CRIME (mODEL).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "crime= pd.read_csv(\"C:\\\\Users\\\\kumar\\\\Python Assign\\\\clustering\\\\Assignments\\\\crime_data.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>Murder</th>\n",
       "      <th>Assault</th>\n",
       "      <th>UrbanPop</th>\n",
       "      <th>Rape</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Alabama</td>\n",
       "      <td>13.2</td>\n",
       "      <td>236</td>\n",
       "      <td>58</td>\n",
       "      <td>21.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Alaska</td>\n",
       "      <td>10.0</td>\n",
       "      <td>263</td>\n",
       "      <td>48</td>\n",
       "      <td>44.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Arizona</td>\n",
       "      <td>8.1</td>\n",
       "      <td>294</td>\n",
       "      <td>80</td>\n",
       "      <td>31.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Arkansas</td>\n",
       "      <td>8.8</td>\n",
       "      <td>190</td>\n",
       "      <td>50</td>\n",
       "      <td>19.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>California</td>\n",
       "      <td>9.0</td>\n",
       "      <td>276</td>\n",
       "      <td>91</td>\n",
       "      <td>40.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Colorado</td>\n",
       "      <td>7.9</td>\n",
       "      <td>204</td>\n",
       "      <td>78</td>\n",
       "      <td>38.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Connecticut</td>\n",
       "      <td>3.3</td>\n",
       "      <td>110</td>\n",
       "      <td>77</td>\n",
       "      <td>11.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Delaware</td>\n",
       "      <td>5.9</td>\n",
       "      <td>238</td>\n",
       "      <td>72</td>\n",
       "      <td>15.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Florida</td>\n",
       "      <td>15.4</td>\n",
       "      <td>335</td>\n",
       "      <td>80</td>\n",
       "      <td>31.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Georgia</td>\n",
       "      <td>17.4</td>\n",
       "      <td>211</td>\n",
       "      <td>60</td>\n",
       "      <td>25.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Hawaii</td>\n",
       "      <td>5.3</td>\n",
       "      <td>46</td>\n",
       "      <td>83</td>\n",
       "      <td>20.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Idaho</td>\n",
       "      <td>2.6</td>\n",
       "      <td>120</td>\n",
       "      <td>54</td>\n",
       "      <td>14.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>Illinois</td>\n",
       "      <td>10.4</td>\n",
       "      <td>249</td>\n",
       "      <td>83</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>Indiana</td>\n",
       "      <td>7.2</td>\n",
       "      <td>113</td>\n",
       "      <td>65</td>\n",
       "      <td>21.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>Iowa</td>\n",
       "      <td>2.2</td>\n",
       "      <td>56</td>\n",
       "      <td>57</td>\n",
       "      <td>11.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>Kansas</td>\n",
       "      <td>6.0</td>\n",
       "      <td>115</td>\n",
       "      <td>66</td>\n",
       "      <td>18.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>Kentucky</td>\n",
       "      <td>9.7</td>\n",
       "      <td>109</td>\n",
       "      <td>52</td>\n",
       "      <td>16.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>Louisiana</td>\n",
       "      <td>15.4</td>\n",
       "      <td>249</td>\n",
       "      <td>66</td>\n",
       "      <td>22.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>Maine</td>\n",
       "      <td>2.1</td>\n",
       "      <td>83</td>\n",
       "      <td>51</td>\n",
       "      <td>7.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>Maryland</td>\n",
       "      <td>11.3</td>\n",
       "      <td>300</td>\n",
       "      <td>67</td>\n",
       "      <td>27.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>Massachusetts</td>\n",
       "      <td>4.4</td>\n",
       "      <td>149</td>\n",
       "      <td>85</td>\n",
       "      <td>16.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>Michigan</td>\n",
       "      <td>12.1</td>\n",
       "      <td>255</td>\n",
       "      <td>74</td>\n",
       "      <td>35.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>Minnesota</td>\n",
       "      <td>2.7</td>\n",
       "      <td>72</td>\n",
       "      <td>66</td>\n",
       "      <td>14.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>Mississippi</td>\n",
       "      <td>16.1</td>\n",
       "      <td>259</td>\n",
       "      <td>44</td>\n",
       "      <td>17.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>Missouri</td>\n",
       "      <td>9.0</td>\n",
       "      <td>178</td>\n",
       "      <td>70</td>\n",
       "      <td>28.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>Montana</td>\n",
       "      <td>6.0</td>\n",
       "      <td>109</td>\n",
       "      <td>53</td>\n",
       "      <td>16.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>Nebraska</td>\n",
       "      <td>4.3</td>\n",
       "      <td>102</td>\n",
       "      <td>62</td>\n",
       "      <td>16.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>Nevada</td>\n",
       "      <td>12.2</td>\n",
       "      <td>252</td>\n",
       "      <td>81</td>\n",
       "      <td>46.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>New Hampshire</td>\n",
       "      <td>2.1</td>\n",
       "      <td>57</td>\n",
       "      <td>56</td>\n",
       "      <td>9.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>New Jersey</td>\n",
       "      <td>7.4</td>\n",
       "      <td>159</td>\n",
       "      <td>89</td>\n",
       "      <td>18.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>New Mexico</td>\n",
       "      <td>11.4</td>\n",
       "      <td>285</td>\n",
       "      <td>70</td>\n",
       "      <td>32.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>New York</td>\n",
       "      <td>11.1</td>\n",
       "      <td>254</td>\n",
       "      <td>86</td>\n",
       "      <td>26.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>North Carolina</td>\n",
       "      <td>13.0</td>\n",
       "      <td>337</td>\n",
       "      <td>45</td>\n",
       "      <td>16.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>North Dakota</td>\n",
       "      <td>0.8</td>\n",
       "      <td>45</td>\n",
       "      <td>44</td>\n",
       "      <td>7.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>Ohio</td>\n",
       "      <td>7.3</td>\n",
       "      <td>120</td>\n",
       "      <td>75</td>\n",
       "      <td>21.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>Oklahoma</td>\n",
       "      <td>6.6</td>\n",
       "      <td>151</td>\n",
       "      <td>68</td>\n",
       "      <td>20.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>Oregon</td>\n",
       "      <td>4.9</td>\n",
       "      <td>159</td>\n",
       "      <td>67</td>\n",
       "      <td>29.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>Pennsylvania</td>\n",
       "      <td>6.3</td>\n",
       "      <td>106</td>\n",
       "      <td>72</td>\n",
       "      <td>14.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>Rhode Island</td>\n",
       "      <td>3.4</td>\n",
       "      <td>174</td>\n",
       "      <td>87</td>\n",
       "      <td>8.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>South Carolina</td>\n",
       "      <td>14.4</td>\n",
       "      <td>279</td>\n",
       "      <td>48</td>\n",
       "      <td>22.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>South Dakota</td>\n",
       "      <td>3.8</td>\n",
       "      <td>86</td>\n",
       "      <td>45</td>\n",
       "      <td>12.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>Tennessee</td>\n",
       "      <td>13.2</td>\n",
       "      <td>188</td>\n",
