R4_Internal_Lab-Clustering-1.ipynb

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   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zfsiaKcDho8W"
   },
   "source": [
    "### The data set has information about features of silhouette extracted from the images of different cars\n",
    "\n",
    "Four \"Corgie\" model vehicles were used for the experiment: a double decker bus, Cheverolet van, Saab 9000 and an Opel Manta 400 cars. This particular combination of vehicles was chosen with the expectation that the bus, van and either one of the cars would be readily distinguishable, but it would be more difficult to distinguish between the cars.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.preprocessing import normalize\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.cluster.hierarchy as sch\n",
    "from sklearn.cluster import KMeans\n",
    "from scipy.cluster.hierarchy import cophenet, dendrogram, linkage\n",
    "from scipy.spatial.distance import pdist\n",
    "from sklearn.cluster import AgglomerativeClustering\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "kVtZqLhGho8c"
   },
   "source": [
    "### 1. Read the dataset using function .dropna() - to avoid dealing with NAs as of now"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "VbKTspg4ho8g"
   },
   "outputs": [],
   "source": [
    "data = pd.read_csv('./Data/vehicle.csv').dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>compactness</th>\n",
       "      <th>circularity</th>\n",
       "      <th>distance_circularity</th>\n",
       "      <th>radius_ratio</th>\n",
       "      <th>pr.axis_aspect_ratio</th>\n",
       "      <th>max.length_aspect_ratio</th>\n",
       "      <th>scatter_ratio</th>\n",
       "      <th>elongatedness</th>\n",
       "      <th>pr.axis_rectangularity</th>\n",
       "      <th>max.length_rectangularity</th>\n",
       "      <th>scaled_variance</th>\n",
       "      <th>scaled_variance.1</th>\n",
       "      <th>scaled_radius_of_gyration</th>\n",
       "      <th>scaled_radius_of_gyration.1</th>\n",
       "      <th>skewness_about</th>\n",
       "      <th>skewness_about.1</th>\n",
       "      <th>skewness_about.2</th>\n",
       "      <th>hollows_ratio</th>\n",
       "      <th>class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>95</td>\n",
       "      <td>48.0</td>\n",
       "      <td>83.0</td>\n",
       "      <td>178.0</td>\n",
       "      <td>72.0</td>\n",
       "      <td>10</td>\n",
       "      <td>162.0</td>\n",
       "      <td>42.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>159</td>\n",
       "      <td>176.0</td>\n",
       "      <td>379.0</td>\n",
       "      <td>184.0</td>\n",
       "      <td>70.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>187.0</td>\n",
       "      <td>197</td>\n",
       "      <td>van</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>91</td>\n",
       "      <td>41.0</td>\n",
       "      <td>84.0</td>\n",
       "      <td>141.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>9</td>\n",
       "      <td>149.0</td>\n",
       "      <td>45.0</td>\n",
       "      <td>19.0</td>\n",
       "      <td>143</td>\n",
       "      <td>170.0</td>\n",
       "      <td>330.0</td>\n",
       "      <td>158.0</td>\n",
       "      <td>72.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>189.0</td>\n",
       "      <td>199</td>\n",
       "      <td>van</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>104</td>\n",
       "      <td>50.0</td>\n",
       "      <td>106.0</td>\n",
       "      <td>209.0</td>\n",
       "      <td>66.0</td>\n",
       "      <td>10</td>\n",
       "      <td>207.0</td>\n",
       "      <td>32.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>158</td>\n",
       "      <td>223.0</td>\n",
       "      <td>635.0</td>\n",
       "      <td>220.0</td>\n",
       "      <td>73.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>188.0</td>\n",
       "      <td>196</td>\n",
       "      <td>car</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>93</td>\n",
       "      <td>41.0</td>\n",
       "      <td>82.0</td>\n",
       "      <td>159.0</td>\n",
       "      <td>63.0</td>\n",
       "      <td>9</td>\n",
       "      <td>144.0</td>\n",
       "      <td>46.0</td>\n",
       "      <td>19.0</td>\n",
       "      <td>143</td>\n",
       "      <td>160.0</td>\n",
       "      <td>309.0</td>\n",
       "      <td>127.0</td>\n",
       "      <td>63.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>199.0</td>\n",
       "      <td>207</td>\n",
       "      <td>van</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>85</td>\n",
       "      <td>44.0</td>\n",
       "      <td>70.0</td>\n",
       "      <td>205.0</td>\n",
       "      <td>103.0</td>\n",
       "      <td>52</td>\n",
       "      <td>149.0</td>\n",
       "      <td>45.0</td>\n",
       "      <td>19.0</td>\n",
       "      <td>144</td>\n",
       "      <td>241.0</td>\n",
       "      <td>325.0</td>\n",
       "      <td>188.0</td>\n",
       "      <td>127.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>180.0</td>\n",
       "      <td>183</td>\n",
       "      <td>bus</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "text/plain": [
       "   compactness  circularity  distance_circularity  radius_ratio  \\\n",
       "0           95         48.0                  83.0         178.0   \n",
       "1           91         41.0                  84.0         141.0   \n",
       "2          104         50.0                 106.0         209.0   \n",
       "3           93         41.0                  82.0         159.0   \n",
       "4           85         44.0                  70.0         205.0   \n",
       "\n",
       "   pr.axis_aspect_ratio  max.length_aspect_ratio  scatter_ratio  \\\n",
       "0                  72.0                       10          162.0   \n",
       "1                  57.0                        9          149.0   \n",
       "2                  66.0                       10          207.0   \n",
       "3                  63.0                        9          144.0   \n",
       "4                 103.0                       52          149.0   \n",
       "\n",
       "   elongatedness  pr.axis_rectangularity  max.length_rectangularity  \\\n",
