PCA_and_Clustering.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pylab as pl\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 1\n",
    "Read the data from csv file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2100, 19)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vstable = pd.read_csv(\"C:/Users/USER/Desktop/DSC/DSC_478 Programming to Machine Learning A/Assignment/Assignment_4/Problem_1/segmentation_data.txt\", header = None)\n",
    "vstable.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Int64Index([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], dtype='int64')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vstable.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "      <th>18</th>\n",
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       "      <th>0</th>\n",
       "      <td>110.0</td>\n",
       "      <td>189.0</td>\n",
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       "      <td>17.222221</td>\n",
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       "      <td>0.508139</td>\n",
       "      <td>1.910864</td>\n",
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       "      <th>1</th>\n",
       "      <td>86.0</td>\n",
       "      <td>187.0</td>\n",
       "      <td>9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.111111</td>\n",
       "      <td>0.720082</td>\n",
       "      <td>1.444444</td>\n",
       "      <td>0.750309</td>\n",
       "      <td>13.740741</td>\n",
       "      <td>11.666667</td>\n",
       "      <td>10.333334</td>\n",
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       "      <td>-6.222222</td>\n",
       "      <td>-10.222222</td>\n",
       "      <td>16.444445</td>\n",
       "      <td>19.222221</td>\n",
       "      <td>0.463329</td>\n",
       "      <td>1.941465</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>225.0</td>\n",
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       "      <td>9</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>3.000000</td>\n",
       "      <td>1.520234</td>\n",
       "      <td>12.259259</td>\n",
       "      <td>10.333334</td>\n",
       "      <td>9.333334</td>\n",
       "      <td>17.111110</td>\n",
       "      <td>-5.777778</td>\n",
       "      <td>-8.777778</td>\n",
       "      <td>14.555555</td>\n",
       "      <td>17.111110</td>\n",
       "      <td>0.480149</td>\n",
       "      <td>1.987902</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>47.0</td>\n",
       "      <td>232.0</td>\n",
       "      <td>9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.277778</td>\n",
       "      <td>1.254621</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.894427</td>\n",
       "      <td>12.703704</td>\n",
       "      <td>11.000000</td>\n",
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       "      <th>4</th>\n",
       "      <td>97.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>1.166667</td>\n",
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       "      <td>1.166667</td>\n",
       "      <td>1.005540</td>\n",
       "      <td>15.592592</td>\n",
       "      <td>13.888889</td>\n",
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       "      <td>-5.111111</td>\n",
       "      <td>-11.444445</td>\n",
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       "      <td>21.111110</td>\n",
       "      <td>0.442661</td>\n",
       "      <td>1.863654</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>157.0</td>\n",
       "      <td>221.0</td>\n",
       "      <td>9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>1.222222</td>\n",
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       "      <td>17.666666</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>0.549180</td>\n",
       "      <td>1.877146</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>62.0</td>\n",
       "      <td>224.0</td>\n",
       "      <td>9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>1.083547</td>\n",
       "      <td>2.333333</td>\n",
       "      <td>1.632993</td>\n",
       "      <td>14.629630</td>\n",
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       "      <td>11.444445</td>\n",
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       "      <td>-4.222222</td>\n",
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       "      <td>19.222221</td>\n",
       "      <td>0.408965</td>\n",
       "      <td>1.860191</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>27.0</td>\n",
       "      <td>248.0</td>\n",
       "      <td>9</td>\n",
       "      <td>0.111111</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.611111</td>\n",
       "      <td>0.646930</td>\n",
       "      <td>3.166667</td>\n",
       "      <td>1.722401</td>\n",
       "      <td>15.296296</td>\n",
       "      <td>14.777778</td>\n",
       "      <td>12.888889</td>\n",
       "      <td>18.222221</td>\n",
       "      <td>-1.555556</td>\n",
       "      <td>-7.222222</td>\n",
       "      <td>8.777778</td>\n",
       "      <td>18.222221</td>\n",
       "      <td>0.312227</td>\n",
       "      <td>1.783512</td>\n",
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       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>44.0</td>\n",
       "      <td>233.0</td>\n",
       "      <td>9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.222222</td>\n",
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       "      <td>2.111111</td>\n",
       "      <td>1.327766</td>\n",
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       "      <td>0.422174</td>\n",
       "      <td>1.950405</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>17.0</td>\n",
       "      <td>229.0</td>\n",
       "      <td>9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.111111</td>\n",
       "      <td>1.985130</td>\n",
       "      <td>2.444445</td>\n",
       "      <td>1.614747</td>\n",
       "      <td>13.703704</td>\n",
       "      <td>11.222222</td>\n",
       "      <td>11.111111</td>\n",
       "      <td>18.777779</td>\n",
       "      <td>-7.444445</td>\n",
       "      <td>-7.777778</td>\n",
       "      <td>15.222222</td>\n",
       "      <td>18.777779</td>\n",
       "      <td>0.439852</td>\n",
       "      <td>2.099904</td>\n",
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       "      0      1   2         3    4         5         6         7         8   \\\n",
       "0  110.0  189.0   9  0.000000  0.0  1.000000  0.666667  1.222222  1.186342   \n",
       "1   86.0  187.0   9  0.000000  0.0  1.111111  0.720082  1.444444  0.750309   \n",
       "2  225.0  244.0   9  0.000000  0.0  3.388889  2.195113  3.000000  1.520234   \n",
       "3   47.0  232.0   9  0.000000  0.0  1.277778  1.254621  1.000000  0.894427   \n",
       "4   97.0  186.0   9  0.000000  0.0  1.166667  0.691215  1.166667  1.005540   \n",
       "5  157.0  221.0   9  0.000000  0.0  1.055556  0.646930  1.222222  0.620633   \n",
       "6   62.0  224.0   9  0.000000  0.0  0.944445  1.083547  2.333333  1.632993   \n",
       "7   27.0  248.0   9  0.111111  0.0  1.611111  0.646930  3.166667  1.722401   \n",
       "8   44.0  233.0   9  0.000000  0.0  2.222222  2.146487  2.111111  1.327766   \n",
       "9   17.0  229.0   9  0.000000  0.0  2.111111  1.985130  2.444445  1.614747   \n",
       "\n",
       "          9          10         11         12        13         14         15  \\\n",
       "0  12.925926  10.888889   9.222222  18.666668 -6.111111 -11.111111  17.222221   \n",
       "1  13.740741  11.666667  10.333334  19.222221 -6.222222 -10.222222  16.444445   \n",
       "2  12.259259  10.333334   9.333334  17.111110 -5.777778  -8.777778  14.555555   \n",
       "3  12.703704  11.000000   9.000000  18.111110 -5.111111 -11.111111  16.222221   \n",
       "4  15.592592  13.888889  11.777778  21.111110 -5.111111 -11.444445  16.555555   \n",
       "5  12.111111  10.222222   8.111112  18.000000 -5.666666 -12.000000  17.666666   \n",
       "6  14.629630  13.222222  11.444445  19.222221 -4.222222  -9.555555  13.777778   \n",
       "7  15.296296  14.777778  12.888889  18.222221 -1.555556  -7.222222   8.777778   \n",
       "8  14.481482  12.555555  11.333333  19.555555 -5.777778  -9.444445  15.222222   \n",
       "9  13.703704  11.222222  11.111111  18.777779 -7.444445  -7.777778  15.222222   \n",
       "\n",
       "          16        17        18  \n",
       "0  18.666668  0.508139  1.910864  \n",
       "1  19.222221  0.463329  1.941465  \n",
       "2  17.111110  0.480149  1.987902  \n",
       "3  18.111110  0.500966  1.875362  \n",
       "4  21.111110  0.442661  1.863654  \n",
       "5  18.000000  0.549180  1.877146  \n",
       "6  19.222221  0.408965  1.860191  \n",
       "7  18.222221  0.312227  1.783512  \n",
       "8  19.555555  0.422174  1.950405  \n",
       "9  18.777779  0.439852  2.099904  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vstable.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 2100 entries, 0 to 2099\n",
      "Data columns (total 19 columns):\n",
      " #   Column  Non-Null Count  Dtype  \n",
      "---  ------  --------------  -----  \n",