       "      <td>59</td>\n",
       "      <td>26.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>Texas</td>\n",
       "      <td>12.7</td>\n",
       "      <td>201</td>\n",
       "      <td>80</td>\n",
       "      <td>25.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>Utah</td>\n",
       "      <td>3.2</td>\n",
       "      <td>120</td>\n",
       "      <td>80</td>\n",
       "      <td>22.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>Vermont</td>\n",
       "      <td>2.2</td>\n",
       "      <td>48</td>\n",
       "      <td>32</td>\n",
       "      <td>11.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>Virginia</td>\n",
       "      <td>8.5</td>\n",
       "      <td>156</td>\n",
       "      <td>63</td>\n",
       "      <td>20.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>Washington</td>\n",
       "      <td>4.0</td>\n",
       "      <td>145</td>\n",
       "      <td>73</td>\n",
       "      <td>26.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>West Virginia</td>\n",
       "      <td>5.7</td>\n",
       "      <td>81</td>\n",
       "      <td>39</td>\n",
       "      <td>9.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>Wisconsin</td>\n",
       "      <td>2.6</td>\n",
       "      <td>53</td>\n",
       "      <td>66</td>\n",
       "      <td>10.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>Wyoming</td>\n",
       "      <td>6.8</td>\n",
       "      <td>161</td>\n",
       "      <td>60</td>\n",
       "      <td>15.6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Unnamed: 0  Murder  Assault  UrbanPop  Rape\n",
       "0          Alabama    13.2      236        58  21.2\n",
       "1           Alaska    10.0      263        48  44.5\n",
       "2          Arizona     8.1      294        80  31.0\n",
       "3         Arkansas     8.8      190        50  19.5\n",
       "4       California     9.0      276        91  40.6\n",
       "5         Colorado     7.9      204        78  38.7\n",
       "6      Connecticut     3.3      110        77  11.1\n",
       "7         Delaware     5.9      238        72  15.8\n",
       "8          Florida    15.4      335        80  31.9\n",
       "9          Georgia    17.4      211        60  25.8\n",
       "10          Hawaii     5.3       46        83  20.2\n",
       "11           Idaho     2.6      120        54  14.2\n",
       "12        Illinois    10.4      249        83  24.0\n",
       "13         Indiana     7.2      113        65  21.0\n",
       "14            Iowa     2.2       56        57  11.3\n",
       "15          Kansas     6.0      115        66  18.0\n",
       "16        Kentucky     9.7      109        52  16.3\n",
       "17       Louisiana    15.4      249        66  22.2\n",
       "18           Maine     2.1       83        51   7.8\n",
       "19        Maryland    11.3      300        67  27.8\n",
       "20   Massachusetts     4.4      149        85  16.3\n",
       "21        Michigan    12.1      255        74  35.1\n",
       "22       Minnesota     2.7       72        66  14.9\n",
       "23     Mississippi    16.1      259        44  17.1\n",
       "24        Missouri     9.0      178        70  28.2\n",
       "25         Montana     6.0      109        53  16.4\n",
       "26        Nebraska     4.3      102        62  16.5\n",
       "27          Nevada    12.2      252        81  46.0\n",
       "28   New Hampshire     2.1       57        56   9.5\n",
       "29      New Jersey     7.4      159        89  18.8\n",
       "30      New Mexico    11.4      285        70  32.1\n",
       "31        New York    11.1      254        86  26.1\n",
       "32  North Carolina    13.0      337        45  16.1\n",
       "33    North Dakota     0.8       45        44   7.3\n",
       "34            Ohio     7.3      120        75  21.4\n",
       "35        Oklahoma     6.6      151        68  20.0\n",
       "36          Oregon     4.9      159        67  29.3\n",
       "37    Pennsylvania     6.3      106        72  14.9\n",
       "38    Rhode Island     3.4      174        87   8.3\n",
       "39  South Carolina    14.4      279        48  22.5\n",
       "40    South Dakota     3.8       86        45  12.8\n",
       "41       Tennessee    13.2      188        59  26.9\n",
       "42           Texas    12.7      201        80  25.5\n",
       "43            Utah     3.2      120        80  22.9\n",
       "44         Vermont     2.2       48        32  11.2\n",
       "45        Virginia     8.5      156        63  20.7\n",
       "46      Washington     4.0      145        73  26.2\n",
       "47   West Virginia     5.7       81        39   9.3\n",
       "48       Wisconsin     2.6       53        66  10.8\n",
       "49         Wyoming     6.8      161        60  15.6"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "crime.drop(['Unnamed: 0'],inplace=True,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Murder</th>\n",
       "      <th>Assault</th>\n",
       "      <th>UrbanPop</th>\n",
       "      <th>Rape</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>13.2</td>\n",
       "      <td>236</td>\n",
       "      <td>58</td>\n",
       "      <td>21.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10.0</td>\n",
       "      <td>263</td>\n",
       "      <td>48</td>\n",
       "      <td>44.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.1</td>\n",
       "      <td>294</td>\n",
       "      <td>80</td>\n",
       "      <td>31.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8.8</td>\n",
       "      <td>190</td>\n",
       "      <td>50</td>\n",
       "      <td>19.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9.0</td>\n",
       "      <td>276</td>\n",
       "      <td>91</td>\n",
       "      <td>40.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>7.9</td>\n",
       "      <td>204</td>\n",
       "      <td>78</td>\n",
       "      <td>38.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3.3</td>\n",
       "      <td>110</td>\n",
       "      <td>77</td>\n",
       "      <td>11.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.9</td>\n",
       "      <td>238</td>\n",
       "      <td>72</td>\n",
       "      <td>15.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>15.4</td>\n",
       "      <td>335</td>\n",
       "      <td>80</td>\n",
       "      <td>31.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>17.4</td>\n",
       "      <td>211</td>\n",
       "      <td>60</td>\n",
       "      <td>25.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5.3</td>\n",
       "      <td>46</td>\n",
       "      <td>83</td>\n",
       "      <td>20.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>2.6</td>\n",
       "      <td>120</td>\n",
       "      <td>54</td>\n",
       "      <td>14.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>10.4</td>\n",
       "      <td>249</td>\n",
       "      <td>83</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>7.2</td>\n",
       "      <td>113</td>\n",
       "      <td>65</td>\n",
       "      <td>21.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>2.2</td>\n",
       "      <td>56</td>\n",
       "      <td>57</td>\n",
       "      <td>11.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>6.0</td>\n",
       "      <td>115</td>\n",
       "      <td>66</td>\n",
       "      <td>18.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>9.7</td>\n",
       "      <td>109</td>\n",
       "      <td>52</td>\n",
       "      <td>16.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>15.4</td>\n",
       "      <td>249</td>\n",
       "      <td>66</td>\n",
       "      <td>22.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>2.1</td>\n",
       "      <td>83</td>\n",
       "      <td>51</td>\n",
       "      <td>7.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>11.3</td>\n",
       "      <td>300</td>\n",
       "      <td>67</td>\n",
