blue\")\n",
    "plt.scatter(c2[:, 0], c2[:, 1], c='black')\n",
    "plt.scatter(pt_c2[0], pt_c2[1], color='red')\n",
    "plt.scatter(closest_pt[0], closest_pt[1], color='red')\n",
    "plt.plot([pt_c2[0], closest_pt[0]], [pt_c2[1], closest_pt[1]], 'ro-')\n",
    "\n",
    "plt.xticks([], [])\n",
    "plt.yticks([], []);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def compute_a(cluster, target_pt_id):\n",
    "    distances = []\n",
    "    for other_pt_id in range(len(cluster)):\n",
    "        if target_pt_id != other_pt_id:\n",
    "            distances.append(distance.euclidean(cluster[target_pt_id], cluster[other_pt_id]))\n",
    "            \n",
    "    return np.mean(distances)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# plt.figure(figsize=(5, 5))\n",
    "# plt.scatter(c1[:,0], c1[:, 1], c=\"blue\", alpha=0.3)\n",
    "# plt.scatter(c2[:,0], c2[:, 1], c='black', alpha=0.3)\n",
    "\n",
    "# for pt1 in c2:\n",
    "#     if pt2 in c2:\n",
    "#         plt.plot([pt1[0], pt2[0]], [pt1[1], pt2[1]], 'r-', alpha=0.3)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0634996210278405"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pt_id_c2 = 10\n",
    "compute_a(c2, pt_id_c2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pt_id_c2 = 10\n",
    "pt_c2 = c2[pt_id_c2]\n",
    "\n",
    "plt.figure(figsize=(5, 5))\n",
    "plt.scatter(c1[:,0], c1[:, 1], c=\"blue\", alpha=0.3)\n",
    "plt.scatter(c2[:,0], c2[:, 1], c='black', alpha=0.3)\n",
    "\n",
    "plt.xticks([], [])\n",
    "plt.yticks([], [])\n",
    "\n",
    "for other_pt_id, other_pt in enumerate(c2):\n",
    "    if other_pt_id != pt_id_c2:\n",
    "        plt.plot([pt_c2[0], other_pt[0]], [pt_c2[1], other_pt[1]], 'r-', alpha=0.3)\n",
    "        \n",
    "plt.scatter(pt_c2[0], pt_c2[1], c='k', marker=\"s\", alpha=1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7712550573479948"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def pt_silhouette(cluster, target_pt_id, other_cluster):\n",
    "    a_i = compute_a(cluster, target_pt_id)\n",
    "    _, b_i = compute_b(cluster[target_pt_id], other_cluster)\n",
    "    \n",
    "    return (b_i - a_i) / max(a_i, b_i)\n",
    "\n",
    "pt_silhouette(c2, pt_id_c2, c1)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.2875797273328715\n",
      "6.982568942283778\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.8156008572237964"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pt_id_c1 = 21\n",
    "pt_c1 = c1[pt_id_c1]\n",
    "\n",
    "print(compute_a(c1, pt_id_c1))\n",
    "print(compute_b(pt_c1, c2)[1])\n",
    "\n",
    "pt_silhouette(c1, pt_id_c1, c2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8156008572237964"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pt_id_c1 = 21\n",
    "pt_c1 = c1[pt_id_c1]\n",
    "\n",
    "pt_silhouette(c1, pt_id_c1, c2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5, 5))\n",
    "plt.scatter(c1[:,0], c1[:, 1], c=\"blue\", alpha=0.3)\n",
    "plt.scatter(c2[:,0], c2[:, 1], c='black', alpha=0.3)\n",
    "\n",
    "plt.xticks([], [])\n",
    "plt.yticks([], [])\n",
    "\n",
    "for other_pt in c1:\n",
    "    if other_pt_id != pt_id_c1:\n",
    "        plt.plot([pt_c1[0], other_pt[0]], [pt_c1[1], other_pt[1]], 'r-', alpha=0.3)\n",
    "        \n",
    "plt.scatter(pt_c1[0], pt_c1[1], c='k', marker=\"s\", alpha=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Computing Cluster-Wide Silhouette Coefficient\n",
    "\n",
    "* Average silhouette coefficients within cluster \n",
    "  * A good indicator of the quality of the entire cluster\n",
    "  * Same observations as before; large values denote good separation\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Computig Cluster-Wide Silhouette Coefficient -- Cont'd\n",
    "\n",
    "* Average over the silhouette coefficients for all data points\n",
    "\n",
    "  * Provides a good estimate of the quality of the overall clustering\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# For simplicity, the solution assumes two clusters \n",