      " 0   0       2100 non-null   float64\n",
      " 1   1       2100 non-null   float64\n",
      " 2   2       2100 non-null   int64  \n",
      " 3   3       2100 non-null   float64\n",
      " 4   4       2100 non-null   float64\n",
      " 5   5       2100 non-null   float64\n",
      " 6   6       2100 non-null   float64\n",
      " 7   7       2100 non-null   float64\n",
      " 8   8       2100 non-null   float64\n",
      " 9   9       2100 non-null   float64\n",
      " 10  10      2100 non-null   float64\n",
      " 11  11      2100 non-null   float64\n",
      " 12  12      2100 non-null   float64\n",
      " 13  13      2100 non-null   float64\n",
      " 14  14      2100 non-null   float64\n",
      " 15  15      2100 non-null   float64\n",
      " 16  16      2100 non-null   float64\n",
      " 17  17      2100 non-null   float64\n",
      " 18  18      2100 non-null   float64\n",
      "dtypes: float64(18), int64(1)\n",
      "memory usage: 311.8 KB\n"
     ]
    }
   ],
   "source": [
    "vstable.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
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       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>2100.000000</td>\n",
       "      <td>2100.000000</td>\n",
       "      <td>2100.0</td>\n",
       "      <td>2100.000000</td>\n",
       "      <td>2100.000000</td>\n",
       "      <td>2100.000000</td>\n",
       "      <td>2100.000000</td>\n",
       "      <td>2100.000000</td>\n",
       "      <td>2.100000e+03</td>\n",
       "      <td>2100.000000</td>\n",
       "      <td>2100.000000</td>\n",
       "      <td>2100.000000</td>\n",
       "      <td>2100.000000</td>\n",
       "      <td>2100.000000</td>\n",
       "      <td>2100.000000</td>\n",
       "      <td>2100.000000</td>\n",
       "      <td>2100.000000</td>\n",
       "      <td>2100.000000</td>\n",
       "      <td>2100.000000</td>\n",
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       "      <th>mean</th>\n",
       "      <td>124.940476</td>\n",
       "      <td>123.483333</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0.014921</td>\n",
       "      <td>0.004550</td>\n",
       "      <td>1.890820</td>\n",
       "      <td>5.708299</td>\n",
       "      <td>2.406772</td>\n",
       "      <td>7.904224e+00</td>\n",
       "      <td>37.047654</td>\n",
       "      <td>32.806667</td>\n",
       "      <td>44.205556</td>\n",
       "      <td>34.130741</td>\n",
       "      <td>-12.722963</td>\n",
       "      <td>21.473704</td>\n",
       "      <td>-8.750741</td>\n",
       "      <td>45.162381</td>\n",
       "      <td>0.427259</td>\n",
       "      <td>-1.365147</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>72.858637</td>\n",
       "      <td>57.431428</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.041024</td>\n",
       "      <td>0.023573</td>\n",
       "      <td>2.649453</td>\n",
       "      <td>44.989359</td>\n",
       "      <td>3.469954</td>\n",
       "      <td>5.347107e+01</td>\n",
       "      <td>38.135291</td>\n",
       "      <td>34.994538</td>\n",
       "      <td>43.510119</td>\n",
       "      <td>36.303768</td>\n",
       "      <td>11.588214</td>\n",
       "      <td>19.654107</td>\n",
       "      <td>11.606996</td>\n",
       "      <td>42.900582</td>\n",
       "      <td>0.228458</td>\n",
       "      <td>1.544278</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>11.000000</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-1.589457e-08</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-49.666668</td>\n",
       "      <td>-12.444445</td>\n",
       "      <td>-33.888890</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-3.044175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>62.000000</td>\n",
       "      <td>81.000000</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.722222</td>\n",
       "      <td>0.349603</td>\n",
       "      <td>0.833332</td>\n",
       "      <td>4.216377e-01</td>\n",
       "      <td>7.472222</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>9.666667</td>\n",
       "      <td>6.222222</td>\n",
       "      <td>-18.583333</td>\n",
       "      <td>4.305556</td>\n",
       "      <td>-17.000000</td>\n",
       "      <td>11.777778</td>\n",
       "      <td>0.284934</td>\n",
       "      <td>-2.188539</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>121.000000</td>\n",
       "      <td>122.000000</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.277776</td>\n",
       "      <td>0.833333</td>\n",
       "      <td>1.444444</td>\n",
       "      <td>9.897442e-01</td>\n",
       "      <td>21.666666</td>\n",
       "      <td>19.666668</td>\n",
       "      <td>27.777779</td>\n",
       "      <td>20.444445</td>\n",
       "      <td>-10.888889</td>\n",
       "      <td>19.666666</td>\n",
       "      <td>-11.000000</td>\n",
       "      <td>28.666666</td>\n",
       "      <td>0.375064</td>\n",
       "      <td>-2.052625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>188.250000</td>\n",
       "      <td>171.250000</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>2.222221</td>\n",
       "      <td>1.807406</td>\n",
       "      <td>2.555556</td>\n",
       "      <td>2.251852e+00</td>\n",
       "      <td>53.277778</td>\n",
       "      <td>47.333332</td>\n",
       "      <td>65.000000</td>\n",
       "      <td>46.388888</td>\n",
       "      <td>-4.222222</td>\n",
       "      <td>36.111110</td>\n",
       "      <td>-3.222222</td>\n",
       "      <td>65.000000</td>\n",
       "      <td>0.540228</td>\n",
       "      <td>-1.565745</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>254.000000</td>\n",
       "      <td>251.000000</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.222222</td>\n",
       "      <td>29.222221</td>\n",
       "      <td>991.718400</td>\n",
       "      <td>44.722225</td>\n",
       "      <td>1.386329e+03</td>\n",
       "      <td>143.444440</td>\n",
       "      <td>137.111110</td>\n",
       "      <td>150.888890</td>\n",
       "      <td>142.555560</td>\n",
       "      <td>9.888889</td>\n",
       "      <td>82.000000</td>\n",
       "      <td>24.666666</td>\n",
       "      <td>150.888890</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.912480</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                0            1       2            3            4   \\\n",
       "count  2100.000000  2100.000000  2100.0  2100.000000  2100.000000   \n",
       "mean    124.940476   123.483333     9.0     0.014921     0.004550   \n",
       "std      72.858637    57.431428     0.0     0.041024     0.023573   \n",
       "min       1.000000    11.000000     9.0     0.000000     0.000000   \n",
       "25%      62.000000    81.000000     9.0     0.000000     0.000000   \n",
       "50%     121.000000   122.000000     9.0     0.000000     0.000000   \n",
       "75%     188.250000   171.250000     9.0     0.000000     0.000000   \n",
       "max     254.000000   251.000000     9.0     0.333333     0.222222   \n",
       "\n",
       "                5            6            7             8            9   \\\n",
       "count  2100.000000  2100.000000  2100.000000  2.100000e+03  2100.000000   \n",
       "mean      1.890820     5.708299     2.406772  7.904224e+00    37.047654   \n",
       "std       2.649453    44.989359     3.469954  5.347107e+01    38.135291   \n",
       "min       0.000000     0.000000     0.000000 -1.589457e-08     0.000000   \n",
       "25%       0.722222     0.349603     0.833332  4.216377e-01     7.472222   \n",
       "50%       1.277776     0.833333     1.444444  9.897442e-01    21.666666   \n",
       "75%       2.222221     1.807406     2.555556  2.251852e+00    53.277778   \n",
       "max      29.222221   991.718400    44.722225  1.386329e+03   143.444440   \n",
       "\n",
       "                10           11           12           13           14  \\\n",
       "count  2100.000000  2100.000000  2100.000000  2100.000000  2100.000000   \n",
       "mean     32.806667    44.205556    34.130741   -12.722963    21.473704   \n",
       "std      34.994538    43.510119    36.303768    11.588214    19.654107   \n",
       "min       0.000000     0.000000     0.000000   -49.666668   -12.444445   \n",
       "25%       7.000000     9.666667     6.222222   -18.583333     4.305556   \n",
       "50%      19.666668    27.777779    20.444445   -10.888889    19.666666   \n",
       "75%      47.333332    65.000000    46.388888    -4.222222    36.111110   \n",
       "max     137.111110   150.888890   142.555560     9.888889    82.000000   \n",
       "\n",
       "                15           16           17           18  \n",
       "count  2100.000000  2100.000000  2100.000000  2100.000000  \n",
       "mean     -8.750741    45.162381     0.427259    -1.365147  \n",
       "std      11.606996    42.900582     0.228458     1.544278  \n",
       "min     -33.888890     0.000000     0.000000    -3.044175  \n",
       "25%     -17.000000    11.777778     0.284934    -2.188539  \n",
       "50%     -11.000000    28.666666     0.375064    -2.052625  \n",