       "0           42.0                    20.0                        159   \n",
       "1           45.0                    19.0                        143   \n",
       "2           32.0                    23.0                        158   \n",
       "3           46.0                    19.0                        143   \n",
       "4           45.0                    19.0                        144   \n",
       "\n",
       "   scaled_variance  scaled_variance.1  scaled_radius_of_gyration  \\\n",
       "0            176.0              379.0                      184.0   \n",
       "1            170.0              330.0                      158.0   \n",
       "2            223.0              635.0                      220.0   \n",
       "3            160.0              309.0                      127.0   \n",
       "4            241.0              325.0                      188.0   \n",
       "\n",
       "   scaled_radius_of_gyration.1  skewness_about  skewness_about.1  \\\n",
       "0                         70.0             6.0              16.0   \n",
       "1                         72.0             9.0              14.0   \n",
       "2                         73.0            14.0               9.0   \n",
       "3                         63.0             6.0              10.0   \n",
       "4                        127.0             9.0              11.0   \n",
       "\n",
       "   skewness_about.2  hollows_ratio class  \n",
       "0             187.0            197   van  \n",
       "1             189.0            199   van  \n",
       "2             188.0            196   car  \n",
       "3             199.0            207   van  \n",
       "4             180.0            183   bus  "
      ]
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     "execution_count": 22,
     "metadata": {},
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   "source": [
    "data.head()"
   ]
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  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 813 entries, 0 to 845\n",
      "Data columns (total 19 columns):\n",
      "compactness                    813 non-null int64\n",
      "circularity                    813 non-null float64\n",
      "distance_circularity           813 non-null float64\n",
      "radius_ratio                   813 non-null float64\n",
      "pr.axis_aspect_ratio           813 non-null float64\n",
      "max.length_aspect_ratio        813 non-null int64\n",
      "scatter_ratio                  813 non-null float64\n",
      "elongatedness                  813 non-null float64\n",
      "pr.axis_rectangularity         813 non-null float64\n",
      "max.length_rectangularity      813 non-null int64\n",
      "scaled_variance                813 non-null float64\n",
      "scaled_variance.1              813 non-null float64\n",
      "scaled_radius_of_gyration      813 non-null float64\n",
      "scaled_radius_of_gyration.1    813 non-null float64\n",
      "skewness_about                 813 non-null float64\n",
      "skewness_about.1               813 non-null float64\n",
      "skewness_about.2               813 non-null float64\n",
      "hollows_ratio                  813 non-null int64\n",
      "class                          813 non-null object\n",
      "dtypes: float64(14), int64(4), object(1)\n",
      "memory usage: 127.0+ KB\n"
     ]
    }
   ],
   "source": [
    "data.info()"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All the rows are having 813 values and so there are no missing values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>compactness</th>\n",
       "      <td>813.0</td>\n",
       "      <td>93.656827</td>\n",
       "      <td>8.233751</td>\n",
       "      <td>73.0</td>\n",
       "      <td>87.0</td>\n",
       "      <td>93.0</td>\n",
       "      <td>100.0</td>\n",
       "      <td>119.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>circularity</th>\n",
       "      <td>813.0</td>\n",
       "      <td>44.803198</td>\n",
       "      <td>6.146659</td>\n",
       "      <td>33.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>44.0</td>\n",
       "      <td>49.0</td>\n",
       "      <td>59.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>distance_circularity</th>\n",
       "      <td>813.0</td>\n",
       "      <td>82.043050</td>\n",
       "      <td>15.783070</td>\n",
       "      <td>40.0</td>\n",
       "      <td>70.0</td>\n",
       "      <td>79.0</td>\n",
       "      <td>98.0</td>\n",
       "      <td>112.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>radius_ratio</th>\n",
       "      <td>813.0</td>\n",
       "      <td>169.098401</td>\n",
       "      <td>33.615402</td>\n",
       "      <td>104.0</td>\n",
       "      <td>141.0</td>\n",
       "      <td>167.0</td>\n",
       "      <td>195.0</td>\n",
       "      <td>333.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pr.axis_aspect_ratio</th>\n",
       "      <td>813.0</td>\n",
       "      <td>61.774908</td>\n",
       "      <td>7.973000</td>\n",
       "      <td>47.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>61.0</td>\n",
       "      <td>65.0</td>\n",
       "      <td>138.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max.length_aspect_ratio</th>\n",
       "      <td>813.0</td>\n",
       "      <td>8.599016</td>\n",
       "      <td>4.677174</td>\n",
       "      <td>2.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>55.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>scatter_ratio</th>\n",
       "      <td>813.0</td>\n",
       "      <td>168.563346</td>\n",
       "      <td>33.082186</td>\n",
       "      <td>112.0</td>\n",
       "      <td>146.0</td>\n",
       "      <td>157.0</td>\n",
       "      <td>198.0</td>\n",
       "      <td>265.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>elongatedness</th>\n",
       "      <td>813.0</td>\n",
       "      <td>40.988930</td>\n",
       "      <td>7.803380</td>\n",
       "      <td>26.0</td>\n",
       "      <td>33.0</td>\n",
       "      <td>43.0</td>\n",
       "      <td>46.0</td>\n",
       "      <td>61.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pr.axis_rectangularity</th>\n",
       "      <td>813.0</td>\n",
       "      <td>20.558426</td>\n",
       "      <td>2.573184</td>\n",