       "      <td>27.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>4.4</td>\n",
       "      <td>149</td>\n",
       "      <td>85</td>\n",
       "      <td>16.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>12.1</td>\n",
       "      <td>255</td>\n",
       "      <td>74</td>\n",
       "      <td>35.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>2.7</td>\n",
       "      <td>72</td>\n",
       "      <td>66</td>\n",
       "      <td>14.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>16.1</td>\n",
       "      <td>259</td>\n",
       "      <td>44</td>\n",
       "      <td>17.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>9.0</td>\n",
       "      <td>178</td>\n",
       "      <td>70</td>\n",
       "      <td>28.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>6.0</td>\n",
       "      <td>109</td>\n",
       "      <td>53</td>\n",
       "      <td>16.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>4.3</td>\n",
       "      <td>102</td>\n",
       "      <td>62</td>\n",
       "      <td>16.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>12.2</td>\n",
       "      <td>252</td>\n",
       "      <td>81</td>\n",
       "      <td>46.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>2.1</td>\n",
       "      <td>57</td>\n",
       "      <td>56</td>\n",
       "      <td>9.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>7.4</td>\n",
       "      <td>159</td>\n",
       "      <td>89</td>\n",
       "      <td>18.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>11.4</td>\n",
       "      <td>285</td>\n",
       "      <td>70</td>\n",
       "      <td>32.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>11.1</td>\n",
       "      <td>254</td>\n",
       "      <td>86</td>\n",
       "      <td>26.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>13.0</td>\n",
       "      <td>337</td>\n",
       "      <td>45</td>\n",
       "      <td>16.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>0.8</td>\n",
       "      <td>45</td>\n",
       "      <td>44</td>\n",
       "      <td>7.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>7.3</td>\n",
       "      <td>120</td>\n",
       "      <td>75</td>\n",
       "      <td>21.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>6.6</td>\n",
       "      <td>151</td>\n",
       "      <td>68</td>\n",
       "      <td>20.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>4.9</td>\n",
       "      <td>159</td>\n",
       "      <td>67</td>\n",
       "      <td>29.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>6.3</td>\n",
       "      <td>106</td>\n",
       "      <td>72</td>\n",
       "      <td>14.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>3.4</td>\n",
       "      <td>174</td>\n",
       "      <td>87</td>\n",
       "      <td>8.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>14.4</td>\n",
       "      <td>279</td>\n",
       "      <td>48</td>\n",
       "      <td>22.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>3.8</td>\n",
       "      <td>86</td>\n",
       "      <td>45</td>\n",
       "      <td>12.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>13.2</td>\n",
       "      <td>188</td>\n",
       "      <td>59</td>\n",
       "      <td>26.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>12.7</td>\n",
       "      <td>201</td>\n",
       "      <td>80</td>\n",
       "      <td>25.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>3.2</td>\n",
       "      <td>120</td>\n",
       "      <td>80</td>\n",
       "      <td>22.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>2.2</td>\n",
       "      <td>48</td>\n",
       "      <td>32</td>\n",
       "      <td>11.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>8.5</td>\n",
       "      <td>156</td>\n",
       "      <td>63</td>\n",
       "      <td>20.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>4.0</td>\n",
       "      <td>145</td>\n",
       "      <td>73</td>\n",
       "      <td>26.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>5.7</td>\n",
       "      <td>81</td>\n",
       "      <td>39</td>\n",
       "      <td>9.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>2.6</td>\n",
       "      <td>53</td>\n",
       "      <td>66</td>\n",
       "      <td>10.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>6.8</td>\n",
       "      <td>161</td>\n",
       "      <td>60</td>\n",
       "      <td>15.6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Murder  Assault  UrbanPop  Rape\n",
       "0     13.2      236        58  21.2\n",
       "1     10.0      263        48  44.5\n",
       "2      8.1      294        80  31.0\n",
       "3      8.8      190        50  19.5\n",
       "4      9.0      276        91  40.6\n",
       "5      7.9      204        78  38.7\n",
       "6      3.3      110        77  11.1\n",
       "7      5.9      238        72  15.8\n",
       "8     15.4      335        80  31.9\n",
       "9     17.4      211        60  25.8\n",
       "10     5.3       46        83  20.2\n",
       "11     2.6      120        54  14.2\n",
       "12    10.4      249        83  24.0\n",
       "13     7.2      113        65  21.0\n",
       "14     2.2       56        57  11.3\n",
       "15     6.0      115        66  18.0\n",
       "16     9.7      109        52  16.3\n",
       "17    15.4      249        66  22.2\n",
       "18     2.1       83        51   7.8\n",
       "19    11.3      300        67  27.8\n",
       "20     4.4      149        85  16.3\n",
       "21    12.1      255        74  35.1\n",
       "22     2.7       72        66  14.9\n",
       "23    16.1      259        44  17.1\n",
       "24     9.0      178        70  28.2\n",
       "25     6.0      109        53  16.4\n",
       "26     4.3      102        62  16.5\n",
       "27    12.2      252        81  46.0\n",
       "28     2.1       57        56   9.5\n",
       "29     7.4      159        89  18.8\n",
       "30    11.4      285        70  32.1\n",
       "31    11.1      254        86  26.1\n",
       "32    13.0      337        45  16.1\n",
       "33     0.8       45        44   7.3\n",
       "34     7.3      120        75  21.4\n",
       "35     6.6      151        68  20.0\n",
       "36     4.9      159        67  29.3\n",
       "37     6.3      106        72  14.9\n",
       "38     3.4      174        87   8.3\n",
       "39    14.4      279        48  22.5\n",
       "40     3.8       86        45  12.8\n",
       "41    13.2      188        59  26.9\n",
       "42    12.7      201        80  25.5\n",
       "43     3.2      120        80  22.9\n",
       "44     2.2       48        32  11.2\n",
       "45     8.5      156        63  20.7\n",
       "46     4.0      145        73  26.2\n",
       "47     5.7       81        39   9.3\n",
       "48     2.6       53        66  10.8\n",
       "49     6.8      161        60  15.6"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Murder      0\n",
       "Assault     0\n",
       "UrbanPop    0\n",
       "Rape        0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crime.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 4)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crime.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### NO NAN VALUES ... IF NAN VALUES ARE PRESENT REPLACE WITH MEAN OR MODE ACCORDINGLY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>Murder</th>\n",
       "      <th>Assault</th>\n",
       "      <th>UrbanPop</th>\n",
       "      <th>Rape</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>50.00000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>7.78800</td>\n",
       "      <td>170.760000</td>\n",
       "      <td>65.540000</td>\n",
       "      <td>21.232000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>4.35551</td>\n",
       "      <td>83.337661</td>\n",
       "      <td>14.474763</td>\n",
       "      <td>9.366385</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.80000</td>\n",