       "75%      -3.222222    65.000000     0.540228    -1.565745  \n",
       "max      24.666666   150.888890     1.000000     2.912480  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vstable.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "      <th>13</th>\n",
       "      <th>14</th>\n",
       "      <th>15</th>\n",
       "      <th>16</th>\n",
       "      <th>17</th>\n",
       "      <th>18</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>110.0</td>\n",
       "      <td>189.0</td>\n",
       "      <td>9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.666667</td>\n",
       "      <td>1.222222</td>\n",
       "      <td>1.186342</td>\n",
       "      <td>12.925926</td>\n",
       "      <td>10.888889</td>\n",
       "      <td>9.222222</td>\n",
       "      <td>18.666668</td>\n",
       "      <td>-6.111111</td>\n",
       "      <td>-11.111111</td>\n",
       "      <td>17.222221</td>\n",
       "      <td>18.666668</td>\n",
       "      <td>0.508139</td>\n",
       "      <td>1.910864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>86.0</td>\n",
       "      <td>187.0</td>\n",
       "      <td>9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.111111</td>\n",
       "      <td>0.720082</td>\n",
       "      <td>1.444444</td>\n",
       "      <td>0.750309</td>\n",
       "      <td>13.740741</td>\n",
       "      <td>11.666667</td>\n",
       "      <td>10.333334</td>\n",
       "      <td>19.222221</td>\n",
       "      <td>-6.222222</td>\n",
       "      <td>-10.222222</td>\n",
       "      <td>16.444445</td>\n",
       "      <td>19.222221</td>\n",
       "      <td>0.463329</td>\n",
       "      <td>1.941465</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>225.0</td>\n",
       "      <td>244.0</td>\n",
       "      <td>9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.388889</td>\n",
       "      <td>2.195113</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.520234</td>\n",
       "      <td>12.259259</td>\n",
       "      <td>10.333334</td>\n",
       "      <td>9.333334</td>\n",
       "      <td>17.111110</td>\n",
       "      <td>-5.777778</td>\n",
       "      <td>-8.777778</td>\n",
       "      <td>14.555555</td>\n",
       "      <td>17.111110</td>\n",
       "      <td>0.480149</td>\n",
       "      <td>1.987902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>47.0</td>\n",
       "      <td>232.0</td>\n",
       "      <td>9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.277778</td>\n",
       "      <td>1.254621</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.894427</td>\n",
       "      <td>12.703704</td>\n",
       "      <td>11.000000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>18.111110</td>\n",
       "      <td>-5.111111</td>\n",
       "      <td>-11.111111</td>\n",
       "      <td>16.222221</td>\n",
       "      <td>18.111110</td>\n",
       "      <td>0.500966</td>\n",
       "      <td>1.875362</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>97.0</td>\n",
       "      <td>186.0</td>\n",
       "      <td>9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.166667</td>\n",
       "      <td>0.691215</td>\n",
       "      <td>1.166667</td>\n",
       "      <td>1.005540</td>\n",
       "      <td>15.592592</td>\n",
       "      <td>13.888889</td>\n",
       "      <td>11.777778</td>\n",
       "      <td>21.111110</td>\n",
       "      <td>-5.111111</td>\n",
       "      <td>-11.444445</td>\n",
       "      <td>16.555555</td>\n",
       "      <td>21.111110</td>\n",
       "      <td>0.442661</td>\n",
       "      <td>1.863654</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>157.0</td>\n",
       "      <td>221.0</td>\n",
       "      <td>9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.055556</td>\n",
       "      <td>0.646930</td>\n",
       "      <td>1.222222</td>\n",
       "      <td>0.620633</td>\n",
       "      <td>12.111111</td>\n",
       "      <td>10.222222</td>\n",
       "      <td>8.111112</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>-5.666666</td>\n",
       "      <td>-12.000000</td>\n",
       "      <td>17.666666</td>\n",
       "      <td>18.000000</td>\n",
       "      <td>0.549180</td>\n",
       "      <td>1.877146</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>62.0</td>\n",
       "      <td>224.0</td>\n",
       "      <td>9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.944445</td>\n",
       "      <td>1.083547</td>\n",
       "      <td>2.333333</td>\n",
       "      <td>1.632993</td>\n",
       "      <td>14.629630</td>\n",
       "      <td>13.222222</td>\n",
       "      <td>11.444445</td>\n",
       "      <td>19.222221</td>\n",
       "      <td>-4.222222</td>\n",
       "      <td>-9.555555</td>\n",
       "      <td>13.777778</td>\n",
       "      <td>19.222221</td>\n",
       "      <td>0.408965</td>\n",
       "      <td>1.860191</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>27.0</td>\n",
       "      <td>248.0</td>\n",
       "      <td>9</td>\n",
       "      <td>0.111111</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.611111</td>\n",
       "      <td>0.646930</td>\n",
       "      <td>3.166667</td>\n",
       "      <td>1.722401</td>\n",
       "      <td>15.296296</td>\n",
       "      <td>14.777778</td>\n",
       "      <td>12.888889</td>\n",
       "      <td>18.222221</td>\n",
       "      <td>-1.555556</td>\n",
       "      <td>-7.222222</td>\n",
       "      <td>8.777778</td>\n",
       "      <td>18.222221</td>\n",
       "      <td>0.312227</td>\n",
       "      <td>1.783512</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>44.0</td>\n",
       "      <td>233.0</td>\n",
       "      <td>9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.222222</td>\n",
       "      <td>2.146487</td>\n",
       "      <td>2.111111</td>\n",
       "      <td>1.327766</td>\n",
       "      <td>14.481482</td>\n",
       "      <td>12.555555</td>\n",
       "      <td>11.333333</td>\n",
       "      <td>19.555555</td>\n",
       "      <td>-5.777778</td>\n",
       "      <td>-9.444445</td>\n",
       "      <td>15.222222</td>\n",
       "      <td>19.555555</td>\n",
       "      <td>0.422174</td>\n",
       "      <td>1.950405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>17.0</td>\n",
       "      <td>229.0</td>\n",
       "      <td>9</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.111111</td>\n",
       "      <td>1.985130</td>\n",
       "      <td>2.444445</td>\n",
       "      <td>1.614747</td>\n",
       "      <td>13.703704</td>\n",
       "      <td>11.222222</td>\n",
       "      <td>11.111111</td>\n",
       "      <td>18.777779</td>\n",
       "      <td>-7.444445</td>\n",
       "      <td>-7.777778</td>\n",
       "      <td>15.222222</td>\n",
       "      <td>18.777779</td>\n",
       "      <td>0.439852</td>\n",
       "      <td>2.099904</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      0      1   2         3    4         5         6         7         8   \\\n",
       "0  110.0  189.0   9  0.000000  0.0  1.000000  0.666667  1.222222  1.186342   \n",
       "1   86.0  187.0   9  0.000000  0.0  1.111111  0.720082  1.444444  0.750309   \n",
       "2  225.0  244.0   9  0.000000  0.0  3.388889  2.195113  3.000000  1.520234   \n",
       "3   47.0  232.0   9  0.000000  0.0  1.277778  1.254621  1.000000  0.894427   \n",
       "4   97.0  186.0   9  0.000000  0.0  1.166667  0.691215  1.166667  1.005540   \n",
       "5  157.0  221.0   9  0.000000  0.0  1.055556  0.646930  1.222222  0.620633   \n",
       "6   62.0  224.0   9  0.000000  0.0  0.944445  1.083547  2.333333  1.632993   \n",
       "7   27.0  248.0   9  0.111111  0.0  1.611111  0.646930  3.166667  1.722401   \n",
       "8   44.0  233.0   9  0.000000  0.0  2.222222  2.146487  2.111111  1.327766   \n",
       "9   17.0  229.0   9  0.000000  0.0  2.111111  1.985130  2.444445  1.614747   \n",
       "\n",
       "          9          10         11         12        13         14         15  \\\n",
       "0  12.925926  10.888889   9.222222  18.666668 -6.111111 -11.111111  17.222221   \n",
       "1  13.740741  11.666667  10.333334  19.222221 -6.222222 -10.222222  16.444445   \n",
       "2  12.259259  10.333334   9.333334  17.111110 -5.777778  -8.777778  14.555555   \n",
       "3  12.703704  11.000000   9.000000  18.111110 -5.111111 -11.111111  16.222221   \n",
       "4  15.592592  13.888889  11.777778  21.111110 -5.111111 -11.444445  16.555555   \n",
       "5  12.111111  10.222222   8.111112  18.000000 -5.666666 -12.000000  17.666666   \n",
       "6  14.629630  13.222222  11.444445  19.222221 -4.222222  -9.555555  13.777778   \n",
       "7  15.296296  14.777778  12.888889  18.222221 -1.555556  -7.222222   8.777778   \n",
       "8  14.481482  12.555555  11.333333  19.555555 -5.777778  -9.444445  15.222222   \n",
       "9  13.703704  11.222222  11.111111  18.777779 -7.444445  -7.777778  15.222222   \n",
       "\n",
       "          16        17        18  \n",
       "0  18.666668  0.508139  1.910864  \n",
       "1  19.222221  0.463329  1.941465  \n",