       "      <td>17.0</td>\n",
       "      <td>19.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>29.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max.length_rectangularity</th>\n",
       "      <td>813.0</td>\n",
       "      <td>147.891759</td>\n",
       "      <td>14.504648</td>\n",
       "      <td>118.0</td>\n",
       "      <td>137.0</td>\n",
       "      <td>146.0</td>\n",
       "      <td>159.0</td>\n",
       "      <td>188.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>scaled_variance</th>\n",
       "      <td>813.0</td>\n",
       "      <td>188.377614</td>\n",
       "      <td>31.165873</td>\n",
       "      <td>130.0</td>\n",
       "      <td>167.0</td>\n",
       "      <td>179.0</td>\n",
       "      <td>217.0</td>\n",
       "      <td>320.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>scaled_variance.1</th>\n",
       "      <td>813.0</td>\n",
       "      <td>438.382534</td>\n",
       "      <td>175.270368</td>\n",
       "      <td>184.0</td>\n",
       "      <td>318.0</td>\n",
       "      <td>364.0</td>\n",
       "      <td>586.0</td>\n",
       "      <td>1018.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>scaled_radius_of_gyration</th>\n",
       "      <td>813.0</td>\n",
       "      <td>174.252153</td>\n",
       "      <td>32.332161</td>\n",
       "      <td>109.0</td>\n",
       "      <td>149.0</td>\n",
       "      <td>173.0</td>\n",
       "      <td>198.0</td>\n",
       "      <td>268.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>scaled_radius_of_gyration.1</th>\n",
       "      <td>813.0</td>\n",
       "      <td>72.399754</td>\n",
       "      <td>7.475994</td>\n",
       "      <td>59.0</td>\n",
       "      <td>67.0</td>\n",
       "      <td>71.0</td>\n",
       "      <td>75.0</td>\n",
       "      <td>135.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>skewness_about</th>\n",
       "      <td>813.0</td>\n",
       "      <td>6.351784</td>\n",
       "      <td>4.921476</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>22.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>skewness_about.1</th>\n",
       "      <td>813.0</td>\n",
       "      <td>12.687577</td>\n",
       "      <td>8.926951</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>19.0</td>\n",
       "      <td>41.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>skewness_about.2</th>\n",
       "      <td>813.0</td>\n",
       "      <td>188.979090</td>\n",
       "      <td>6.153681</td>\n",
       "      <td>176.0</td>\n",
       "      <td>184.0</td>\n",
       "      <td>189.0</td>\n",
       "      <td>193.0</td>\n",
       "      <td>206.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hollows_ratio</th>\n",
       "      <td>813.0</td>\n",
       "      <td>195.729397</td>\n",
       "      <td>7.398781</td>\n",
       "      <td>181.0</td>\n",
       "      <td>191.0</td>\n",
       "      <td>197.0</td>\n",
       "      <td>201.0</td>\n",
       "      <td>211.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             count        mean         std    min    25%  \\\n",
       "compactness                  813.0   93.656827    8.233751   73.0   87.0   \n",
       "circularity                  813.0   44.803198    6.146659   33.0   40.0   \n",
       "distance_circularity         813.0   82.043050   15.783070   40.0   70.0   \n",
       "radius_ratio                 813.0  169.098401   33.615402  104.0  141.0   \n",
       "pr.axis_aspect_ratio         813.0   61.774908    7.973000   47.0   57.0   \n",
       "max.length_aspect_ratio      813.0    8.599016    4.677174    2.0    7.0   \n",
       "scatter_ratio                813.0  168.563346   33.082186  112.0  146.0   \n",
       "elongatedness                813.0   40.988930    7.803380   26.0   33.0   \n",
       "pr.axis_rectangularity       813.0   20.558426    2.573184   17.0   19.0   \n",
       "max.length_rectangularity    813.0  147.891759   14.504648  118.0  137.0   \n",
       "scaled_variance              813.0  188.377614   31.165873  130.0  167.0   \n",
       "scaled_variance.1            813.0  438.382534  175.270368  184.0  318.0   \n",
       "scaled_radius_of_gyration    813.0  174.252153   32.332161  109.0  149.0   \n",
       "scaled_radius_of_gyration.1  813.0   72.399754    7.475994   59.0   67.0   \n",
       "skewness_about               813.0    6.351784    4.921476    0.0    2.0   \n",
       "skewness_about.1             813.0   12.687577    8.926951    0.0    6.0   \n",
       "skewness_about.2             813.0  188.979090    6.153681  176.0  184.0   \n",
       "hollows_ratio                813.0  195.729397    7.398781  181.0  191.0   \n",
       "\n",
       "                               50%    75%     max  \n",
       "compactness                   93.0  100.0   119.0  \n",
       "circularity                   44.0   49.0    59.0  \n",
       "distance_circularity          79.0   98.0   112.0  \n",
       "radius_ratio                 167.0  195.0   333.0  \n",
       "pr.axis_aspect_ratio          61.0   65.0   138.0  \n",
       "max.length_aspect_ratio        8.0   10.0    55.0  \n",
       "scatter_ratio                157.0  198.0   265.0  \n",
       "elongatedness                 43.0   46.0    61.0  \n",
       "pr.axis_rectangularity        20.0   23.0    29.0  \n",
       "max.length_rectangularity    146.0  159.0   188.0  \n",
       "scaled_variance              179.0  217.0   320.0  \n",
       "scaled_variance.1            364.0  586.0  1018.0  \n",
       "scaled_radius_of_gyration    173.0  198.0   268.0  \n",
       "scaled_radius_of_gyration.1   71.0   75.0   135.0  \n",
       "skewness_about                 6.0    9.0    22.0  \n",
       "skewness_about.1              11.0   19.0    41.0  \n",
       "skewness_about.2             189.0  193.0   206.0  \n",
       "hollows_ratio                197.0  201.0   211.0  "
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe().T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Ku4eS0ZAho8s"
   },
   "source": [
    "### 2. Print/ Plot the dependent (categorical variable) - Class column"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "R1mfF_hiho8v"
   },
   "source": [