       "      <td>45.000000</td>\n",
       "      <td>32.000000</td>\n",
       "      <td>7.300000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>4.07500</td>\n",
       "      <td>109.000000</td>\n",
       "      <td>54.500000</td>\n",
       "      <td>15.075000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>7.25000</td>\n",
       "      <td>159.000000</td>\n",
       "      <td>66.000000</td>\n",
       "      <td>20.100000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>11.25000</td>\n",
       "      <td>249.000000</td>\n",
       "      <td>77.750000</td>\n",
       "      <td>26.175000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>17.40000</td>\n",
       "      <td>337.000000</td>\n",
       "      <td>91.000000</td>\n",
       "      <td>46.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Murder     Assault   UrbanPop       Rape\n",
       "count  50.00000   50.000000  50.000000  50.000000\n",
       "mean    7.78800  170.760000  65.540000  21.232000\n",
       "std     4.35551   83.337661  14.474763   9.366385\n",
       "min     0.80000   45.000000  32.000000   7.300000\n",
       "25%     4.07500  109.000000  54.500000  15.075000\n",
       "50%     7.25000  159.000000  66.000000  20.100000\n",
       "75%    11.25000  249.000000  77.750000  26.175000\n",
       "max    17.40000  337.000000  91.000000  46.000000"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crime.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### FEATURE SACLING OR STANDARDIZING"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "WE USED STANDARD SCALER BECAUSE CLUSTERING IS DONE ON EUCLIDEAN DISTANCES AND STANDARD SCALER SHOULD BE USED IN PCA,CLUSTERING .REGRESSSION,SVM FOR FEATURE SCALING"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "MIN MAX SCALER SHOULD BE USED WHEN WE WANT DATA VALUES RANGE SHOULD BE BETWEEN 0 AND 1 ,LIKE IMAGE PROCESSING."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "DISADVANATAGE OF MIN MAX SCALER IS AS IT BOUND THE RANGE BETWEEN 0 AND 1 WE WILL HAVE LOWER STANDARD DEVIATIONS AND IT DOES NOT SHOW THE EFFECT OF OUTLIERS.."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler= StandardScaler()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\kumar\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:1: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n",
      "C:\\Users\\kumar\\Anaconda3\\lib\\site-packages\\sklearn\\preprocessing\\data.py:645: DataConversionWarning: Data with input dtype int64 were all converted to float64 by StandardScaler.\n",
      "  return self.partial_fit(X, y)\n",
      "C:\\Users\\kumar\\Anaconda3\\lib\\site-packages\\sklearn\\base.py:464: DataConversionWarning: Data with input dtype int64 were all converted to float64 by StandardScaler.\n",
      "  return self.fit(X, **fit_params).transform(X)\n",
      "C:\\Users\\kumar\\Anaconda3\\lib\\site-packages\\sklearn\\preprocessing\\data.py:645: DataConversionWarning: Data with input dtype int64 were all converted to float64 by StandardScaler.\n",
      "  return self.partial_fit(X, y)\n",
      "C:\\Users\\kumar\\Anaconda3\\lib\\site-packages\\sklearn\\base.py:464: DataConversionWarning: Data with input dtype int64 were all converted to float64 by StandardScaler.\n",
      "  return self.fit(X, **fit_params).transform(X)\n"
     ]
    }
   ],
   "source": [
    "crime.murder=scaler.fit_transform(crime[['Murder']])\n",
    "crime.Assault=scaler.fit_transform(crime[['Assault']])\n",
    "crime.UrbanPop=scaler.fit_transform(crime[['UrbanPop']])\n",
    "crime.Rape=scaler.fit_transform(crime[['Rape']])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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>Murder</th>\n",
       "      <th>Assault</th>\n",
       "      <th>UrbanPop</th>\n",
       "      <th>Rape</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>13.2</td>\n",
       "      <td>0.790787</td>\n",
       "      <td>-0.526195</td>\n",
       "      <td>-0.003451</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10.0</td>\n",
       "      <td>1.118060</td>\n",
       "      <td>-1.224067</td>\n",
       "      <td>2.509424</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.1</td>\n",
       "      <td>1.493817</td>\n",
       "      <td>1.009122</td>\n",
       "      <td>1.053466</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8.8</td>\n",
       "      <td>0.233212</td>\n",
       "      <td>-1.084492</td>\n",
       "      <td>-0.186794</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9.0</td>\n",
       "      <td>1.275635</td>\n",
       "      <td>1.776781</td>\n",
       "      <td>2.088814</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>7.9</td>\n",
       "      <td>0.402909</td>\n",
       "      <td>0.869548</td>\n",
       "      <td>1.883901</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3.3</td>\n",
       "      <td>-0.736484</td>\n",
       "      <td>0.799761</td>\n",
       "      <td>-1.092723</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.9</td>\n",
       "      <td>0.815030</td>\n",
       "      <td>0.450825</td>\n",
       "      <td>-0.585834</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>15.4</td>\n",
       "      <td>1.990786</td>\n",
       "      <td>1.009122</td>\n",
       "      <td>1.150530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>17.4</td>\n",
       "      <td>0.487757</td>\n",
       "      <td>-0.386621</td>\n",
       "      <td>0.492653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5.3</td>\n",
       "      <td>-1.512241</td>\n",
       "      <td>1.218484</td>\n",
       "      <td>-0.111300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>2.6</td>\n",
       "      <td>-0.615272</td>\n",
       "      <td>-0.805344</td>\n",
       "      <td>-0.758392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>10.4</td>\n",
       "      <td>0.948363</td>\n",
       "      <td>1.218484</td>\n",
       "      <td>0.298525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>7.2</td>\n",
       "      <td>-0.700121</td>\n",
       "      <td>-0.037685</td>\n",
       "      <td>-0.025021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>2.2</td>\n",
       "      <td>-1.391029</td>\n",
       "      <td>-0.595982</td>\n",
       "      <td>-1.071153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>6.0</td>\n",
       "      <td>-0.675878</td>\n",
       "      <td>0.032102</td>\n",
       "      <td>-0.348567</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>9.7</td>\n",
       "      <td>-0.748605</td>\n",
       "      <td>-0.944918</td>\n",
       "      <td>-0.531910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>15.4</td>\n",
       "      <td>0.948363</td>\n",
       "      <td>0.032102</td>\n",
       "      <td>0.104398</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>2.1</td>\n",
       "      <td>-1.063757</td>\n",
       "      <td>-1.014705</td>\n",
       "      <td>-1.448624</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>11.3</td>\n",
       "      <td>1.566544</td>\n",
       "      <td>0.101889</td>\n",
       "      <td>0.708350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>4.4</td>\n",
       "      <td>-0.263757</td>\n",
       "      <td>1.358058</td>\n",
       "      <td>-0.531910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>12.1</td>\n",
       "      <td>1.021090</td>\n",
       "      <td>0.590399</td>\n",
       "      <td>1.495646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>2.7</td>\n",
       "      <td>-1.197090</td>\n",
       "      <td>0.032102</td>\n",
       "      <td>-0.682898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>16.1</td>\n",
       "      <td>1.069575</td>\n",
       "      <td>-1.503215</td>\n",
       "      <td>-0.445631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>9.0</td>\n",
       "      <td>0.087757</td>\n",
       "      <td>0.311251</td>\n",