       "2  17.111110  0.480149  1.987902  \n",
       "3  18.111110  0.500966  1.875362  \n",
       "4  21.111110  0.442661  1.863654  \n",
       "5  18.000000  0.549180  1.877146  \n",
       "6  19.222221  0.408965  1.860191  \n",
       "7  18.222221  0.312227  1.783512  \n",
       "8  19.555555  0.422174  1.950405  \n",
       "9  18.777779  0.439852  2.099904  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vs_train = vstable.copy()\n",
    "vs_train.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(19, 1)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The list of our index terms\n",
    "terms = pd.read_csv(\"C:/Users/USER/Desktop/DSC/DSC_478 Programming to Machine Learning A/Assignment/Assignment_4/Problem_1/segmentation_names.txt\" , header=None)\n",
    "terms.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      REGION-CENTROID-COL\n",
       "1      REGION-CENTROID-ROW\n",
       "2       REGION-PIXEL-COUNT\n",
       "3     SHORT-LINE-DENSITY-5\n",
       "4     SHORT-LINE-DENSITY-2\n",
       "5               VEDGE-MEAN\n",
       "6                 VEDGE-SD\n",
       "7               HEDGE-MEAN\n",
       "8                 HEDGE-SD\n",
       "9           INTENSITY-MEAN\n",
       "10             RAWRED-MEAN\n",
       "11            RAWBLUE-MEAN\n",
       "12           RAWGREEN-MEAN\n",
       "13              EXRED-MEAN\n",
       "14             EXBLUE-MEAN\n",
       "15            EXGREEN-MEAN\n",
       "16              VALUE-MEAN\n",
       "17         SATURATION-MEAN\n",
       "18                HUE-MEAN\n",
       "Name: 0, dtype: object"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "terms[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Section a)\n",
    "Min-Max normalization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>REGION-CENTROID-COL</th>\n",
       "      <th>REGION-CENTROID-ROW</th>\n",
       "      <th>REGION-PIXEL-COUNT</th>\n",
       "      <th>SHORT-LINE-DENSITY-5</th>\n",
       "      <th>SHORT-LINE-DENSITY-2</th>\n",
       "      <th>VEDGE-MEAN</th>\n",
       "      <th>VEDGE-SD</th>\n",
       "      <th>HEDGE-MEAN</th>\n",
       "      <th>HEDGE-SD</th>\n",
       "      <th>INTENSITY-MEAN</th>\n",
       "      <th>RAWRED-MEAN</th>\n",
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       "      <th>HUE-MEAN</th>\n",
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       "      <td>0.027329</td>\n",
       "      <td>0.000856</td>\n",
       "      <td>0.090111</td>\n",
       "      <td>0.079417</td>\n",
       "      <td>0.061119</td>\n",
       "      <td>0.130943</td>\n",
       "      <td>0.731343</td>\n",
       "      <td>0.014118</td>\n",
       "      <td>0.872865</td>\n",
       "      <td>0.123711</td>\n",
       "      <td>0.508139</td>\n",
       "      <td>0.831849</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.335968</td>\n",
       "      <td>0.733333</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.038023</td>\n",
       "      <td>0.000726</td>\n",
       "      <td>0.032298</td>\n",
       "      <td>0.000541</td>\n",
       "      <td>0.095791</td>\n",
       "      <td>0.085089</td>\n",
       "      <td>0.068483</td>\n",
       "      <td>0.134840</td>\n",
       "      <td>0.729478</td>\n",
       "      <td>0.023529</td>\n",
       "      <td>0.859583</td>\n",
       "      <td>0.127393</td>\n",
       "      <td>0.463329</td>\n",
       "      <td>0.836986</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.885375</td>\n",
       "      <td>0.970833</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.115970</td>\n",
       "      <td>0.002213</td>\n",
       "      <td>0.067081</td>\n",
       "      <td>0.001097</td>\n",
       "      <td>0.085463</td>\n",
       "      <td>0.075365</td>\n",
       "      <td>0.061856</td>\n",
       "      <td>0.120031</td>\n",
       "      <td>0.736940</td>\n",
       "      <td>0.038824</td>\n",
       "      <td>0.827324</td>\n",
       "      <td>0.113402</td>\n",
       "      <td>0.480149</td>\n",
       "      <td>0.844782</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.181818</td>\n",
       "      <td>0.920833</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.043726</td>\n",
       "      <td>0.001265</td>\n",
       "      <td>0.022360</td>\n",
       "      <td>0.000645</td>\n",
       "      <td>0.088562</td>\n",
       "      <td>0.080227</td>\n",
       "      <td>0.059647</td>\n",
       "      <td>0.127046</td>\n",
       "      <td>0.748134</td>\n",
       "      <td>0.014118</td>\n",
       "      <td>0.855787</td>\n",
       "      <td>0.120029</td>\n",
       "      <td>0.500966</td>\n",
       "      <td>0.825889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.379447</td>\n",
       "      <td>0.729167</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.039924</td>\n",
       "      <td>0.000697</td>\n",
       "      <td>0.026087</td>\n",
       "      <td>0.000725</td>\n",
       "      <td>0.108701</td>\n",
       "      <td>0.101297</td>\n",
       "      <td>0.078056</td>\n",
       "      <td>0.148090</td>\n",
       "      <td>0.748134</td>\n",
       "      <td>0.010588</td>\n",
       "      <td>0.861480</td>\n",
       "      <td>0.139912</td>\n",
       "      <td>0.442661</td>\n",
       "      <td>0.823924</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "0  REGION-CENTROID-COL  REGION-CENTROID-ROW  REGION-PIXEL-COUNT  \\\n",
       "0             0.430830             0.741667                 0.0   \n",
       "1             0.335968             0.733333                 0.0   \n",
       "2             0.885375             0.970833                 0.0   \n",
       "3             0.181818             0.920833                 0.0   \n",
       "4             0.379447             0.729167                 0.0   \n",
       "\n",
       "0  SHORT-LINE-DENSITY-5  SHORT-LINE-DENSITY-2  VEDGE-MEAN  VEDGE-SD  \\\n",
       "0                   0.0                   0.0    0.034221  0.000672   \n",
       "1                   0.0                   0.0    0.038023  0.000726   \n",
       "2                   0.0                   0.0    0.115970  0.002213   \n",
       "3                   0.0                   0.0    0.043726  0.001265   \n",
       "4                   0.0                   0.0    0.039924  0.000697   \n",
       "\n",
       "0  HEDGE-MEAN  HEDGE-SD  INTENSITY-MEAN  RAWRED-MEAN  RAWBLUE-MEAN  \\\n",
       "0    0.027329  0.000856        0.090111     0.079417      0.061119   \n",
       "1    0.032298  0.000541        0.095791     0.085089      0.068483   \n",
       "2    0.067081  0.001097        0.085463     0.075365      0.061856   \n",
       "3    0.022360  0.000645        0.088562     0.080227      0.059647   \n",
       "4    0.026087  0.000725        0.108701     0.101297      0.078056   \n",
       "\n",
       "0  RAWGREEN-MEAN  EXRED-MEAN  EXBLUE-MEAN  EXGREEN-MEAN  VALUE-MEAN  \\\n",
       "0       0.130943    0.731343     0.014118      0.872865    0.123711   \n",
       "1       0.134840    0.729478     0.023529      0.859583    0.127393   \n",
       "2       0.120031    0.736940     0.038824      0.827324    0.113402   \n",
       "3       0.127046    0.748134     0.014118      0.855787    0.120029   \n",
       "4       0.148090    0.748134     0.010588      0.861480    0.139912   \n",
       "\n",
       "0  SATURATION-MEAN  HUE-MEAN  \n",
       "0         0.508139  0.831849  \n",
       "1         0.463329  0.836986  \n",
       "2         0.480149  0.844782  \n",
       "3         0.500966  0.825889  \n",
       "4         0.442661  0.823924  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import preprocessing\n",
    "min_max_scaler = preprocessing.MinMaxScaler().fit(vs_train)\n",
    "\n",
    "vs_train_norm = min_max_scaler.transform(vs_train)\n",
    "vs_train_norm = pd.DataFrame(vs_train_norm, columns=terms[0], index=vs_train.index)\n",
    "vs_train_norm.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above cell shows the output of min max normalization using sklearn.\n",
    "\n",
    "#### Section b)\n",
    "Implementing the Kmeans in scikit-learn with 7 clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "kmeans = KMeans(n_clusters=7, max_iter=500, verbose=1) # initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialization complete\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 0, inertia 427.2574715301479\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 1, inertia 382.9833496864014\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 2, inertia 380.21473479066503\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 3, inertia 379.7694564721132\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 4, inertia 379.6870121350356\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 5, inertia 379.6474769842597\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 6, inertia 379.6474769842597\n",
      "center shift 0.000000e+00 within tolerance 4.150157e-06\n",
