example/example-02-clustering-samples-in-a-polar-coordinate.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example-02 clustering samples in a polar coordinate\n",
    "\n",
    "Author: https://github.com/ludlows\n",
    "\n",
    "Please install wgmm before using this notebook by the command below:\n",
    "```bash\n",
    "pip install https://github.com/ludlows/wgmm/archive/refs/heads/main.zip\n",
    "```\n",
    "in this notebook, we will use the wrapped Gaussian mixture model to cluster samples in a polar coordinate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from wgmm import WGMixModel\n",
    "from numpy.random import default_rng"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## synthesize samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = default_rng(123321)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_sample = 500 # number of samples\n",
    "means_angle = [355, 100] # unit : degree \n",
    "variances_angle = [50, 60] #  variances\n",
    "split = [0.7, 0.3] #  the weight of each components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "means_radius = [0.4, 0.7]\n",
    "variances_radius = [0.01, 0.01]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "angles1 = means_angle[0] + variances_angle[0] **0.5  * rng.standard_normal(int(split[0] * n_sample))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(337.2641988829006, 375.0618383117922)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "angles1.min(), angles1.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "radius1 = means_radius[0] + variances_radius[0] **0.5  * rng.standard_normal(int(split[0] * n_sample))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.07460469040996676, 0.7548339203315346)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "radius1.min(), radius1.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "angles2 = means_angle[1] + variances_angle[1] **0.5  * rng.standard_normal(int(split[1] * n_sample))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(72.1650294811, 118.40382800357722)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "angles2.min(),angles2.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "radius2 = means_radius[1] + variances_radius[1] **0.5  * rng.standard_normal(int(split[1] * n_sample))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.40656354850218995, 1.0098561756522901)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "radius2.min(),radius2.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "angles = np.vstack([angles1[:,np.newaxis],angles2[:,np.newaxis]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "radius = np.vstack([radius1[:,np.newaxis],radius2[:,np.newaxis]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples  = np.hstack([angles,radius])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(500, 2)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samples.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x17730beea58>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.polar(angles1/180*np.pi, radius1, 'r.', markersize=12)\n",
    "plt.polar(angles2/180*np.pi, radius2, 'b.', markersize=12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## use WGMM\n",
    "here we are using `wgmm` to model the probabilistic distribution of the synthesized samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples_wgmm = samples.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples_wgmm[:,0] = samples_wgmm[:,0] / 180*np.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "weights_init = np.array([0.9,0.1])\n",
    "means_init = np.array([[270.0, 0.5],[180.0, 0.7]]) #/ 180.0 * np.pi\n",
    "means_init[:,0] = means_init[:,0] / 180.0 * np.pi\n",
    "covars_init = np.zeros((2,2,2))\n",
    "covars_init[0,:,:] = np.array([[0.1,0],[0,0.1]])\n",
    "covars_init[1,:,:] = np.array([[0.1,0],[0,0.1]])\n",
    "periods = np.array([2*np.pi, 3]) #3 is big enough here since radius is not a circular variable, and it ranges from 0 to 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = WGMixModel(n_components=2, weights_init=weights_init, means_init=means_init, covars_init=covars_init, periods=periods, \n",
    "                   tol=1e-4, reg_covar=1e-6, max_iter=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "rng.shuffle(samples_wgmm, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(samples_wgmm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "means_estimated = model.means_.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "means_estimated[:,0] = means_estimated[:,0] / np.pi * 180"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[355.11574106,   0.39957169],\n",
       "       [100.05972748,   0.70743917]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "means_estimated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6.19793891, 0.39957169],\n",
       "       [1.74637169, 0.70743917]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.means_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## visualize Predicted Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "labels = model.predict(samples_wgmm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,\n",
       "       0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0,\n",
       "       0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0,\n",
       "       0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0,\n",
       "       0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0,\n",
       "       1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0,\n",
       "       0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0,\n",
       "       0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0,\n",
       "       0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1,\n",
       "       0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0,\n",
       "       1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0,\n",
       "       1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0,\n",
       "       1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1,\n",
       "       0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1,\n",
       "       0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0,\n",
       "       0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1,\n",
       "       1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1,\n",
       "       0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1,\n",
       "       0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0], dtype=int64)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples_label_0 = np.array([ samples_wgmm[i,:] for i,v in enumerate(labels) if v == 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples_label_1 = np.array([ samples_wgmm[i,:] for i,v in enumerate(labels) if v == 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x17730bbce10>]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.polar(samples_label_0[:,0], samples_label_0[:,1], 'c.', markersize=12)\n",
    "plt.polar(samples_label_1[:,0], samples_label_1[:,1], 'k.', markersize=12)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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