       "      <td>0.751490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>6.0</td>\n",
       "      <td>-0.748605</td>\n",
       "      <td>-0.875131</td>\n",
       "      <td>-0.521125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>4.3</td>\n",
       "      <td>-0.833454</td>\n",
       "      <td>-0.247047</td>\n",
       "      <td>-0.510340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>12.2</td>\n",
       "      <td>0.984726</td>\n",
       "      <td>1.078909</td>\n",
       "      <td>2.671197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>2.1</td>\n",
       "      <td>-1.378908</td>\n",
       "      <td>-0.665769</td>\n",
       "      <td>-1.265281</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>7.4</td>\n",
       "      <td>-0.142545</td>\n",
       "      <td>1.637207</td>\n",
       "      <td>-0.262288</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>11.4</td>\n",
       "      <td>1.384726</td>\n",
       "      <td>0.311251</td>\n",
       "      <td>1.172100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>11.1</td>\n",
       "      <td>1.008969</td>\n",
       "      <td>1.427845</td>\n",
       "      <td>0.525008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>13.0</td>\n",
       "      <td>2.015028</td>\n",
       "      <td>-1.433428</td>\n",
       "      <td>-0.553480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>0.8</td>\n",
       "      <td>-1.524362</td>\n",
       "      <td>-1.503215</td>\n",
       "      <td>-1.502548</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>7.3</td>\n",
       "      <td>-0.615272</td>\n",
       "      <td>0.660186</td>\n",
       "      <td>0.018119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>6.6</td>\n",
       "      <td>-0.239515</td>\n",
       "      <td>0.171676</td>\n",
       "      <td>-0.132870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>4.9</td>\n",
       "      <td>-0.142545</td>\n",
       "      <td>0.101889</td>\n",
       "      <td>0.870123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>6.3</td>\n",
       "      <td>-0.784969</td>\n",
       "      <td>0.450825</td>\n",
       "      <td>-0.682898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>3.4</td>\n",
       "      <td>0.039273</td>\n",
       "      <td>1.497632</td>\n",
       "      <td>-1.394700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>14.4</td>\n",
       "      <td>1.311999</td>\n",
       "      <td>-1.224067</td>\n",
       "      <td>0.136752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>3.8</td>\n",
       "      <td>-1.027393</td>\n",
       "      <td>-1.433428</td>\n",
       "      <td>-0.909380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>13.2</td>\n",
       "      <td>0.208970</td>\n",
       "      <td>-0.456408</td>\n",
       "      <td>0.611287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>12.7</td>\n",
       "      <td>0.366545</td>\n",
       "      <td>1.009122</td>\n",
       "      <td>0.460298</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>3.2</td>\n",
       "      <td>-0.615272</td>\n",
       "      <td>1.009122</td>\n",
       "      <td>0.179892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>2.2</td>\n",
       "      <td>-1.487999</td>\n",
       "      <td>-2.340661</td>\n",
       "      <td>-1.081938</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>8.5</td>\n",
       "      <td>-0.178909</td>\n",
       "      <td>-0.177259</td>\n",
       "      <td>-0.057376</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>4.0</td>\n",
       "      <td>-0.312242</td>\n",
       "      <td>0.520612</td>\n",
       "      <td>0.535792</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>5.7</td>\n",
       "      <td>-1.087999</td>\n",
       "      <td>-1.852151</td>\n",
       "      <td>-1.286851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>2.6</td>\n",
       "      <td>-1.427393</td>\n",
       "      <td>0.032102</td>\n",
       "      <td>-1.125078</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>6.8</td>\n",
       "      <td>-0.118303</td>\n",
       "      <td>-0.386621</td>\n",
       "      <td>-0.607404</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Murder   Assault  UrbanPop      Rape\n",
       "0     13.2  0.790787 -0.526195 -0.003451\n",
       "1     10.0  1.118060 -1.224067  2.509424\n",
       "2      8.1  1.493817  1.009122  1.053466\n",
       "3      8.8  0.233212 -1.084492 -0.186794\n",
       "4      9.0  1.275635  1.776781  2.088814\n",
       "5      7.9  0.402909  0.869548  1.883901\n",
       "6      3.3 -0.736484  0.799761 -1.092723\n",
       "7      5.9  0.815030  0.450825 -0.585834\n",
       "8     15.4  1.990786  1.009122  1.150530\n",
       "9     17.4  0.487757 -0.386621  0.492653\n",
       "10     5.3 -1.512241  1.218484 -0.111300\n",
       "11     2.6 -0.615272 -0.805344 -0.758392\n",
       "12    10.4  0.948363  1.218484  0.298525\n",
       "13     7.2 -0.700121 -0.037685 -0.025021\n",
       "14     2.2 -1.391029 -0.595982 -1.071153\n",
       "15     6.0 -0.675878  0.032102 -0.348567\n",
       "16     9.7 -0.748605 -0.944918 -0.531910\n",
       "17    15.4  0.948363  0.032102  0.104398\n",
       "18     2.1 -1.063757 -1.014705 -1.448624\n",
       "19    11.3  1.566544  0.101889  0.708350\n",
       "20     4.4 -0.263757  1.358058 -0.531910\n",
       "21    12.1  1.021090  0.590399  1.495646\n",
       "22     2.7 -1.197090  0.032102 -0.682898\n",
       "23    16.1  1.069575 -1.503215 -0.445631\n",
       "24     9.0  0.087757  0.311251  0.751490\n",
       "25     6.0 -0.748605 -0.875131 -0.521125\n",
       "26     4.3 -0.833454 -0.247047 -0.510340\n",
       "27    12.2  0.984726  1.078909  2.671197\n",
       "28     2.1 -1.378908 -0.665769 -1.265281\n",
       "29     7.4 -0.142545  1.637207 -0.262288\n",
       "30    11.4  1.384726  0.311251  1.172100\n",
       "31    11.1  1.008969  1.427845  0.525008\n",
       "32    13.0  2.015028 -1.433428 -0.553480\n",
       "33     0.8 -1.524362 -1.503215 -1.502548\n",
       "34     7.3 -0.615272  0.660186  0.018119\n",
       "35     6.6 -0.239515  0.171676 -0.132870\n",
       "36     4.9 -0.142545  0.101889  0.870123\n",
       "37     6.3 -0.784969  0.450825 -0.682898\n",
       "38     3.4  0.039273  1.497632 -1.394700\n",
       "39    14.4  1.311999 -1.224067  0.136752\n",
       "40     3.8 -1.027393 -1.433428 -0.909380\n",
       "41    13.2  0.208970 -0.456408  0.611287\n",
       "42    12.7  0.366545  1.009122  0.460298\n",
       "43     3.2 -0.615272  1.009122  0.179892\n",
       "44     2.2 -1.487999 -2.340661 -1.081938\n",
       "45     8.5 -0.178909 -0.177259 -0.057376\n",
       "46     4.0 -0.312242  0.520612  0.535792\n",
       "47     5.7 -1.087999 -1.852151 -1.286851\n",
       "48     2.6 -1.427393  0.032102 -1.125078\n",
       "49     6.8 -0.118303 -0.386621 -0.607404"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " crime"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### ELBOW CURVE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x24ed1d895c0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "\n",
    "k_rng=range(1,12)\n",
    "sse=[] # SUM OF SQUARED ERRORS\n",
    "for k in k_rng:\n",
    "    kmeans=KMeans(n_clusters=k)\n",
    "    kmeans.fit(crime)\n",
    "    sse.append(kmeans.inertia_)\n",
    "plt.xlabel('K')\n",
    "plt.ylabel('SSE')\n",
    "plt.plot(k_rng,sse)\n",
    "from kneed import KneeLocator\n",
    "kn = KneeLocator(k_rng, sse, curve='convex', direction='decreasing')\n",
    "print(kn.knee)\n",
    "plt.vlines(kn.knee, plt.ylim()[0], plt.ylim()[1], linestyles='dashed')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### FROM ELBOW CURVE WE GOT 3 CLUSTERS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "kmeans=KMeans(n_clusters=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=300,\n",
       "    n_clusters=3, n_init=10, n_jobs=None, precompute_distances='auto',\n",