      "Initialization complete\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 0, inertia 436.8456357486948\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 1, inertia 412.0201773053636\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 2, inertia 402.14103569980455\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 3, inertia 399.123013017066\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 4, inertia 397.7236777050305\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 5, inertia 396.61353596529597\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 6, inertia 395.6640008149166\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 7, inertia 395.283642614249\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 8, inertia 395.1996052187011\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 9, inertia 395.18646302409934\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 10, inertia 395.1772772056891\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 11, inertia 395.16582019544535\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 12, inertia 395.15913049186287\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 13, inertia 395.1541110283721\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 14, inertia 395.1394076360783\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 15, inertia 395.115462255389\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 16, inertia 395.1031771192388\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 17, inertia 395.09872752829835\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 18, inertia 395.09872752829835\n",
      "center shift 0.000000e+00 within tolerance 4.150157e-06\n",
      "Initialization complete\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 0, inertia 396.7406863115559\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 1, inertia 371.8433634379944\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 2, inertia 363.62627681200496\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 3, inertia 356.25817160874533\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 4, inertia 352.44314569495236\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 5, inertia 350.8297053805691\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 6, inertia 350.3175571048273\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 7, inertia 350.1327401061413\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 8, inertia 350.0646107678915\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 9, inertia 350.0208034547549\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 10, inertia 350.0115747924538\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 11, inertia 350.0115747924538\n",
      "center shift 0.000000e+00 within tolerance 4.150157e-06\n",
      "Initialization complete\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 0, inertia 386.060137921482\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 1, inertia 367.59973933686723\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 2, inertia 364.18498507155175\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 3, inertia 362.17167536576153\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 4, inertia 359.94438591045974\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 5, inertia 356.68363206613907\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 6, inertia 354.13022053495234\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 7, inertia 351.86616551950897\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 8, inertia 350.6406155871531\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 9, inertia 350.2422008596784\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 10, inertia 350.09078346400395\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 11, inertia 350.047083312248\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 12, inertia 350.0142970109002\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 13, inertia 350.0129027194548\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 14, inertia 350.0129027194548\n",
      "center shift 0.000000e+00 within tolerance 4.150157e-06\n",
      "Initialization complete\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 0, inertia 405.40988216119274\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 1, inertia 396.9357709334206\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 2, inertia 394.41591511190177\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 3, inertia 393.30835707932306\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 4, inertia 392.86947943863674\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
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      "center shift 1.794610e-03 within tolerance 4.150157e-06\n",
      "Initialization complete\n",
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      "Iteration 0, inertia 403.8748364886466\n",
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      "center shift 0.000000e+00 within tolerance 4.150157e-06\n",
      "Initialization complete\n",
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      "Iteration 0, inertia 476.0085932182146\n",
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      "end inner loop\n",
      "Iteration 18, inertia 396.2009231351983\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "start iteration\n",
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      "end inner loop\n",
      "Iteration 44, inertia 390.48377411374963\n",
      "center shift 1.790944e-03 within tolerance 4.150157e-06\n",
      "Initialization complete\n",
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      "end inner loop\n",
      "Iteration 0, inertia 404.3816084557782\n",
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      "end inner loop\n",
      "Iteration 10, inertia 350.0129027194548\n",
      "center shift 0.000000e+00 within tolerance 4.150157e-06\n",
      "Initialization complete\n",
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      "done sorting\n",
      "end inner loop\n",
      "Iteration 0, inertia 392.2528912486433\n",
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      "Iteration 15, inertia 370.3658750061023\n",
      "center shift 0.000000e+00 within tolerance 4.150157e-06\n",
      "Initialization complete\n",
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      "Iteration 0, inertia 448.00818298902266\n",
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      "Iteration 16, inertia 370.358575433164\n",
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      "done sorting\n",
      "end inner loop\n",
      "Iteration 17, inertia 370.358575433164\n",
      "center shift 0.000000e+00 within tolerance 4.150157e-06\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=500,\n",
       "       n_clusters=7, n_init=10, n_jobs=None, precompute_distances='auto',\n",
       "       random_state=None, tol=0.0001, verbose=1)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans.fit(vs_train_norm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "clusters = kmeans.predict(vs_train_norm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<p>2100 rows × 1 columns</p>\n",
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      "text/plain": [
       "      Cluster\n",
       "0           2\n",
       "1           2\n",
       "2           2\n",
       "3           2\n",
       "4           2\n",
       "...       ...\n",
       "2095        5\n",
       "2096        0\n",
       "2097        6\n",
       "2098        6\n",
       "2099        0\n",
       "\n",
       "[2100 rows x 1 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(clusters, columns=[\"Cluster\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Following are the cluster associated with each row."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>0.39</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.18</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.72</td>\n",
       "      <td>0.34</td>\n",
       "      <td>0.35</td>\n",
       "      <td>0.18</td>\n",
       "      <td>0.41</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.75</td>\n",
       "      <td>0.53</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.30</td>\n",
       "      <td>0.28</td>\n",
       "      <td>0.35</td>\n",
       "      <td>0.26</td>\n",
       "      <td>0.59</td>\n",
       "      <td>0.45</td>\n",
       "      <td>0.31</td>\n",
       "      <td>0.35</td>\n",
       "      <td>0.30</td>\n",
       "      <td>0.16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.51</td>\n",
       "      <td>0.81</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.14</td>\n",
       "      <td>0.68</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.82</td>\n",
       "      <td>0.13</td>\n",
       "      <td>0.41</td>\n",
       "      <td>0.89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.54</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.82</td>\n",
       "      <td>0.78</td>\n",
       "      <td>0.89</td>\n",
       "      <td>0.79</td>\n",
       "      <td>0.27</td>\n",
       "      <td>0.67</td>\n",
       "      <td>0.29</td>\n",
       "      <td>0.89</td>\n",
       "      <td>0.21</td>\n",
       "      <td>0.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.30</td>\n",