    "Since the variable is categorical, you can use value_counts function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "_dP5-zpUho81"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "car    413\n",
       "bus    205\n",
       "van    195\n",
       "Name: class, dtype: int64"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['class'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a0d933a518>"
      ]
     },
     "execution_count": 28,
     "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": [
    "sns.countplot(data['class'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ZFsXYI5qho9E"
   },
   "source": [
    "### Check for any missing values in the data "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "qb77DNfwho9J"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(compactness                    False\n",
       " circularity                    False\n",
       " distance_circularity           False\n",
       " radius_ratio                   False\n",
       " pr.axis_aspect_ratio           False\n",
       " max.length_aspect_ratio        False\n",
       " scatter_ratio                  False\n",
       " elongatedness                  False\n",
       " pr.axis_rectangularity         False\n",
       " max.length_rectangularity      False\n",
       " scaled_variance                False\n",
       " scaled_variance.1              False\n",
       " scaled_radius_of_gyration      False\n",
       " scaled_radius_of_gyration.1    False\n",
       " skewness_about                 False\n",
       " skewness_about.1               False\n",
       " skewness_about.2               False\n",
       " hollows_ratio                  False\n",
       " class                          False\n",
       " dtype: bool, compactness                    False\n",
       " circularity                    False\n",
       " distance_circularity           False\n",
       " radius_ratio                   False\n",
       " pr.axis_aspect_ratio           False\n",
       " max.length_aspect_ratio        False\n",
       " scatter_ratio                  False\n",
       " elongatedness                  False\n",
       " pr.axis_rectangularity         False\n",
       " max.length_rectangularity      False\n",
       " scaled_variance                False\n",
       " scaled_variance.1              False\n",
       " scaled_radius_of_gyration      False\n",
       " scaled_radius_of_gyration.1    False\n",
       " skewness_about                 False\n",
       " skewness_about.1               False\n",
       " skewness_about.2               False\n",
       " hollows_ratio                  False\n",
       " class                          False\n",
       " dtype: bool)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.isnull().any(), data.isna().any()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AwUdJm9qho9U"
   },
   "source": [
    "### 3. Standardize the data "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "x6z10bgjho9j"
   },
   "source": [
    "Since the dimensions of the data are not really known to us, it would be wise to standardize the data using z scores before we go for any clustering methods.\n",
    "You can use zscore function to do this"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "qed3MlPjho9n"
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "pbGN_7mhho9y"
   },
   "outputs": [],
   "source": [
    "sc = StandardScaler()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "data.drop(columns=['class'], inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_sc = sc.fit_transform(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(813, 18)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_sc.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "weIwi8cxho-C"
   },
   "source": [
    "### K - Means Clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YdA5yJ1m61-L"
   },
   "source": [
    "### Assign a dummy array called Cluster_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "PRcbAApuho-g"
   },
   "outputs": [],
   "source": [
    "cluster_error = []"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ywuVdFe2ho-t"
   },
   "source": [
    "### 5. Calculate errorrs for each K"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "PJznnrkc68nf"
   },
   "source": [
    "Iterating values of k from 1 to 10 fit K means model\n",
    "Using inertia"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "uc49grvmho-2"
   },
   "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>num_clusters</th>\n",
       "      <th>cluster_errors</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>14634.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>8623.136976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>7037.467395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>5741.138462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>5186.753590</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   num_clusters  cluster_errors\n",
       "0             1    14634.000000\n",
       "1             2     8623.136976\n",
       "2             3     7037.467395\n",
       "3             4     5741.138462\n",
       "4             5     5186.753590"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cluster_range = range( 1, 10)\n",
    "for num_clusters in cluster_range:\n",
    "  clusters = KMeans(num_clusters, n_init = 5)\n",
    "  clusters.fit(data_sc)\n",
    "  labels = clusters.labels_\n",
    "  centroids = clusters.cluster_centers_\n",
    "  cluster_error.append( clusters.inertia_)\n",
    "  \n",
    "clusters_df = pd.DataFrame( { \"num_clusters\":cluster_range, \"cluster_errors\": cluster_error} )\n",
    "clusters_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "JIcSiPyoho_a"
   },
   "source": [
    "### 6. Plotting Elbow/ Scree Plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Z8Yw5XEsho_r"
   },
   "source": [