       "    random_state=None, tol=0.0001, verbose=0)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans.fit(crime)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 1, 0, 0, 1, 0, 0, 2, 1, 2, 1, 2,\n",
       "       1, 2, 0, 0, 1, 2, 1, 0, 2, 2, 2, 1, 0, 0, 1, 0, 1, 2, 1, 2, 2, 1,\n",
       "       1, 0, 1, 1, 1, 0])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "labels=kmeans.labels_ \n",
    "labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 7.82777778e+00,  7.90032950e-02,  2.14324104e-01,\n",
       "         2.58980717e-01],\n",
       "       [ 3.31111111e+00, -9.20995794e-01, -2.16030013e-01,\n",
       "        -7.32628310e-01],\n",
       "       [ 1.34928571e+01,  1.08256178e+00,  2.19331056e-03,\n",
       "         6.08975478e-01]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "centers=kmeans.cluster_centers_\n",
    "centers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### LABELING THE DATA WITH THEIR  RESPECTIVE CLUSTER GROUP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "crime['cluster']=labels\n",
    "crime1=crime[crime.cluster==0]\n",
    "crime2=crime[crime.cluster==1]\n",
    "crime3=crime[crime.cluster==2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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>Murder</th>\n",
       "      <th>Assault</th>\n",
       "      <th>UrbanPop</th>\n",
       "      <th>Rape</th>\n",
       "      <th>cluster</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>13.2</td>\n",
       "      <td>0.790787</td>\n",
       "      <td>-0.526195</td>\n",
       "      <td>-0.003451</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10.0</td>\n",
       "      <td>1.118060</td>\n",
       "      <td>-1.224067</td>\n",
       "      <td>2.509424</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.1</td>\n",
       "      <td>1.493817</td>\n",
       "      <td>1.009122</td>\n",
       "      <td>1.053466</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8.8</td>\n",
       "      <td>0.233212</td>\n",
       "      <td>-1.084492</td>\n",
       "      <td>-0.186794</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9.0</td>\n",
       "      <td>1.275635</td>\n",
       "      <td>1.776781</td>\n",
       "      <td>2.088814</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>7.9</td>\n",
       "      <td>0.402909</td>\n",
       "      <td>0.869548</td>\n",
       "      <td>1.883901</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3.3</td>\n",
       "      <td>-0.736484</td>\n",
       "      <td>0.799761</td>\n",
       "      <td>-1.092723</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.9</td>\n",
       "      <td>0.815030</td>\n",
       "      <td>0.450825</td>\n",
       "      <td>-0.585834</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>15.4</td>\n",
       "      <td>1.990786</td>\n",
       "      <td>1.009122</td>\n",
       "      <td>1.150530</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>17.4</td>\n",
       "      <td>0.487757</td>\n",
       "      <td>-0.386621</td>\n",
       "      <td>0.492653</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5.3</td>\n",
       "      <td>-1.512241</td>\n",
       "      <td>1.218484</td>\n",
       "      <td>-0.111300</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>2.6</td>\n",
       "      <td>-0.615272</td>\n",
       "      <td>-0.805344</td>\n",
       "      <td>-0.758392</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>10.4</td>\n",
       "      <td>0.948363</td>\n",
       "      <td>1.218484</td>\n",
       "      <td>0.298525</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>7.2</td>\n",
       "      <td>-0.700121</td>\n",
       "      <td>-0.037685</td>\n",
       "      <td>-0.025021</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>2.2</td>\n",
       "      <td>-1.391029</td>\n",
       "      <td>-0.595982</td>\n",
       "      <td>-1.071153</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>6.0</td>\n",
       "      <td>-0.675878</td>\n",
       "      <td>0.032102</td>\n",
       "      <td>-0.348567</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>9.7</td>\n",
       "      <td>-0.748605</td>\n",
       "      <td>-0.944918</td>\n",
       "      <td>-0.531910</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>15.4</td>\n",
       "      <td>0.948363</td>\n",
       "      <td>0.032102</td>\n",
       "      <td>0.104398</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>2.1</td>\n",
       "      <td>-1.063757</td>\n",
       "      <td>-1.014705</td>\n",
       "      <td>-1.448624</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>11.3</td>\n",
       "      <td>1.566544</td>\n",
       "      <td>0.101889</td>\n",
       "      <td>0.708350</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>4.4</td>\n",
       "      <td>-0.263757</td>\n",
       "      <td>1.358058</td>\n",
       "      <td>-0.531910</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>12.1</td>\n",
       "      <td>1.021090</td>\n",
       "      <td>0.590399</td>\n",
       "      <td>1.495646</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>2.7</td>\n",
       "      <td>-1.197090</td>\n",
       "      <td>0.032102</td>\n",
       "      <td>-0.682898</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>16.1</td>\n",
       "      <td>1.069575</td>\n",
       "      <td>-1.503215</td>\n",
       "      <td>-0.445631</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>9.0</td>\n",
       "      <td>0.087757</td>\n",
       "      <td>0.311251</td>\n",
       "      <td>0.751490</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>6.0</td>\n",
       "      <td>-0.748605</td>\n",
       "      <td>-0.875131</td>\n",
       "      <td>-0.521125</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>4.3</td>\n",
       "      <td>-0.833454</td>\n",
       "      <td>-0.247047</td>\n",
       "      <td>-0.510340</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>12.2</td>\n",
       "      <td>0.984726</td>\n",
       "      <td>1.078909</td>\n",
       "      <td>2.671197</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>2.1</td>\n",
       "      <td>-1.378908</td>\n",
       "      <td>-0.665769</td>\n",
       "      <td>-1.265281</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>7.4</td>\n",
       "      <td>-0.142545</td>\n",
       "      <td>1.637207</td>\n",
       "      <td>-0.262288</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>11.4</td>\n",
       "      <td>1.384726</td>\n",
       "      <td>0.311251</td>\n",
       "      <td>1.172100</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>11.1</td>\n",
       "      <td>1.008969</td>\n",
       "      <td>1.427845</td>\n",
       "      <td>0.525008</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>13.0</td>\n",
       "      <td>2.015028</td>\n",
       "      <td>-1.433428</td>\n",
       "      <td>-0.553480</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>0.8</td>\n",
       "      <td>-1.524362</td>\n",
       "      <td>-1.503215</td>\n",
       "      <td>-1.502548</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>7.3</td>\n",
       "      <td>-0.615272</td>\n",
       "      <td>0.660186</td>\n",
       "      <td>0.018119</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>6.6</td>\n",
       "      <td>-0.239515</td>\n",
       "      <td>0.171676</td>\n",
       "      <td>-0.132870</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>4.9</td>\n",
       "      <td>-0.142545</td>\n",
       "      <td>0.101889</td>\n",
       "      <td>0.870123</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>6.3</td>\n",
       "      <td>-0.784969</td>\n",
       "      <td>0.450825</td>\n",
       "      <td>-0.682898</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>3.4</td>\n",
       "      <td>0.039273</td>\n",
       "      <td>1.497632</td>\n",