       "      <td>0.53</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.40</td>\n",
       "      <td>0.37</td>\n",
       "      <td>0.47</td>\n",
       "      <td>0.35</td>\n",
       "      <td>0.50</td>\n",
       "      <td>0.57</td>\n",
       "      <td>0.21</td>\n",
       "      <td>0.47</td>\n",
       "      <td>0.30</td>\n",
       "      <td>0.16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.46</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.77</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.51</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.80</td>\n",
       "      <td>0.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.77</td>\n",
       "      <td>0.43</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.04</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.78</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.49</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.54</td>\n",
       "      <td>0.24</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "0  REGION-CENTROID-COL  REGION-CENTROID-ROW  REGION-PIXEL-COUNT  \\\n",
       "0                 0.25                 0.39                0.00   \n",
       "1                 0.75                 0.53                0.00   \n",
       "2                 0.51                 0.81                0.00   \n",
       "3                 0.54                 0.15                0.00   \n",
       "4                 0.30                 0.53                0.00   \n",
       "5                 0.25                 0.46                0.00   \n",
       "6                 0.77                 0.43                0.00   \n",
       "\n",
       "0  SHORT-LINE-DENSITY-5  SHORT-LINE-DENSITY-2  VEDGE-MEAN  VEDGE-SD  \\\n",
       "0                  0.08                  0.02        0.08      0.00   \n",
       "1                  0.04                  0.04        0.11      0.02   \n",
       "2                  0.08                  0.01        0.05      0.00   \n",
       "3                  0.03                  0.00        0.03      0.00   \n",
       "4                  0.05                  0.05        0.10      0.01   \n",
       "5                  0.03                  0.01        0.04      0.00   \n",
       "6                  0.01                  0.02        0.04      0.00   \n",
       "\n",
       "0  HEDGE-MEAN  HEDGE-SD  INTENSITY-MEAN  RAWRED-MEAN  RAWBLUE-MEAN  \\\n",
       "0        0.06      0.01            0.15         0.14          0.18   \n",
       "1        0.11      0.02            0.30         0.28          0.35   \n",
       "2        0.05      0.00            0.11         0.09          0.09   \n",
       "3        0.03      0.00            0.82         0.78          0.89   \n",
       "4        0.08      0.01            0.40         0.37          0.47   \n",
       "5        0.03      0.00            0.03         0.02          0.04   \n",
       "6        0.02      0.00            0.04         0.03          0.06   \n",
       "\n",
       "0  RAWGREEN-MEAN  EXRED-MEAN  EXBLUE-MEAN  EXGREEN-MEAN  VALUE-MEAN  \\\n",
       "0           0.12        0.72         0.34          0.35        0.18   \n",
       "1           0.26        0.59         0.45          0.31        0.35   \n",
       "2           0.14        0.68         0.08          0.82        0.13   \n",
       "3           0.79        0.27         0.67          0.29        0.89   \n",
       "4           0.35        0.50         0.57          0.21        0.47   \n",
       "5           0.02        0.77         0.22          0.51        0.04   \n",
       "6           0.03        0.78         0.22          0.49        0.06   \n",
       "\n",
       "0  SATURATION-MEAN  HUE-MEAN  \n",
       "0             0.41      0.20  \n",
       "1             0.30      0.16  \n",
       "2             0.41      0.89  \n",
       "3             0.21      0.13  \n",
       "4             0.30      0.16  \n",
       "5             0.80      0.18  \n",
       "6             0.54      0.24  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.options.display.float_format='{:,.2f}'.format\n",
    "\n",
    "centroids = pd.DataFrame(kmeans.cluster_centers_, columns=terms[0])\n",
    "centroids"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Following are the cluster centroids for the 7 clusters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cluster_sizes(clusters,data):\n",
    "    #clusters is an array of cluster labels for each instance in the data\n",
    "    \n",
    "    size = {}\n",
    "    cluster_labels = np.unique(clusters)\n",
    "    n_clusters = cluster_labels.shape[0]\n",
    "\n",
    "    for c in cluster_labels:\n",
    "        size[c] = len(data[clusters == c])\n",
    "    return size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of Cluster 0 =  335\n",
      "Size of Cluster 1 =  332\n",
      "Size of Cluster 2 =  297\n",
      "Size of Cluster 3 =  300\n",
      "Size of Cluster 4 =  236\n",
      "Size of Cluster 5 =  291\n",
      "Size of Cluster 6 =  309\n"
     ]
    }
   ],
   "source": [
    "size = cluster_sizes(clusters,vs_train_norm)\n",
    "\n",
    "for c in size.keys():\n",
    "    print(\"Size of Cluster\", c, \"= \", size[c])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Number of records in each cluster\n",
    "##### Silhouette analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.57236961 0.5609926  0.46537332 0.49551578 0.57187855 0.55971567\n",
      " 0.54247867 0.41212038 0.51997981 0.46760414 0.48688779 0.49140278\n",
      " 0.58398756 0.56254708 0.37898897 0.5311416  0.5484396  0.4226305\n",
      " 0.41603628 0.40351227]\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "silhouettes = metrics.silhouette_samples(vs_train_norm, clusters)\n",
    "print(silhouettes[:20])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.33207429088953827\n"
     ]
    }
   ],
   "source": [
    "print(silhouettes.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mean value for silhouettes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_silhouettes(data, clusters, metric='euclidean'):\n",
    "    \n",
    "    from matplotlib import cm\n",
    "    from sklearn.metrics import silhouette_samples\n",
    "\n",
    "    cluster_labels = np.unique(clusters)\n",
    "    n_clusters = cluster_labels.shape[0]\n",
    "    silhouette_vals = metrics.silhouette_samples(data, clusters, metric='euclidean')\n",
    "    c_ax_lower, c_ax_upper = 0, 0\n",
    "    cticks = []\n",
    "    for i, k in enumerate(cluster_labels):\n",
    "        c_silhouette_vals = silhouette_vals[clusters == k]\n",
    "        c_silhouette_vals.sort()\n",
    "        c_ax_upper += len(c_silhouette_vals)\n",
    "        color = cm.jet(float(i) / n_clusters)\n",
    "        pl.barh(range(c_ax_lower, c_ax_upper), c_silhouette_vals, height=1.0, \n",
    "                      edgecolor='none', color=color)\n",
    "\n",
    "        cticks.append((c_ax_lower + c_ax_upper) / 2)\n",
    "        c_ax_lower += len(c_silhouette_vals)\n",
    "    \n",
    "    silhouette_avg = np.mean(silhouette_vals)\n",
    "    pl.axvline(silhouette_avg, color=\"red\", linestyle=\"--\") \n",
    "\n",
    "    pl.yticks(cticks, cluster_labels)\n",
    "    pl.ylabel('Cluster')\n",
    "    pl.xlabel('Silhouette coefficient')\n",
    "    pl.title('Silhouette coefficient vs. Cluster')\n",
    "    pl.tight_layout()\n",
    "    #pl.savefig('images/11_04.png', dpi=300)\n",
    "    pl.show()\n",
    "    \n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plot_silhouettes(vs_train_norm, clusters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above cell shows the plot of various clusters vs. the Silhouette Coefficient. We see all the clusters are above the mean line without much interference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2100, 2)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vs_target = pd.read_csv(\"C:/Users/USER/Desktop/DSC/DSC_478 Programming to Machine Learning A/Assignment/Assignment_4/Problem_1/segmentation_classes.txt\", sep ='\\t',header = None)\n",
    "vs_target.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0       0\n",
      "1       0\n",
      "2       0\n",
      "3       0\n",
      "4       0\n",
      "       ..\n",
      "2095    3\n",
      "2096    3\n",
      "2097    3\n",
      "2098    3\n",
      "2099    3\n",
      "Name: 1, Length: 2100, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "print(vs_target[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 2 2 ... 6 6 0]\n"
     ]
    }
   ],
   "source": [
    "print(clusters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Completeness and Homogeneity values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import completeness_score, homogeneity_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6117374684331666\n"
     ]
    }
   ],
   "source": [
    "print(completeness_score(vs_target[1],clusters))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A clustering result satisfies completeness if all the data points that are members of a given class are elements of the same cluster. If the value is 1, its a perfect cluster. The above cluster shows a completeness score of 0.61."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6100499914689615\n"