    "Use Matplotlib to plot the scree plot - Note: Scree plot plots Errors vs the no of clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "sJ5oE4Csho_v"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a0d99412b0>]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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umzZOEzIS9cjKEjnHrDQAAEB/UaRHiECU6a6iAr27r0pv7z7qdxwAAICIR5EeQT59Sa4ykmK1eOVOv6MAAABEPIr0CBIfE9Dtl03Sqx+Wa/uhGr/jAAAARDSK9Ahz22UTlRAT0JJVJX5HAQAAiGgU6RFmVFKs/rowV8+/W6aD1Y1+xwEAAIhYFOkR6MtzCtTW7vSzN3b5HQUAACBiUaRHoLyMRN1wYbZ+tW6vjjW2+B0HAAAgIlGkR6hFRQWqaWrVk+v2+h0FAAAgIlGkR6hpOWmafVamHn1jl5pb2/2OAwAAEHEo0iPYoqLJOnSsSS+8W+Z3FAAAgIhDkR7B5kwZrXPHp2rJqhK1t3PbcAAAgL6gSI9gZqZFRQXaXl6r17eV+x0HAAAgolCkR7gbLhyvnPQELeYGLQAAAH1CkR7hYgJR+tIV+Vq/q1Lv7D3qdxwAAICIQZGGbvlYntISYrRkJbPSAAAAvUWRhpLionXrrIlavuWgSipq/Y4DAAAQESjSkCTdfvkkxQSitHQNtw0HAADoDYo0JElZKXH6q4tz9eyGUlXUNPkdBwAAIOxRpNHprjn5amlr1+Nv7vY7CgAAQNijSKNTQVay5p83Tj9/a4/qmlr9jgMAABDWzlikzexRMys3s81dxjLM7BUz2+59HuWNm5n9yMx2mNn7ZnZxl3Nu947fbma3dxm/xMw2eef8yMxsoF8kem/h3AJVN7To6bf3+R0FAAAgrPVmRvoxSdedMHa/pFedc1Mkvep9LUnXS5rifSyU9LAULN6SviXpUkkzJX2ro3x7xyzsct6JfxaG0MUTRmnmpAwtW7NLLW3tfscBAAAIW2cs0s65VZIqTxi+SdLj3uPHJS3oMv6EC3pLUrqZjZc0X9IrzrlK59xRSa9Ius57LtU5t9Y55yQ90eV7wSeL5haorKpBL2064HcUAACAsBXqGumxzrkDkuR9HuON50jquiag1Bs73XhpD+M9MrOFZlZsZsUVFRUhRseZXDl1jM4ak6xHVpYo+PMNAAAATjTQFxv2tL7ZhTDeI+fcEudcoXOuMCsrK8SIOJOoKNPCogJtPXBMq7cf9jsOAABAWAq1SB/ylmXI+1zujZdKyutyXK6k/WcYz+1hHD67aXq2xqbGackqbhsOAADQk1CL9IuSOnbeuF3SC13Gb/N275glqdpb+rFc0rVmNsq7yPBaScu952rMbJa3W8dtXb4XfBQXHdAds/O1ZsdhbS6r9jsOAABA2OnN9ndPSloraaqZlZrZnZK+J+kaM9su6Rrva0l6SVKJpB2SfirpbyTJOVcp6d8lve19/Js3Jkn3SFrqnbNT0ssD89LQX5+7dIKS46K1mFlpAACAk1ikXkxWWFjoiouL/Y4x7H33pa1aumaXVtw7T3kZiX7HAQAAGFJmtsE5V9jTc9zZEKd1x+x8RZm0bM0uv6MAAACEFYo0TmtcWrxump6jp9/ep6N1zX7HAQAACBsUaZzRwqICNbS06edv7fE7CgAAQNigSOOMzh6boqvOGaPH3tytxpY2v+MAAACEBYo0emVRUYEq65r1zIbSMx8MAAAwAlCk0Ssz8zM0PS9dS1eXqK09Mnd6AQAAGEgUafSKmWlRUYH2HKnX8g8O+h0HAADAdxRp9Nq154/TpMxELV65U5G6/zgAAMBAoUij1wJRpruKCvReabXW7ao88wkAAADDGEUaffJXF+cqMylWi1fu9DsKAACAryjS6JP4mIC+ePkkvb6tQtsO1vgdBwAAwDcUafTZrZdNVEJMQEtWlfgdBQAAwDcUafRZemKsPvOxPL3wbpkOVDf4HQcAAMAXFGmE5M4r8uUkPbpml99RAAAAfEGRRkjyMhL18QvH68n1+1Td0OJ3HAAAgCFHkUbIFhYVqLapVb9at9fvKAAAAEOOIo2QnZ+dpjlTRuvRN3apqbXN7zgAAABDiiKNfllUNFkVNU16YeN+v6MAAAAMKYo0+mX2WZk6b3yqFq/aqfZ2bhsOAABGDoo0+sXMtGhugXZW1OnVD8v9jgMAADBkKNLotxsuGK+c9AQtWcVtwwEAwMhBkUa/RQeidNecfL29+6g27Kn0Ow4AAMCQoEhjQPz1x/KUnhijxSu5bTgAABgZKNIYEImx0bpt1kS9svWQdlbU+h0HAABg0FGkMWBuu3ySYgNRWrqaWWkAADD8UaQxYEYnx+nmS3L1mw1lKq9p9DsOAADAoKJIY0DdNadALe3teuyN3X5HAQAAGFQUaQyoSaOTdP20cfrFW3tU29TqdxwAAIBBQ5HGgFtYNFnHGlv11Pq9fkcBAAAYNBRpDLjpeemaPDpJ331pq/Lv/4Nmf+81Pb+xzO9YAAAAAyra7wAYfp7fWKZ9RxvU5oJfl1U16IHnNkmSFszI8TEZAADAwGFGGgPuweXb1NzW3m2soaVNDy7f5lMiAACAgUeRxoDbX9XQp3EAAIBIRJHGgMtOT+hx3Ez6+Vt71HrCbDUAAEAkokhjwN03f6oSYgLdxuKio5SfmaT//fxm3fCjNVqz/bBP6QAAAAYGRRoDbsGMHH33UxcoJz1BJiknPUHf/6sL9ed/mKuHP3+x6ppb9YVl6/Tlx4u1+3Cd33EBAABCYs45vzOEpLCw0BUXF/sdAyFobGnTsjW79JPXd6i5rV13zM7X3151llLjY/yOBgAA0I2ZbXDOFfb0HDPSGHLxMQF95cqz9Pq987Rgeo5+urpEVz20Qk+u36u29sj8wQ4AAIw8FGn4ZkxqvB789EV68StXaFJmkh54bpM+8d9r9FbJEb+jAQAAnBFFGr67IDdNz9x9mf77szNU3dCiW5a8pXt+sUH7Kuv9jgYAAHBKFGmEBTPTJy7K1qv/MFffuOZsrdhWoav/c6X+7x8/VG1Tq9/xAAAATkKRRliJjwnoq1dP0Wv3ztUNF4zXT1bs1JUPrdAzxfvUzvppAAAQRijSCEvj0xL0g89M13N/c7ly0hN037Pva8FP3lDx7kq/owEAAEiiSCPMXTxhlJ6753L98DPTVX6sSTc/slZ/9+RGlXG7cQAA4DOKNMJeVJRpwYwcvXbvXH316in60wcHddVDK/Sff9qm+mbWTwMAAH9QpBExEmOj9Y1rztZr987TteeP049e26GrHlqp324sZf00AAAYcv0q0mb2dTP7wMw2m9mTZhZvZvlmts7MtpvZ02YW6x0b5329w3t+Upfv84A3vs3M5vfvJWG4y0lP0H9/doaevfsyZaXE6etPv6dPPfymNu496nc0AAAwgoRcpM0sR9JXJRU656ZJCki6RdL3Jf3AOTdF0lFJd3qn3CnpqHPuLEk/8I6TmZ3nnXe+pOsk/cTMAqHmwshROClDL3xlth68+UKVVTXokz95U19/+l0drG70OxoAABgB+ru0I1pSgplFS0qUdEDSVZKe9Z5/XNIC7/FN3tfynr/azMwbf8o51+Sc2yVph6SZ/cyFESIqyvTpwjy9fu88/c28yfrDpgO68qEV+q8/b1dDc5vf8QAAwDAWcpF2zpVJekjSXgULdLWkDZKqnHMdV4CVSsrxHudI2ued2+odn9l1vIdzujGzhWZWbGbFFRUVoUbHMJQcF61/vO4cvfqNuZo3NUs/+PNHuvr/rdCL7+2Xc6yfBgAAA68/SztGKTibnC8pW1KSpOt7OLSjxdgpnjvV+MmDzi1xzhU65wqzsrL6HhrDXl5Goh7+wiV6auEspSXG6qtPbtSnH1mr90ur/I4GAACGmf4s7fgLSbuccxXOuRZJz0m6XFK6t9RDknIl7fcel0rKkyTv+TRJlV3HezgHCMmsgkz9/u+u0Pc+dYF2H6nTTf/zhu595j2VH2P9NAAAGBj9KdJ7Jc0ys0RvrfPVkrZIel3Szd4xt0t6wXv8ove1vOdfc8Hfub8o6RZvV498SVMkre9HLkCSFIgy3TJzgl67d54WzinQC++W6cqHVuh/Xt+hxhbWTwMAgP6x/qwfNbNvS/qMpFZJGyV9WcH1zU9JyvDGvuCcazKzeEk/lzRDwZnoW5xzJd73+WdJX/K+z987514+059dWFjoiouLQ86OkWf34Tp956WtemXLIeVlJOifrj9X100bp+DPgQAAACczsw3OucIen4vUC7Eo0gjVGzsO699+t0XbDtXo0vwM/csnztP52Wl+xwIAAGHodEWaOxtixJl91mj94atX6N8XTNNHh2r08f9eoweee1+Ha5v8jgYAACIIRRojUnQgSrfOmqgV916pL83O1zPFpbrywRVasmqnmlvb/Y4HAAAiAEUaI1paYoz+98fP0/KvF+lj+Rn6j5c+1LU/WKlXthxi/2kAAHBaFGlA0uSsZD36xY/p8S/NVHQgSnc9Uaxbl63XtoM1fkcDAABhiiINdDH37Cy9/LU5+tdPnKdNZdW6/r9W6X89v0mVdc1+RwMAAGGGIg2cICYQpS/OzteKe+fp1lkT9eT6fZr34OtatmaXWtpYPw0AAIIo0sApjEqK1bdvmqaXvzZHF+Wl699/v0Xzf7hKr39Y7nc0AAAQBijSwBmcPTZFT3xpppbdXijnpDsee1u3P7peO8pZPw0AwEhGkQZ6wcx09bljtfzvi/S/bjhX7+w9qvk/XK1/ffEDVdWzfhoAgJGIIg30QWx0lL48p0Ar7p2nz3wsT0+s3a15D63QE2t3q5X10wAAjCgUaSAEmclx+o9PXqA/fHWOzhufqn954QNd/1+rteqjCr+jAQCAIUKRBvrh3PGp+uWXL9XiWy9RU2u7bnt0ve587G2VVNT6HQ0AAAwyijTQT2am+eeP0yvfKNL915+jdbsqNf+Hq/R/fr9F1Q0tfscDAACDhCINDJC46IDunjtZr907V5+akatlb+zSlQ+t0C/X7VFbO7cbBwBguKFIAwNsTEq8vn/zhfrd316hs7KS9c+/3awbfrRab+487Hc0AAAwgCjSwCCZlpOmpxfN0v987mLVNLbqcz9dp0U/L9beI/V+RwMAAAOAIg0MIjPTDReO16v/MFf3zZ+q1dsP6y/+c6W+9/KHqmlk/TQAAJGMIg0MgfiYgL5y5Vl6/d55+sRF2Xpk5U5d+dBKPf32XtZPAwAQocy5yPxHvLCw0BUXF/sdAwjJe/uq9G+/36INe47q/OxUXXXOGD33Tpn2VzUoOz1B982fqgUzcvyOCQDAiGdmG5xzhT0+R5EG/OGc04vv7de/vLBZ1Q2t3Z5LiAnou5+6gDINAIDPTlekWdoB+MTMdNP0HCXFRp/0XENLmx5cvs2HVAAAoLco0oDPDlQ39jheVtWgTaXVQ5wGAAD0FkUa8Fl2ekKP4ybpEz9eo1uXrdObOw8rUpdhAQAwXFGkAZ/dN3+qEmIC3cYSYgL6j09N0zevO0dbD9Tocz9dpwU/eVN/3HxQ7ezyAQBAWDh5cSaAIdVxQeGDy7f1uGvHHbMn6TfvlGrxyhLd/YsNKshK0t1zJ2vB9BzFRvOzMAAAfmHXDiBCtLa16+XNB/Xwip3acuCYxqfF684r8vXZmROUFMfPxAAADAa2vwOGEeecVm0/rIdX7NBbJZVKS4jR7ZdP0hcvn6SMpFi/4wEAMKxQpIFh6p29R/Xwip16ZcshJcQEdMvMPH15ToFyTnEBIwAA6BuKNDDMbT9Uo0dWluiFd8skSTdNz9Hdcws0ZWyKz8kAAIhsFGlghCiratDS1SV6av0+NbS06ZrzxuqeeZN18YRRfkcDACAiUaSBEaayrlmPv7lbj725W9UNLbo0P0P3zJusuWdnycz8jgcAQMSgSAMjVF1Tq55cv1dLV+/SwWONOm98qu6ZN1nXTxun6ABb5wEAcCYUaWCEa25t1/PvlumRlTtVUlGniZmJWlhUoL+6OFfxJ9wMBgAAHEeRBiBJam93+tOWQ3p4xQ69V1qt0clxuvOKfH1+1gSlxsf4HQ8AgLBDkQbQjXNOa0uO6OEVO7V6+2GlxEXrC5dN1B2zJ2lMSrzf8QAACBsUaQCntKm0Wo+s3KmXNh9QTCBKf12Yq4VzJmtCZqLf0QAA8B1FGsAZ7TpcpyWrduo3G8rU2t6uj1+YrbvnTtZ52al+RwMAwDcUaQC9duhYox5ds0u/eGuP6prbNG9qlu6ZO1kz8zPYOg8AMOJQpDiNhVgAABhoSURBVAH0WXV9i36xbo8eXbNLR+qadfGEdN0z7yxdfc4YRUVRqAEAIwNFGkDIGlva9OvifVq8skRlVQ06e2yy7p47WZ+4KFsx7EUNABjmKNIA+q2lrV1/eP+AHl6xU9sO1SgnPUF3zcnXZz42QQmx7EUNABieKNIABoxzTq9vK9fDK3bq7d1HlZEUqy9ePkm3XTZR6YmxfscDAGBAUaQBDIq3d1fq4RU79dqH5UqMDehzMyfozjn5Gp+W4Hc0AAAGBEUawKDaeuCYFq/cqd+9f0BRJn1yRo4WzZ2syVnJfkcDAKBfKNIAhsS+ynr9dHWJnn57n5rb2nXd+eN099zJuigv3e9oAACEhCINYEgdrm3SY2/s1uNrd6umsVWzz8rUPXPP0uyzMtmLGgAQUU5XpPu1d5WZpZvZs2b2oZltNbPLzCzDzF4xs+3e51