    "# Need to consider additional clusters in solution\n",
    "\n",
    "def cluster_silhouette(cluster, other_cluster):\n",
    "    silhouette_coeffs = []\n",
    "    for pt_id in range(len(cluster)):\n",
    "        silhouette_coeffs.append(pt_silhouette(cluster, pt_id, other_cluster))\n",
    "\n",
    "    return(np.mean(silhouette_coeffs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7671428476008759 0.7364318841721602\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.7517873658865181"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(cluster_silhouette(c1, c2), cluster_silhouette(c2, c1))\n",
    "np.mean([cluster_silhouette(c1, c2), cluster_silhouette(c2, c1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean_c1 = [8, 12]\n",
    "cov_c1 = [[6, 0], [0, 9]]\n",
    "c1 = np.random.multivariate_normal(mean_c1, cov_c1, 40)\n",
    "\n",
    "mean_c2 = [4, 4]\n",
    "cov_c2 = [[2, 0], [0, 2]]\n",
    "c2 = np.random.multivariate_normal(mean_c2, cov_c2, 29)\n",
    "\n",
    "plt.figure(figsize=(4, 4))\n",
    "plt.scatter(c1[:, 0], c1[:, 1])\n",
    "plt.scatter(c2[:, 0], c2[:, 1])\n",
    "\n",
    "plt.xticks([], [])\n",
    "plt.yticks([], []);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.24748093887812347 0.22409011299513776\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.2357855259366306"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(cluster_silhouette(c1, c2), cluster_silhouette(c2, c1))\n",
    "np.mean([cluster_silhouette(c1, c2), cluster_silhouette(c2, c1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean_c1 = [8, 12]\n",
    "cov_c1 = [[8, 0], [0, 15]]\n",
    "c1 = np.random.multivariate_normal(mean_c1, cov_c1, 40)\n",
    "\n",
    "mean_c2 = [4, 4]\n",
    "cov_c2 = [[4, 0], [0, 10]]\n",
    "c2 = np.random.multivariate_normal(mean_c2, cov_c2, 29)\n",
    "\n",
    "plt.figure(figsize=(4, 4))\n",
    "plt.scatter(c1[:, 0], c1[:, 1])\n",
    "plt.scatter(c2[:, 0], c2[:, 1])\n",
    "\n",
    "plt.xticks([], [])\n",
    "plt.yticks([], []);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.053665981224858196 -0.2016209514580024\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "-0.1276434663414303"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(cluster_silhouette(c1, c2), cluster_silhouette(c2, c1))\n",
    "np.mean([cluster_silhouette(c1, c2), cluster_silhouette(c2, c1)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Using Silhouettes to Decide on Best Number of Cluster \n",
    "\n",
    "* Silhouette coefficient can be useful to determine the number of clusters present in the dataset\n",
    "\n",
    "* Run the algorithm several times for each possible value of $k$ and compute the overall silhouette coefficient each time\n",
    "\n",
    "  * We should observe a peak at the best value of $k$\n",
    " \n",
    "<br>\n",
    "\n",
    "### Question\n",
    "\n",
    "* Why do we need to run the $k$-means algorithm *several times* for each value of $k$ we would like to test?"
   ]
  },
  {
   "attachments": {
    "e5adf26a-5080-4054-a2ad-c6cb4ca7583f.png": {
     "image/png": 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"
    }
   },
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     "slide_type": "slide"
    }
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   "source": [
    "### Using Silhouettes to Decide on Best Number of Cluster \n",
    "\n",
    "* Silhouette coefficient can be useful to determine the number of clusters present in the dataset\n",
    "\n",
    "* Run the algorithm several times for each possible value of $k$ and compute the overall silhouette coefficient each time\n",
    "  * We should observe a peak at the best value of $k$\n",
    "\n",
    "\n",
    "![image.png](attachment:e5adf26a-5080-4054-a2ad-c6cb4ca7583f.png)\n",
    "\n",
    "\n",
    "Source: A. Geron, 2019"
   ]
  }
 ],
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