     ]
    }
   ],
   "source": [
    "print(homogeneity_score(vs_target[1],clusters))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A clustering result satisfies homogeneity if all of its clusters contain only data points which are members of a single class. The above cluster shows a homogeneity score of 0.61.\n",
    "#### Section c)\n",
    "PCA on the normalized image data matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import decomposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca = decomposition.PCA()\n",
    "DTtrans = pca.fit(vs_train_norm).transform(vs_train_norm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-6.89082181e-01  5.32951033e-01  2.46098334e-01 ... -3.11214118e-09\n",
      "   1.10281143e-08  3.79638070e-17]\n",
      " [-6.66919524e-01  5.10674647e-01  3.37971716e-01 ...  2.10646064e-09\n",
      "  -9.82754297e-09  4.42018916e-17]\n",
      " [-7.12027478e-01  7.70943647e-01 -1.55821890e-01 ...  3.11649253e-09\n",
      "   2.08700516e-09  3.83727704e-17]\n",
      " ...\n",
      " [-5.07744749e-01 -1.29415329e-01 -8.22455123e-02 ... -1.62643358e-09\n",
      "   3.38481914e-09  1.87065118e-17]\n",
      " [-4.79090569e-01 -8.63446712e-02 -1.58711407e-01 ... -4.39254155e-09\n",
      "   1.67499508e-09  1.31081034e-17]\n",
      " [-4.42253816e-01 -1.06225249e-01 -4.71272464e-02 ... -3.03500806e-09\n",
      "   3.98533628e-09  6.64530337e-17]]\n"
     ]
    }
   ],
   "source": [
    "print(DTtrans)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.6071 0.132  0.1012 0.0454 0.0355 0.0199 0.0189 0.0162 0.0107 0.0071 0.0039 0.0016 0.0005 0.     0.     0.     0.\n",
      " 0.     0.    ]\n"
     ]
    }
   ],
   "source": [
    "np.set_printoptions(suppress=True, precision=4, linewidth=120)\n",
    "print(pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to capture 95% variance, we would need at least 7 components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.08  0.    0.   -0.   -0.   -0.    0.   -0.    0.    0.    0.    0.01  0.01 -0.01  0.    0.\n",
      "   0.01 -0.01  0.  ]\n",
      " [ 0.    0.06  0.    0.    0.    0.   -0.    0.   -0.   -0.03 -0.03 -0.03 -0.03  0.02 -0.02  0.02\n",
      "  -0.03  0.    0.04]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.\n",
      "   0.    0.    0.  ]\n",
      " [-0.    0.    0.    0.02 -0.   -0.   -0.   -0.   -0.   -0.   -0.   -0.   -0.    0.   -0.    0.\n",
      "  -0.   -0.    0.  ]\n",
      " [-0.    0.    0.   -0.    0.01  0.    0.    0.    0.   -0.   -0.   -0.   -0.   -0.    0.   -0.\n",
      "  -0.    0.   -0.  ]\n",
      " [-0.    0.    0.   -0.    0.    0.01  0.    0.    0.   -0.   -0.    0.   -0.   -0.    0.   -0.\n",
      "   0.   -0.   -0.  ]\n",
      " [ 0.   -0.    0.   -0.    0.    0.    0.    0.    0.   -0.   -0.    0.    0.   -0.    0.    0.\n",
      "   0.    0.   -0.  ]\n",
      " [-0.    0.    0.   -0.    0.    0.    0.    0.01  0.    0.    0.    0.    0.   -0.    0.   -0.\n",
      "   0.   -0.   -0.  ]\n",
      " [ 0.   -0.    0.   -0.    0.    0.    0.    0.    0.    0.    0.    0.    0.   -0.    0.   -0.\n",
      "   0.   -0.   -0.  ]\n",
      " [ 0.   -0.03  0.   -0.   -0.   -0.   -0.    0.    0.    0.07  0.07  0.08  0.07 -0.04  0.04 -0.03\n",
      "   0.08 -0.04 -0.02]\n",
      " [ 0.   -0.03  0.   -0.   -0.   -0.   -0.    0.    0.    0.07  0.07  0.07  0.06 -0.04  0.04 -0.03\n",
      "   0.07 -0.04 -0.02]\n",
      " [ 0.01 -0.03  0.   -0.   -0.    0.    0.    0.    0.    0.08  0.07  0.08  0.07 -0.05  0.05 -0.03\n",
      "   0.08 -0.04 -0.03]\n",
      " [ 0.01 -0.03  0.   -0.   -0.   -0.    0.    0.    0.    0.07  0.06  0.07  0.06 -0.04  0.04 -0.02\n",
      "   0.07 -0.04 -0.02]\n",
      " [-0.01  0.02  0.    0.   -0.   -0.   -0.   -0.   -0.   -0.04 -0.04 -0.05 -0.04  0.04 -0.03  0.02\n",
      "  -0.05  0.02  0.01]\n",
      " [ 0.   -0.02  0.   -0.    0.    0.    0.    0.    0.    0.04  0.04  0.05  0.04 -0.03  0.04 -0.03\n",
      "   0.05 -0.02 -0.03]\n",
      " [ 0.    0.02  0.    0.   -0.   -0.    0.   -0.   -0.   -0.03 -0.03 -0.03 -0.02  0.02 -0.03  0.04\n",
      "  -0.03  0.01  0.04]\n",
      " [ 0.01 -0.03  0.   -0.   -0.    0.    0.    0.    0.    0.08  0.07  0.08  0.07 -0.05  0.05 -0.03\n",
      "   0.08 -0.04 -0.03]\n",
      " [-0.01  0.    0.   -0.    0.   -0.    0.   -0.   -0.   -0.04 -0.04 -0.04 -0.04  0.02 -0.02  0.01\n",
      "  -0.04  0.05 -0.  ]\n",
      " [ 0.    0.04  0.    0.   -0.   -0.   -0.   -0.   -0.   -0.02 -0.02 -0.03 -0.02  0.01 -0.03  0.04\n",
      "  -0.03 -0.    0.07]]\n"
     ]
    }
   ],
   "source": [
    "meanVals = np.mean(vs_train_norm, axis=0)\n",
    "meanRemoved = vs_train_norm - meanVals #remove mean\n",
    "covMat = np.cov(meanRemoved, rowvar=0)\n",
    "\n",
    "np.set_printoptions(precision=2,suppress=True,linewidth=100)\n",
    "print(covMat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy.linalg as la\n",
    "eigVals,eigVects = la.eig(np.mat(covMat))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.48 0.1  0.08 0.04 0.03 0.02 0.01 0.01 0.01 0.01 0.   0.   0.   0.   0.   0.   0.   0.   0.  ]\n"
     ]
    }
   ],
   "source": [
    "print(eigVals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.03 -0.35  0.93  0.04  0.01 -0.03  0.01  0.03 -0.   -0.02 -0.01  0.01 -0.    0.    0.    0.\n",
      "  -0.    0.    0.  ]\n",
      " [-0.19 -0.38 -0.12 -0.66  0.47 -0.14 -0.24  0.22  0.06  0.07  0.06 -0.04 -0.01 -0.01 -0.    0.\n",
      "  -0.    0.    0.  ]\n",
      " [ 0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.\n",
      "   0.    0.    1.  ]\n",
      " [-0.01 -0.03 -0.04 -0.03 -0.06 -0.6   0.72  0.32  0.06  0.08  0.01 -0.01 -0.   -0.   -0.    0.\n",
      "   0.   -0.    0.  ]\n",
      " [-0.    0.02  0.01 -0.1   0.09  0.44  0.28  0.32 -0.77  0.05  0.07 -0.    0.01  0.    0.   -0.\n",
      "   0.    0.    0.  ]\n",
      " [ 0.    0.02  0.01 -0.12  0.03  0.42  0.3   0.11  0.44 -0.34  0.55  0.28 -0.11 -0.01  0.    0.\n",
      "  -0.    0.    0.  ]\n",
      " [ 0.    0.01  0.01 -0.01  0.01  0.18  0.12  0.07  0.18 -0.14  0.05 -0.77  0.55  0.01 -0.   -0.\n",
      "  -0.    0.    0.  ]\n",
      " [ 0.01  0.   -0.   -0.14  0.03  0.33  0.19  0.16  0.29 -0.02 -0.77  0.29  0.21 -0.01  0.   -0.\n",
      "   0.   -0.    0.  ]\n",
      " [ 0.    0.    0.   -0.02  0.01  0.16  0.09  0.07  0.13 -0.05 -0.24 -0.49 -0.8   0.01  0.    0.\n",
      "   0.   -0.    0.  ]\n",
      " [ 0.38 -0.11 -0.06  0.09  0.05 -0.02 -0.08  0.16  0.01 -0.05  0.    0.   -0.   -0.21 -0.04  0.45\n",
      "   0.7  -0.36  0.  ]\n",
      " [ 0.36 -0.11 -0.07  0.09 -0.01 -0.04 -0.13  0.24  0.   -0.11 -0.    0.01 -0.   -0.21 -0.48  0.36\n",
      "  -0.43  0.44  0.  ]\n",
      " [ 0.41 -0.07 -0.04  0.03  0.08 -0.03 -0.04  0.07 -0.01 -0.06 -0.01 -0.   -0.   -0.22  0.81 -0.11\n",
      "  -0.17  0.25  0.  ]\n",
      " [ 0.36 -0.16 -0.08  0.14  0.06  0.01 -0.08  0.18  0.04  0.02  0.02  0.   -0.   -0.21 -0.23 -0.71\n",
      "  -0.09 -0.34  0.  ]\n",
      " [-0.24  0.06  0.    0.01 -0.39 -0.13 -0.31  0.5  -0.05 -0.42 -0.04  0.03 -0.    0.08  0.03 -0.24\n",
      "   0.28  0.29  0.  ]\n",
      " [ 0.26  0.18  0.08 -0.27  0.18 -0.04  0.18 -0.4  -0.08 -0.08 -0.04 -0.02  0.   -0.08 -0.23 -0.28\n",
      "   0.39  0.51  0.  ]\n",
      " [-0.18 -0.34 -0.13  0.43  0.11  0.2   0.03  0.14  0.17  0.55  0.1   0.    0.    0.05 -0.   -0.09\n",
      "   0.23  0.39  0.  ]\n",
      " [ 0.41 -0.1  -0.06  0.04  0.1  -0.02 -0.03  0.06 -0.   -0.07 -0.01  0.02  0.    0.89  0.   -0.\n",
      "  -0.    0.    0.  ]\n",
      " [-0.2   0.31  0.08  0.42  0.74 -0.12 -0.03  0.13 -0.01 -0.3  -0.06  0.03  0.   -0.01 -0.    0.\n",
      "  -0.    0.    0.  ]\n",
      " [-0.17 -0.64 -0.24  0.2  -0.01 -0.02  0.18 -0.35 -0.18 -0.5  -0.12  0.02  0.   -0.04 -0.   -0.\n",
      "  -0.    0.    0.  ]]\n"
     ]
    }
   ],
   "source": [
    "print(eigVects)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Following are the eigenvalues and eigenvectors associated with each component."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.48 0.1  0.08 0.04 0.03 0.02 0.01 0.01 0.01 0.01 0.   0.   0.   0.   0.   0.   0.   0.   0.  ]\n",
      "[60.71 13.2  10.12  4.54  3.55  1.99  1.89  1.62  1.07  0.71  0.39  0.16  0.05  0.    0.    0.\n",
      "  0.    0.    0.  ]\n"
     ]
    }
   ],
   "source": [
    "eigValInd = np.argsort(eigVals)  #sort, sort goes smallest to largest\n",
    "eigValInd = eigValInd[::-1]   #reverse\n",
    "sortedEigVals = eigVals[eigValInd]\n",
    "print(sortedEigVals)\n",
    "total = sum(sortedEigVals)\n",
    "varPercentage = sortedEigVals/total*100\n",
    "print(varPercentage)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to capture 95% variance, we would need at least 7 components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(range(1, 11), varPercentage[:10], marker='^')\n",
    "plt.xlabel('Principal Component Number')\n",
    "plt.ylabel('Percentage of Variance')\n",