HesWZmPzKzHWb2vpld3OX73O4dv93Mbu9PJgD+G50cp3vnT9Wb91+lf/rLc7T9UK2+sGydbvzxG3pp0wG1tUfmD/AAAHTVrxlpM3tc0mrn3FIzi5WUKOmfJFU6575nZvdLGuWc+6aZ/aWkv5P0l5IulfRfzrlLzSxDUrGkQklO0gZJlzjnjp7uz2ZGGogcTa1teu6dMi1euVO7j9SrYHSSFs0t0IIZOYqLZus8AED4GpSlHWaWKuk9SQWuyzcxs22S5jnnDpjZeEkrnHNTzWyx9/jJrsd1fDjnFnnj3Y47FYo0EHna2p3+uPmgHl65Q5vLjmlsapy+fEWBPnvpBCXHRfsdDwCAkwzW0o4CSRWSfmZmG81sqZklSRrrnDsgSd7nMd7xOZL2dTm/1Bs71XhPL2ShmRWbWXFFRUU/ogPwQyDKdMOF4/W7v71CP79zpiZnJes7L23V5d99Vf/vT9t0pLbJ74gAAPRaf4p0tKSLJT3snJshqU7S/ac5vqcrjNxpxk8edG6Jc67QOVeYlZXV17wAwoSZac6ULP3qrll6/iuzdfnk0frx6zs0+/uv6VsvbNa+ynq/IwIAcEb9KdKlkkqdc+u8r59VsFgf8pZ0yPtc3uX4vC7n50raf5pxACPA9Lx0PXLrJXrl63P1iQuz9av1ezXvoRX6+tPvatvBGr/jAQBwSiEXaefcQUn7zGyqN3S1pC2SXpTUsfPG7ZJe8B6/KOk2b/eOWZKqvaUfyyVda2ajvB0+rvXGAIwgZ41J1oOfvkgr77tSX7x8kpZ/cFDzf7hKdz72tjbsqfQ7HgAAJ+nvrh3TJS2VFCupRNIdCpbzX0uaIGmvpE875yotuHnsjyVdJ6le0h3OuWLv+3xJwd0+JOk7zrmfnenP5mJDYHg7WtesJ9bu0WNv7tLR+hbNnJShe+ZN1rypWXrh3f16cPk27a9qUHZ6gu6bP1ULZvR4aQUAAP3CDVkARKz65lY9/fY+/XRVifZXN2p8apwO1zWrpe34310JMQF991MXUKYBAANu0G7IAgCDLTE2WnfMzteK+67UQ5++SBW13Uu0JDW0tOnB5dt8SggAGKko0gAiQmx0lG6+JPeUd0Usq2rQt17YrGc3lGrbwRq1trUPcUIAwEjDHRAARJTs9ASVVTWcNB4biNIzG0r1+No9kqT4mCidn52mC3K8j9w0Tc5KViCqpx03AQDoO4o0gIhy3/ypeuC5TWpoaesc61gj/YmLsrXrcK02lVXr/dJqbS6r1q+L9+mxN3d3Hnd+dqqmeeX6wtw0FVCuAQAh4mJDABHn+Y1lvd61o63dqaQiWK43lVVrU2m1Pth/rLOIJ8aeXK7zR1OuAQBB7NoBAF20tTvtrKjVptLqzoK9pYdyfUFOui7IDX4uGJ2kKMo1AIw4FGkAOIPWtnbtrKjTprLgkpD3S6u05cAxNbYEL1pMig0E11znBmeup+WkUa4BYAQ4XZFmjTQASIoORGnquBRNHZeimy/JlXS8XL9fWqXN3sz1L97ao6bWYLlOjovWedmputC7mHFaTpryMynXADBSMCMNAH3Q2tauHRW1nRczdiwL6Vqug8tCjs9eT6JcA0DEYmkHAAyi1rZ2bS+v7byYcVNZtbYeOF6uU+KidX5OR7lO1wU5aZqYkUi5BoAIQJEGgCHW0tau7YdqO2et3/fKdXOXcj2ty6z1BTlpmpiZKDPKNQCEE4o0AISBlrZ2fXSoprNcbyqt1taDNcfLdXx0Z6me5m3FNyGDcg0AfqJIA0CY6ijXHUtCNpdVa+uBGjV7tzhPjY/uvJDxgpw0XZiTrryMBMo1AAwRdu0AgDAVEwjeyvz87DTd4o01t3rluux4uf7Zmt2d5TotIUbTcrx9rr2CTbkGgKFHkQaAMBMbHaVp3vKOz3pjHeX6/S4z18vWlKilLfhbxbSEmG47hVyQk6bcUcfLdV/uBgkA6B2KNABEgK7lukNTa5s+Othx+/MqbSqr1tLVx8t1emKwXMdGR2n1RxVq9sbLqhr0wHObJIkyDQD9QJEGgAgVFx0IzkDnpkmaIClYrrcdrOm2Fd8H+4+ddG5DS5u+9eJmZSTF6uyxKRqbGsfSEADoIy42BIBhLv/+P+hMf9OnxEdr6tgUTRmborPHJuvssSk6e2yKRifHUrABjGhcbAgAI1h2eoLKqhpOGh+fFq8ffGa6PjpU433U6uXNB/Tk+pbOY0YlxmjK2BRN9Qr2FK9gZyTFDuVLAICwRJEGgGHuvvlT9cBzm9TQ0tY5lhAT0DevO0ezCjI1qyCzc9w5p4raJm0/VNutYD//bplqGls7jxudHNc5cz1lbHLnbHZaQsyQvjYA8BNFGgCGuY4LCnuza4eZaUxKvMakxGv2WaM7x51zOnSsSdsO1Wi7V7C3HarVM8X7VNd8vKCPTY3rXBbSMYM9ZUyyUuIp2ACGH9ZIAwBC1t7utL+6QdsP1WqbV7C3H6rV9vIaNba0dx6Xk57Qbeb67LHJOmtMshJjmc8BEN5YIw0AGBRRUabcUYnKHZWoK88Z0zne1u5UerReH52wROTNnUc6b4luJuWNSuyy9jq4VGRyVrLiYwJ+vSQA6DWKNABgwAWiTBMzkzQxM0nXnDe2c7y1rV17Kuu95SG1nUtFVmyrUGt78DekUSZNzEzSlDHJmjru+Ax2wehkxUZH+fWSAOAkFGkAwJCJDkRpclayJmcl67ppx8db2tq1+3CdtzykVtsP1WjboRq9+mG52ryCHR1lmjQ6KTiDPSZFU8cFC/bEzCTFBCjYAIYeRRoA4LuYQFTwwsSxKd3Gm1rbVFJR1215yJb9x/Ty5oPquMQnJmCanOUtDxkT/Dx1XIomZCQqEMUe2AAGD0UaABC24qIDOnd8qs4dn9ptvKG5TTsrajvL9UeHarRx71H97r39Xc4Nzn6fPTZZZ49L0dljgruJ5I5KUBQFG8AAoEgDACJOQmxA03LSNC0nrdt4XVOrtpfXeruHBEv2ul2Vev7d4wU7ISagKd7ykM6SPTZF2WnxnXdxfH5jWa+2CwQwslGkAQDDRlJctKbnpWt6Xnq38WONLd1uMrP9UK1Wb6/Qb94p7TwmOS5aU8YmKy4QpQ17j6qlLbh2pKyqQQ88t0mSKNMAumEfaQDAiFVV33zCFn01Wr+rUu09/NMYG4jSjdOzlTcqUXkZCcrLSFTeqESNSYljqQgwjLGPNAAAPUhPjNXM/AzNzM/oHMu//w89Htvc1q7V2yt06FhTt/HY6CjlpicoNyNReaOOF+y8jATljUpUemJM55IRAMMLRRoAgC6y0xNUVtVw0nhOeoLeuP8qNba0qayqQfsq67XvaINKK+u172i99lU26P3SKlXVt3Q7LzkuWrldCnbnY69oJ8XxTzEQqfi/FwCALu6bP1UPPLdJDS1tnWMJMQHdN3+qJCk+JtC5F3ZPahpbtK+ywSvX9So9Gizde47Uac32w92+ryRlJMUqb1THjPbxgp2Xkaic9ARuQgOEMYo0AABddFxQGOquHSnxMTovO0bnZaee9JxzTkfqmjtns4NFOzibvbmsWn/64GDnRY5S8Dbq41LjgzPZXQp2xxKSsanx7JUN+IiLDQEACBNt7U4HjzUGi3bHbPbRepV6M9wHjzWq6z/bMQFTTnqwVOd2mc3uWD6SmRTL+mygn7jYEACACBCIChbjnPQEzSrIPOn5ptY27a/yirY3kx0s2vVavv+gKuuaux2fGBsIlmpvJjv3hIshU+JjhuqlAcMSRRoAgAgRFx1Q/ugk5Y9O6vH52qbWzqUiXct26dF6vVVyRHXN3ddnpyfGdFuX3XXnkZz0BMXHBHqVixvYYKSiSAMAMEwkx0XrnHGpOmdcz+uzj9a3nDSbva+yXh8eqNGft5Srua292zljU+O6rcvuekHkuNR4RQei9PzGsm4XZ3IDG4wkFGkAAEYAM1NGUqwykmJ10Ql3fpSk9nan8pqmznLdtWiv31WpF95t6Hajmugo0/j0eJUfa1JTa/cC3tDSpu/98UPdeFE2N6vBsMbFhgAA4IyaW9t1oLqhW8Hed7RBv3tv/ynPiY4yZaXEKSslTmNS4pSVEq8xKXEakxqnMSnxXcbjFBNgmz+EJy42BAAA/RIbHaWJmUmamNl9ffY7e472eAObtIRofe7SiSo/1qSK2iaVHm3Qxr1VOnLCBZEdMpJiO0t115LdUbo7HifGUl0QPvivEQAAhOxUN7D59o3Telwj3dLWrsO1TSo/1qTymiZV1DSpvKZR5TXBsYqaRu0or1VFTZNa20/+rXlSbEBjUrsU7ZR4jUmNU1Zy99LNrdkxFCjSAAAgZH29gU1MIErj0xI0Pi3htN+3vd2pqqElWLK90t3xuKK2SRXHmrS5rFrlNeWqP2E3EkmKDUR1Lis5sXR3fZyZFKtolpUgRKyRBgAAEa22qVXlxxq92e3jpbuiSwGvqGnS0fqWk841kzKTYo+v3/aWkARnuOO7le7ebgeI4YU10gAAYNhKjotWclayCrKST3tcU2ubDtc2q/xYY2fhrqgJLifpmPX+8OAxHa5tVlsPy0pS4qO7reM+cQ13x3hqQvRpl5Ww7/bwQZEGAAAjQlx0oPPOkafT1u5UWdfcbf12RU1TZwGvqGnSu/uqVF7TqMaW9pPOj4uO6racpOuFkzvLa/X42j2dWway73Zk6/fSDjMLSCqWVOac+7iZ5Ut6SlKGpHck3eqcazazOElPSLpE0hFJn3HO7fa+xwOS7pTUJumrzrnlZ/pzWdoBAAD85JxTTVOrN5vd6M1ue8tJusx6lx9r1LHG1tN+r9hAlK46Z4wykmOV6e33nZEUq8ykOGV6Y6OSYtkm0AeDvbTja5K2Suq4jdL3Jf3AOfeUmT2iYEF+2Pt81Dl3lpnd4h33GTM7T9Itks6XlC3pz2Z2tnPu5CsHAAAAwoSZKTU+RqnxMTprzOmXlTS2tKmipklF//d19TSF2dzWrp0VtXp7d7Mq65t1qnnO1PhoZSbHdRbt0ckdpTuuWwEfnRynUUkxiotmXfdg6leRNrNcSTdI+o6kb1hwQdBVkj7nHfK4pH9VsEjf5D2WpGcl/dg7/iZJTznnmiTtMrMdkmZKWtufbAAAAOEiPiagvIxEZacn9Ljvdk56gl75xlxJwaUlVfXNqqxr1pG6Lp9rm3Wkrqnz8d4j9dq4t0pH63te0y1JKXHRykjumN32PifHnTTr3TETzgWVfdPfGekfSvpHSSne15mSqpxzHb+/KJXUseAnR9I+SXLOtZpZtXd8jqS3unzPrud0Y2YLJS2UpAkTJvQzOgAAwNA61b7b982f2vl1IMqCZTc5TlN68T3b252qG1o6S3dll7J9pLOMB2+K835ptSrrmnvco1sK7tMdLN7Hy3ZmUqwyk0+e9c5Mjh3xN8gJ+dWb2ccllTvnNpjZvI7hHg51Z3judOd0H3RuiaQlUnCNdJ8CAwAA+Kyv+273RlSUaZS3hro3nHM61tganOmubepSwJt1pPZ4ET9Y3agt+4+psq5ZzW0nX1QpSfExUZ3ruDOSus58x3Up4MdnvZNiA32+UU4473LSnx8jZku60cz+UlK8gmukfygp3cyivVnpXEn7veNLJeVJKjWzaElpkiq7jHfoeg4AAMCwsmBGjq9F0MyUlhCjtIQY5Y9OOuPxzjnVNrWecolJx/iR2mZ9dLBGR+qaO3clOVFsdNSpZ7hPXHqSHKtXtxzSP/12c+cMfrjtchJykXbOPSDpAUnyZqTvdc593syekXSzgjt33C7pBe+UF72v13rPv+acc2b2oqRfmdl/Knix4RRJ60PNBQAAgIFjZkqJj1FKfIwmZvaueNc3t3VZ492kI7Vd1nt7s96Vdc0qqahVZV1zj3enPJWGljY9uHxbZBfp0/impKfM7P9I2ihpmTe+TNLPvYsJKxXcqUPOuQ/M7NeStkhqlfQVduwAAACITGampLhoJcVFKy8jsVfnNDS36YhXrrvOdH/npa09Hr+/hws2/TAgRdo5t0LSCu9xiYK7bpx4TKOkT5/i/O8ouPMHAAAARpiE2IByYxOVO6p78X7szd097nKSfYab6gwVdvUGAABAWLpv/lQlnLAl34m7nPhpZO9ZAgAAgLA1GLucDCSKNAAAAMKW37ucnA5LOwAAAIAQUKQBAACAEFCkAQAAgBBQpAEAAIAQUKQBAACAEFCkAQAAgBBQpAEAAIAQUKQBAACAEFCkAQAAgBBQpAEAAIAQmHPO7wwhMbMKSXt8+KNHSzrsw58bqXi/+ob3q294v/qO96xveL/6hverb3i/+sav92uicy6rpycitkj7xcyKnXOFfueIFLxffcP71Te8X33He9Y3vF99w/vVN7