       "      <td>-1.394700</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>14.4</td>\n",
       "      <td>1.311999</td>\n",
       "      <td>-1.224067</td>\n",
       "      <td>0.136752</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>3.8</td>\n",
       "      <td>-1.027393</td>\n",
       "      <td>-1.433428</td>\n",
       "      <td>-0.909380</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>13.2</td>\n",
       "      <td>0.208970</td>\n",
       "      <td>-0.456408</td>\n",
       "      <td>0.611287</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>12.7</td>\n",
       "      <td>0.366545</td>\n",
       "      <td>1.009122</td>\n",
       "      <td>0.460298</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>3.2</td>\n",
       "      <td>-0.615272</td>\n",
       "      <td>1.009122</td>\n",
       "      <td>0.179892</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>2.2</td>\n",
       "      <td>-1.487999</td>\n",
       "      <td>-2.340661</td>\n",
       "      <td>-1.081938</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>8.5</td>\n",
       "      <td>-0.178909</td>\n",
       "      <td>-0.177259</td>\n",
       "      <td>-0.057376</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>4.0</td>\n",
       "      <td>-0.312242</td>\n",
       "      <td>0.520612</td>\n",
       "      <td>0.535792</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>5.7</td>\n",
       "      <td>-1.087999</td>\n",
       "      <td>-1.852151</td>\n",
       "      <td>-1.286851</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>2.6</td>\n",
       "      <td>-1.427393</td>\n",
       "      <td>0.032102</td>\n",
       "      <td>-1.125078</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>6.8</td>\n",
       "      <td>-0.118303</td>\n",
       "      <td>-0.386621</td>\n",
       "      <td>-0.607404</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Murder   Assault  UrbanPop      Rape  cluster\n",
       "0     13.2  0.790787 -0.526195 -0.003451        2\n",
       "1     10.0  1.118060 -1.224067  2.509424        0\n",
       "2      8.1  1.493817  1.009122  1.053466        0\n",
       "3      8.8  0.233212 -1.084492 -0.186794        0\n",
       "4      9.0  1.275635  1.776781  2.088814        0\n",
       "5      7.9  0.402909  0.869548  1.883901        0\n",
       "6      3.3 -0.736484  0.799761 -1.092723        1\n",
       "7      5.9  0.815030  0.450825 -0.585834        0\n",
       "8     15.4  1.990786  1.009122  1.150530        2\n",
       "9     17.4  0.487757 -0.386621  0.492653        2\n",
       "10     5.3 -1.512241  1.218484 -0.111300        1\n",
       "11     2.6 -0.615272 -0.805344 -0.758392        1\n",
       "12    10.4  0.948363  1.218484  0.298525        0\n",
       "13     7.2 -0.700121 -0.037685 -0.025021        0\n",
       "14     2.2 -1.391029 -0.595982 -1.071153        1\n",
       "15     6.0 -0.675878  0.032102 -0.348567        0\n",
       "16     9.7 -0.748605 -0.944918 -0.531910        0\n",
       "17    15.4  0.948363  0.032102  0.104398        2\n",
       "18     2.1 -1.063757 -1.014705 -1.448624        1\n",
       "19    11.3  1.566544  0.101889  0.708350        2\n",
       "20     4.4 -0.263757  1.358058 -0.531910        1\n",
       "21    12.1  1.021090  0.590399  1.495646        2\n",
       "22     2.7 -1.197090  0.032102 -0.682898        1\n",
       "23    16.1  1.069575 -1.503215 -0.445631        2\n",
       "24     9.0  0.087757  0.311251  0.751490        0\n",
       "25     6.0 -0.748605 -0.875131 -0.521125        0\n",
       "26     4.3 -0.833454 -0.247047 -0.510340        1\n",
       "27    12.2  0.984726  1.078909  2.671197        2\n",
       "28     2.1 -1.378908 -0.665769 -1.265281        1\n",
       "29     7.4 -0.142545  1.637207 -0.262288        0\n",
       "30    11.4  1.384726  0.311251  1.172100        2\n",
       "31    11.1  1.008969  1.427845  0.525008        2\n",
       "32    13.0  2.015028 -1.433428 -0.553480        2\n",
       "33     0.8 -1.524362 -1.503215 -1.502548        1\n",
       "34     7.3 -0.615272  0.660186  0.018119        0\n",
       "35     6.6 -0.239515  0.171676 -0.132870        0\n",
       "36     4.9 -0.142545  0.101889  0.870123        1\n",
       "37     6.3 -0.784969  0.450825 -0.682898        0\n",
       "38     3.4  0.039273  1.497632 -1.394700        1\n",
       "39    14.4  1.311999 -1.224067  0.136752        2\n",
       "40     3.8 -1.027393 -1.433428 -0.909380        1\n",
       "41    13.2  0.208970 -0.456408  0.611287        2\n",
       "42    12.7  0.366545  1.009122  0.460298        2\n",
       "43     3.2 -0.615272  1.009122  0.179892        1\n",
       "44     2.2 -1.487999 -2.340661 -1.081938        1\n",
       "45     8.5 -0.178909 -0.177259 -0.057376        0\n",
       "46     4.0 -0.312242  0.520612  0.535792        1\n",
       "47     5.7 -1.087999 -1.852151 -1.286851        1\n",
       "48     2.6 -1.427393  0.032102 -1.125078        1\n",
       "49     6.8 -0.118303 -0.386621 -0.607404        0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crime"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "DATA POINTS WHICH BELONG TO CLUSTER 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "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>Murder</th>\n",
       "      <th>Assault</th>\n",
       "      <th>UrbanPop</th>\n",
       "      <th>Rape</th>\n",
       "      <th>cluster</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10.0</td>\n",
       "      <td>1.118060</td>\n",
       "      <td>-1.224067</td>\n",
       "      <td>2.509424</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.1</td>\n",
       "      <td>1.493817</td>\n",
       "      <td>1.009122</td>\n",
       "      <td>1.053466</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8.8</td>\n",
       "      <td>0.233212</td>\n",
       "      <td>-1.084492</td>\n",
       "      <td>-0.186794</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9.0</td>\n",
       "      <td>1.275635</td>\n",
       "      <td>1.776781</td>\n",
       "      <td>2.088814</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>7.9</td>\n",
       "      <td>0.402909</td>\n",
       "      <td>0.869548</td>\n",
       "      <td>1.883901</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.9</td>\n",
       "      <td>0.815030</td>\n",
       "      <td>0.450825</td>\n",
       "      <td>-0.585834</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>10.4</td>\n",
       "      <td>0.948363</td>\n",
       "      <td>1.218484</td>\n",
       "      <td>0.298525</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>7.2</td>\n",
       "      <td>-0.700121</td>\n",
       "      <td>-0.037685</td>\n",
       "      <td>-0.025021</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>6.0</td>\n",
       "      <td>-0.675878</td>\n",
       "      <td>0.032102</td>\n",
       "      <td>-0.348567</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>9.7</td>\n",
       "      <td>-0.748605</td>\n",
       "      <td>-0.944918</td>\n",
       "      <td>-0.531910</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>9.0</td>\n",
       "      <td>0.087757</td>\n",
       "      <td>0.311251</td>\n",
       "      <td>0.751490</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>6.0</td>\n",
       "      <td>-0.748605</td>\n",
       "      <td>-0.875131</td>\n",
       "      <td>-0.521125</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>7.4</td>\n",
       "      <td>-0.142545</td>\n",
       "      <td>1.637207</td>\n",
       "      <td>-0.262288</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>7.3</td>\n",
       "      <td>-0.615272</td>\n",
       "      <td>0.660186</td>\n",
       "      <td>0.018119</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>6.6</td>\n",
       "      <td>-0.239515</td>\n",
       "      <td>0.171676</td>\n",
       "      <td>-0.132870</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>6.3</td>\n",