    "plt.title ('Percentage of Variance vs. Principal Component Number')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following scree plot shows the curve flatening around 4 components. Since we need to capture 95% variance, we are consuming 7 components.\n",
    "#### Section d)\n",
    "Kmeans on the lower dimensional transformed data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca_95 = decomposition.PCA(n_components=7)\n",
    "DTtrans_95 = pca_95.fit(vs_train_norm).transform(vs_train_norm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using 7 components to transform the data into lower dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.69  0.53  0.25 ... -0.08  0.05 -0.05]\n",
      " [-0.67  0.51  0.34 ... -0.04  0.06 -0.04]\n",
      " [-0.71  0.77 -0.16 ... -0.17  0.04 -0.06]\n",
      " ...\n",
      " [-0.51 -0.13 -0.08 ... -0.03 -0.03 -0.11]\n",
      " [-0.48 -0.09 -0.16 ...  0.   -0.   -0.09]\n",
      " [-0.44 -0.11 -0.05 ...  0.02 -0.21  0.15]]\n"
     ]
    }
   ],
   "source": [
    "print(DTtrans_95)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Performing Kmeans on transformed data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "kmeans_95 = KMeans(n_clusters=7, max_iter=500, verbose=1) # initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialization complete\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 0, inertia 343.09233916385904\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 1, inertia 317.80398076147577\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 2, inertia 308.6480444995848\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 3, inertia 306.11918744229524\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 4, inertia 305.06644293296335\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 5, inertia 304.4112946111894\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 6, inertia 304.0531764291633\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 7, inertia 303.9891739498929\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 8, inertia 303.88361301412056\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 9, inertia 303.8300374152801\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 10, inertia 303.8230516732996\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 11, inertia 303.8230516732996\n",
      "center shift 0.000000e+00 within tolerance 1.081479e-05\n",
      "Initialization complete\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 0, inertia 314.63017214031305\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 1, inertia 305.6680196893339\n",
      "start iteration\n",
      "done sorting\n",
      "end inner loop\n",
      "Iteration 2, inertia 304.88754166286856\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "end inner loop\n",
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     ]
    },
    {
     "data": {
      "text/plain": [
       "KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=500,\n",
       "       n_clusters=7, n_init=10, n_jobs=None, precompute_distances='auto',\n",
       "       random_state=None, tol=0.0001, verbose=1)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans_95.fit(DTtrans_95)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "clusters_95 = kmeans_95.predict(DTtrans_95)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "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>Cluster</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2095</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2096</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2097</th>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2098</th>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2099</th>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2100 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Cluster\n",
       "0           3\n",
       "1           3\n",
       "2           3\n",
       "3           3\n",
       "4           3\n",
       "...       ...\n",
       "2095        0\n",
       "2096        2\n",
       "2097        6\n",
       "2098        6\n",
       "2099        2\n",
       "\n",
       "[2100 rows x 1 columns]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(clusters_95, columns=[\"Cluster\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Following are the clusters associated with lower dimensional transformed data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of Cluster 0 =  287\n",
      "Size of Cluster 1 =  238\n",
      "Size of Cluster 2 =  339\n",
      "Size of Cluster 3 =  297\n",
      "Size of Cluster 4 =  300\n",
      "Size of Cluster 5 =  328\n",
      "Size of Cluster 6 =  311\n"
     ]
    }
   ],
   "source": [
    "size = cluster_sizes(clusters_95,DTtrans_95)\n",
    "\n",
    "for c in size.keys():\n",
    "    print(\"Size of Cluster\", c, \"= \", size[c])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lower dimensional transformed data - Number of records in each cluster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.60</td>\n",
       "      <td>-0.36</td>\n",
       "      <td>0.11</td>\n",
       "      <td>-0.13</td>\n",
       "      <td>-0.13</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>-0.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.44</td>\n",
       "      <td>-0.10</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.23</td>\n",
       "      <td>-0.05</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.21</td>\n",
       "      <td>-0.25</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.13</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.62</td>\n",
       "      <td>0.64</td>\n",
       "      <td>0.20</td>\n",
       "      <td>-0.09</td>\n",
       "      <td>-0.07</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.41</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-0.17</td>\n",
       "      <td>-0.03</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>-0.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.18</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-0.27</td>\n",
       "      <td>0.18</td>\n",
       "      <td>0.03</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-0.51</td>\n",
       "      <td>-0.06</td>\n",
       "      <td>-0.34</td>\n",
       "      <td>-0.07</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.01</td>\n",
       "      <td>-0.03</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      0     1     2     3     4     5     6\n",
       "0 -0.60 -0.36  0.11 -0.13 -0.13 -0.02 -0.04\n",
       "1  0.44 -0.10  0.16  0.23 -0.05 -0.01  0.02\n",
       "2 -0.21 -0.25  0.15  0.06  0.13 -0.01  0.03\n",
       "3 -0.62  0.64  0.20 -0.09 -0.07  0.01  0.04\n",
       "4  1.41  0.09  0.04 -0.17 -0.03 -0.01 -0.02\n",
       "5  0.18  0.04 -0.27  0.18  0.03  0.02  0.00\n",
       "6 -0.51 -0.06 -0.34 -0.07  0.08  0.01 -0.03"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.options.display.float_format='{:,.2f}'.format\n",
    "\n",
    "centroids_95 = pd.DataFrame(kmeans_95.cluster_centers_)\n",
    "centroids_95"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lower dimensional transformed data - Following are the cluster centroids for the 7 clusters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.59 0.57 0.48 0.51 0.59 0.58 0.56 0.43 0.54 0.48 0.5  0.51 0.59 0.57 0.4  0.54 0.56 0.43 0.42\n",
      " 0.43]\n"
     ]
    }
   ],
   "source": [
    "silhouettes_95 = metrics.silhouette_samples(DTtrans_95, clusters_95)\n",
    "print(silhouettes_95[:20])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.35982029813495525\n"
     ]
    }
   ],
   "source": [
    "print(silhouettes_95.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lower dimensional transformed data - Mean value for silhouettes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plot_silhouettes(DTtrans_95, clusters_95)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lower dimensional transformed data - The above cell shows the plot of various clusters vs. the Silhouette Coefficient. We see all the clusters are above the mean line without much interference.\n",
    "##### Completeness and Homogeneity values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6107955063694606\n"
     ]
    }
   ],
   "source": [
    "print(completeness_score(vs_target[1],clusters_95))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A clustering result satisfies completeness if all the data points that are members of a given class are elements of the same cluster. If the value is 1, its a perfect cluster. The above cluster shows a completeness score of 0.61."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.609136404973329\n"
     ]
    }
   ],
   "source": [
    "print(homogeneity_score(vs_target[1],clusters_95))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A clustering result satisfies homogeneity if all of its clusters contain only data points which are members of a single class. The above cluster shows a homogeneity score of 0.61.\n",
    "\n",
    "We do not see any change in results with Kmeans performed on original data as well as lower dimensional transformed data. The Completeness and Homogeneity values on original data and lower dimensional transformed data are exactly the same."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}