xffROO7xdLOwAAAIAQUKQBAACAEFCk+26J3wEiDO9X3/B+9Q3vV9/xnvUN71ff8H71De9X34Td+8UaaQAAACAEzEgDAAAAIaBI95KZPWpm5Wa22e8skcDM8szsdTPbamYfmNnX/M4Uzsws3szWm9l73vv1bb8zRQIzC5jZRjP7vd9Zwp2Z7TazTWb2rpkV+50n3JlZupk9a2Yfen+PXeZ3pnBlZlO9/646Po6Z2d/7nSucmdnXvb/rN5vZk2YW73emcGZmX/Peqw/C7b8tlnb0kpkVSaqV9IRzbprfecKdmY2XNN45946ZpUjaIGmBc26Lz9HCkpmZpCTnXK2ZxUhaI+lrzrm3fI4W1szsG5IKJaU65z7ud55wZma7JRU659izthfM7HFJq51zS80sVlKic67K71zhzswCksokXeqc8+NeD2HPzHIU/Dv+POdcg5n9WtJLzrnH/E0WnsxsmqSnJM2U1Czpj5Lucc5t9zWYhxnpXnLOrZJU6XeOSOGcO+Cce8d7XCNpq6Qcf1OFLxdU630Z433wU+5pmFmupBskLfU7C4YXM0uVVCRpmSQ555op0b12taSdlOgzipaUYGbRkhIl7fc5Tzg7V9Jbzrl651yrpJWSPulzpk4UaQw6M5skaYakdf4mCW/eMoV3JZVLesU5x/t1ej+U9I+S2v0OEiGcpD+Z2QYzW+h3mDBXIKlC0s+8pUNLzSzJ71AR4hZJT/odIpw558okPSRpr6QDkqqdc3/yN1VY2yypyMwyzSxR0l9KyvM5UyeKNAaVmSVL+o2kv3fOHfM7TzhzzrU556ZLypU00/t1FnpgZh+XVO6c2+B3lggy2zl3saTrJX3FW66GnkVLuljSw865GZLqJN3vb6Tw5y2BuVHSM35nCWdmNkrSTZLyJWVLSjKzL/ibKnw557ZK+r6kVxRc1vGepFZfQ3VBkcag8db6/kbSL51zz/mdJ1J4v0JeIek6n6OEs9mSbvTW/T4l6Soz+4W/kcKbc26/97lc0m8VXG+InpVKKu3yW6FnFSzWOL3rJb3jnDvkd5Aw9xeSdjnnKpxzLZKek3S5z5nCmnNumXPuYudckYLLbMNifbREkcYg8S6eWyZpq3PuP/3OE+7MLMvM0r3HCQr+Rfuhv6nCl3PuAedcrnNukoK/Sn7NOceMzimYWZJ30a+8JQrXKvjrUvTAOXdQ0j4zm+oNXS2JC6XP7LNiWUdv7JU0y8wSvX8rr1bwOiKcgpmN8T5PkPQphdF/Z9F+B4gUZvakpHmSRptZqaRvOeeW+ZsqrM2WdKukTd66X0n6J+fcSz5mCmfjJT3uXfEeJenXzjm2dMNAGSvpt8F/sxUt6VfOuT/6Gyns/Z2kX3rLFUok3eFznrDmrV29RtIiv7OEO+fcOjN7VtI7Ci5R2KgwvGNfmPmNmWVKapH0FefcUb8DdWD7OwAAACAELO0AAAAAQkCRBgAAAEJAkQYAAABCQJEGAAAAQkCRBgAAAEJAkQYAAABCQJEGAAAAQkCRBgAAAELw/wGeoF6iPitvegAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,6))\n",
    "plt.plot(clusters_df.num_clusters, clusters_df.cluster_errors, marker = \"o\" )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "sGx_Q_4Iho_7"
   },
   "source": [
    "### Find out the optimal value of K"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the above curve, 4 may be a good value but the 4 groups don't seemed to be balanced where we find out the cluster. One of them is having 8 data points whereas the are other 3 are having more than 200 data points.\n",
    "\n",
    "Therefore, taking 3 as optimal number of cluster"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "5EoRD5PHhpAT"
   },
   "source": [
    "### Using optimal value of K - Cluster the data. \n",
    "Note: Since the data has more than 2 dimension we cannot visualize the data. As an alternative, we can observe the centroids and note how they are distributed across different dimensions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "fY5IjhFihpAm"
   },
   "source": [
    "You can use kmeans.cluster_centers_ function to pull the centroid information from the instance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "i2JjEPrcho__"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.91987072 -0.52009251 -0.89320752 -1.06435572 -0.50042171 -0.2190738\n",
      "  -0.7791213   0.86589322 -0.74535635 -0.484632   -0.78240328 -0.78341064\n",
      "  -0.38498232  0.83878747 -0.09524349 -0.30171562 -1.05420601 -1.11069466]\n",
      " [-0.2339617  -0.57387481 -0.30776905 -0.03041322  0.2050726  -0.11653151\n",
      "  -0.45904181  0.32506329 -0.48798836 -0.53604446 -0.41380935 -0.46366305\n",
      "  -0.60155031 -0.61924057 -0.06177969  0.01066762  0.81278556  0.69897299]\n",
      " [ 1.13076532  1.17094237  1.19500584  1.01909505  0.21505188  0.34250798\n",
      "   1.27180461 -1.19061224  1.27548416  1.09266768  1.22038121  1.28132727\n",
      "   1.07954232 -0.02879497  0.16229031  0.26566456 -0.00535553  0.18380067]]\n"
     ]
    }
   ],
   "source": [
    "clusters = KMeans(3, n_init = 5)\n",
    "clusters.fit(data_sc)\n",
    "centroids = clusters.cluster_centers_\n",
    "print(centroids)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "A2T8SxBdhpBL"
   },
   "source": [
    "### 7. Store the centroids in a dataframe with column names from the original dataset given "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "xpjTngRNhpBP"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>compactness</th>\n",
       "      <th>circularity</th>\n",
       "      <th>distance_circularity</th>\n",
       "      <th>radius_ratio</th>\n",
       "      <th>pr.axis_aspect_ratio</th>\n",
       "      <th>max.length_aspect_ratio</th>\n",
       "      <th>scatter_ratio</th>\n",
       "      <th>elongatedness</th>\n",
       "      <th>pr.axis_rectangularity</th>\n",
       "      <th>max.length_rectangularity</th>\n",
       "      <th>scaled_variance</th>\n",
       "      <th>scaled_variance.1</th>\n",
       "      <th>scaled_radius_of_gyration</th>\n",
       "      <th>scaled_radius_of_gyration.1</th>\n",
       "      <th>skewness_about</th>\n",
       "      <th>skewness_about.1</th>\n",
       "      <th>skewness_about.2</th>\n",
       "      <th>hollows_ratio</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.919871</td>\n",
       "      <td>-0.520093</td>\n",
       "      <td>-0.893208</td>\n",
       "      <td>-1.064356</td>\n",
       "      <td>-0.500422</td>\n",
       "      <td>-0.219074</td>\n",
       "      <td>-0.779121</td>\n",
       "      <td>0.865893</td>\n",
       "      <td>-0.745356</td>\n",
       "      <td>-0.484632</td>\n",
       "      <td>-0.782403</td>\n",
       "      <td>-0.783411</td>\n",
       "      <td>-0.384982</td>\n",
       "      <td>0.838787</td>\n",
       "      <td>-0.095243</td>\n",
       "      <td>-0.301716</td>\n",
       "      <td>-1.054206</td>\n",
       "      <td>-1.110695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.233962</td>\n",
       "      <td>-0.573875</td>\n",
       "      <td>-0.307769</td>\n",
       "      <td>-0.030413</td>\n",
       "      <td>0.205073</td>\n",
       "      <td>-0.116532</td>\n",
       "      <td>-0.459042</td>\n",
       "      <td>0.325063</td>\n",
       "      <td>-0.487988</td>\n",
       "      <td>-0.536044</td>\n",
       "      <td>-0.413809</td>\n",
       "      <td>-0.463663</td>\n",
       "      <td>-0.601550</td>\n",
       "      <td>-0.619241</td>\n",
       "      <td>-0.061780</td>\n",
       "      <td>0.010668</td>\n",
       "      <td>0.812786</td>\n",
       "      <td>0.698973</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.130765</td>\n",
       "      <td>1.170942</td>\n",
       "      <td>1.195006</td>\n",