       "      <td>-0.784969</td>\n",
       "      <td>0.450825</td>\n",
       "      <td>-0.682898</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>8.5</td>\n",
       "      <td>-0.178909</td>\n",
       "      <td>-0.177259</td>\n",
       "      <td>-0.057376</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>6.8</td>\n",
       "      <td>-0.118303</td>\n",
       "      <td>-0.386621</td>\n",
       "      <td>-0.607404</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Murder   Assault  UrbanPop      Rape  cluster\n",
       "1     10.0  1.118060 -1.224067  2.509424        0\n",
       "2      8.1  1.493817  1.009122  1.053466        0\n",
       "3      8.8  0.233212 -1.084492 -0.186794        0\n",
       "4      9.0  1.275635  1.776781  2.088814        0\n",
       "5      7.9  0.402909  0.869548  1.883901        0\n",
       "7      5.9  0.815030  0.450825 -0.585834        0\n",
       "12    10.4  0.948363  1.218484  0.298525        0\n",
       "13     7.2 -0.700121 -0.037685 -0.025021        0\n",
       "15     6.0 -0.675878  0.032102 -0.348567        0\n",
       "16     9.7 -0.748605 -0.944918 -0.531910        0\n",
       "24     9.0  0.087757  0.311251  0.751490        0\n",
       "25     6.0 -0.748605 -0.875131 -0.521125        0\n",
       "29     7.4 -0.142545  1.637207 -0.262288        0\n",
       "34     7.3 -0.615272  0.660186  0.018119        0\n",
       "35     6.6 -0.239515  0.171676 -0.132870        0\n",
       "37     6.3 -0.784969  0.450825 -0.682898        0\n",
       "45     8.5 -0.178909 -0.177259 -0.057376        0\n",
       "49     6.8 -0.118303 -0.386621 -0.607404        0"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "crime1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24ed1e93518>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(crime1.Murder,crime1.Assault,color='green')\n",
    "plt.scatter(crime2.Murder,crime2.Assault,color='red')\n",
    "plt.scatter(crime3.Murder,crime3.Assault,color='yellow')\n",
    "plt.scatter(centers[:,0],centers[:,1],color='purple',marker='*',label='centroid',cmap='virdis')\n",
    "plt.xlabel('Murder')\n",
    "plt.ylabel('Assault')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### IF YOU WANT TO PREDICT WHICH CLUSTER BELONG TO IF NEW DATA GIVEN\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "crime_0= pd.read_csv(\"C:\\\\Users\\\\kumar\\\\Python Assign\\\\clustering\\\\Assignments\\\\crime_data.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "crime_0.drop(['Unnamed: 0'],inplace=True,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\kumar\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:3: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n",
      "C:\\Users\\kumar\\Anaconda3\\lib\\site-packages\\sklearn\\preprocessing\\data.py:645: DataConversionWarning: Data with input dtype int64 were all converted to float64 by StandardScaler.\n",
      "  return self.partial_fit(X, y)\n",
      "C:\\Users\\kumar\\Anaconda3\\lib\\site-packages\\sklearn\\base.py:464: DataConversionWarning: Data with input dtype int64 were all converted to float64 by StandardScaler.\n",
      "  return self.fit(X, **fit_params).transform(X)\n",
      "C:\\Users\\kumar\\Anaconda3\\lib\\site-packages\\sklearn\\preprocessing\\data.py:645: DataConversionWarning: Data with input dtype int64 were all converted to float64 by StandardScaler.\n",
      "  return self.partial_fit(X, y)\n",
      "C:\\Users\\kumar\\Anaconda3\\lib\\site-packages\\sklearn\\base.py:464: DataConversionWarning: Data with input dtype int64 were all converted to float64 by StandardScaler.\n",
      "  return self.fit(X, **fit_params).transform(X)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler= StandardScaler()\n",
    "crime_0.murder=scaler.fit_transform(crime_0[['Murder']])\n",
    "crime_0.Assault=scaler.fit_transform(crime_0[['Assault']])\n",
    "crime_0.UrbanPop=scaler.fit_transform(crime_0[['UrbanPop']])\n",
    "crime_0.Rape=scaler.fit_transform(crime_0[['Rape']])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, 0, 0, 0, 2, 0, 1, 1, 2, 2, 0, 0, 2, 0, 0, 1, 2, 1, 2, 1,\n",
       "       2, 1, 0, 0, 2, 1, 2, 0, 1, 1, 1, 2, 0, 0, 2, 0, 2, 1, 2, 1, 1, 2,\n",
       "       2, 0, 2, 2, 2, 0])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans1=KMeans(n_clusters=3)\n",
    "kmeans1.fit(crime_0)\n",
    "labels1=kmeans1.labels_\n",
    "labels1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "centers1=kmeans.cluster_centers_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 7.82777778e+00,  7.90032950e-02,  2.14324104e-01,\n",
       "         2.58980717e-01],\n",
       "       [ 3.31111111e+00, -9.20995794e-01, -2.16030013e-01,\n",
       "        -7.32628310e-01],\n",
       "       [ 1.34928571e+01,  1.08256178e+00,  2.19331056e-03,\n",
       "         6.08975478e-01]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "centers1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_observation = [[0.089,0.1378908,-0.66576,-11.265281]]\n",
    "kmeans1.predict(new_observation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## INFERENCES"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " AFTER SCALING\n",
    "1) IF MURDER RATE IS GRATER >10 BELONGS TO CLUSTER 0\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2)IF MURDER RATE IS LESS THAN 10 AND GREATEER THAN 5 BELONGS TO CLUSTER 1\n",
    "ELSE BELONG TO CLUSTER 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### EVALUATING CLUSTERING USING METRICS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "INTRA CLUSTER DISTANCE SHOULD BE LESS ### USE SILHOUETTE SCORE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "INTER CLUSTER DISTANCE SHOULD BE HIGH."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics.pairwise import euclidean_distances\n",
    "dists = euclidean_distances(crime_0\n",
    "                           )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4980269908840838"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import silhouette_score\n",
    "silhouette_score(dists, labels, metric='euclidean', sample_size=None, random_state=None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### SILHOUETEE SCORE IS >0 AND NEAR TO 1 . SO LESS INTRA CLUSTER DISTANCE"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "FOR INTER CLUSTER OR BOTHH INTRA AND INTER USE DAVIES BOULDIN SCORE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The DB index captures the intuition that clusters that are (1) well-spaced from each other and (2) themselves very dense are likely a ‘good’ clustering. This is because the measure’s ‘max’ statement repeatedly selects the values where the average point is farthest away from its centroid, and where the centroids are closest together. As the DB index shrinks, the clustering is considered ‘better’."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    " from sklearn.metrics import davies_bouldin_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\kumar\\Anaconda3\\lib\\site-packages\\sklearn\\metrics\\cluster\\unsupervised.py:342: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  score = (intra_dists[:, None] + intra_dists) / centroid_distances\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.750403266986127"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "davies_bouldin_score(crime_0, labels1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### BY OBBSERVATION AS DAVIES BOULDIN SCORE IS LESS CLUSTERS ARE SEPARATED WELL"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "NOTE:  IF CLUSTERING IS TO BE DONE PERFECTLY WE SHOULD DO PCA THEN CLUSTERING IS TO BE PERFORMED."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "HERE WE DON'T NEED TO DO PCA AS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1)LESS DIMENSIONS AND SIZE OF DATA\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2)METRICS SHOW CLUSTERING IS GOOD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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