       "      <td>1.019095</td>\n",
       "      <td>0.215052</td>\n",
       "      <td>0.342508</td>\n",
       "      <td>1.271805</td>\n",
       "      <td>-1.190612</td>\n",
       "      <td>1.275484</td>\n",
       "      <td>1.092668</td>\n",
       "      <td>1.220381</td>\n",
       "      <td>1.281327</td>\n",
       "      <td>1.079542</td>\n",
       "      <td>-0.028795</td>\n",
       "      <td>0.162290</td>\n",
       "      <td>0.265665</td>\n",
       "      <td>-0.005356</td>\n",
       "      <td>0.183801</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   compactness  circularity  distance_circularity  radius_ratio  \\\n",
       "0    -0.919871    -0.520093             -0.893208     -1.064356   \n",
       "1    -0.233962    -0.573875             -0.307769     -0.030413   \n",
       "2     1.130765     1.170942              1.195006      1.019095   \n",
       "\n",
       "   pr.axis_aspect_ratio  max.length_aspect_ratio  scatter_ratio  \\\n",
       "0             -0.500422                -0.219074      -0.779121   \n",
       "1              0.205073                -0.116532      -0.459042   \n",
       "2              0.215052                 0.342508       1.271805   \n",
       "\n",
       "   elongatedness  pr.axis_rectangularity  max.length_rectangularity  \\\n",
       "0       0.865893               -0.745356                  -0.484632   \n",
       "1       0.325063               -0.487988                  -0.536044   \n",
       "2      -1.190612                1.275484                   1.092668   \n",
       "\n",
       "   scaled_variance  scaled_variance.1  scaled_radius_of_gyration  \\\n",
       "0        -0.782403          -0.783411                  -0.384982   \n",
       "1        -0.413809          -0.463663                  -0.601550   \n",
       "2         1.220381           1.281327                   1.079542   \n",
       "\n",
       "   scaled_radius_of_gyration.1  skewness_about  skewness_about.1  \\\n",
       "0                     0.838787       -0.095243         -0.301716   \n",
       "1                    -0.619241       -0.061780          0.010668   \n",
       "2                    -0.028795        0.162290          0.265665   \n",
       "\n",
       "   skewness_about.2  hollows_ratio  \n",
       "0         -1.054206      -1.110695  \n",
       "1          0.812786       0.698973  \n",
       "2         -0.005356       0.183801  "
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "centroids_df = pd.DataFrame(centroids, columns=data.columns)\n",
    "centroids_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "n2kFVi2GhpBn"
   },
   "source": [
    "### Use kmeans.labels_ function to print out the labels of the classes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Ahx91q_ghpBp"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "       2, 1, 1, 1, 0, 2, 0, 0, 1, 0, 1, 1, 0, 0, 2, 2, 0, 1, 2, 1, 2, 1,\n",
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       "       1, 2, 0, 1, 1, 1, 0, 0, 0, 1, 2, 1, 2, 0, 1, 1, 1, 1, 2, 1, 0, 2,\n",
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       "       0, 1, 0, 1, 1, 0, 1, 2, 2, 1, 1, 2, 2, 1, 1, 0, 1, 2, 2, 2, 2, 1,\n",
       "       2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 0, 2, 1, 0, 2, 2, 2, 1, 2, 0, 0, 2,\n",
       "       2, 2, 1, 2, 1, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 1, 1, 0, 2, 0, 0,\n",
       "       0, 2, 2, 0, 2, 2, 0, 1, 1, 2, 1, 0, 2, 2, 0, 1, 1, 2, 2, 2, 0, 2,\n",
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       "       0, 1, 2, 0, 0, 1, 1, 2, 0, 0, 2, 0, 1, 1, 1, 1, 1, 1, 2, 1, 0])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "labels = clusters.labels_\n",
    "labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
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       "      <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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>labels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
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       "      <th>0</th>\n",
       "      <td>240</td>\n",
       "      <td>240</td>\n",
       "      <td>240</td>\n",
       "      <td>240</td>\n",
       "      <td>240</td>\n",
       "      <td>240</td>\n",
       "      <td>240</td>\n",
       "      <td>240</td>\n",
       "      <td>240</td>\n",
       "      <td>240</td>\n",
       "      <td>240</td>\n",
       "      <td>240</td>\n",
       "      <td>240</td>\n",
       "      <td>240</td>\n",
       "      <td>240</td>\n",
       "      <td>240</td>\n",
       "      <td>240</td>\n",
       "      <td>240</td>\n",
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       "      <th>1</th>\n",
       "      <td>313</td>\n",
       "      <td>313</td>\n",
       "      <td>313</td>\n",
       "      <td>313</td>\n",
       "      <td>313</td>\n",
       "      <td>313</td>\n",
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       "      <td>260</td>\n",
       "      <td>260</td>\n",
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       "      <td>260</td>\n",
       "      <td>260</td>\n",
       "      <td>260</td>\n",
       "      <td>260</td>\n",
       "      <td>260</td>\n",
       "      <td>260</td>\n",
       "      <td>260</td>\n",
       "      <td>260</td>\n",
       "      <td>260</td>\n",
       "      <td>260</td>\n",
       "      <td>260</td>\n",
       "      <td>260</td>\n",
       "      <td>260</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         0    1    2    3    4    5    6    7    8    9    10   11   12   13  \\\n",
       "labels                                                                         \n",
       "0       240  240  240  240  240  240  240  240  240  240  240  240  240  240   \n",
       "1       313  313  313  313  313  313  313  313  313  313  313  313  313  313   \n",
       "2       260  260  260  260  260  260  260  260  260  260  260  260  260  260   \n",
       "\n",
       "         14   15   16   17  \n",
       "labels                      \n",
       "0       240  240  240  240  \n",
       "1       313  313  313  313  \n",
       "2       260  260  260  260  "
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_sc_final = pd.DataFrame(data_sc)\n",
    "data_sc_final['labels'] = labels\n",
    "data_sc_final.groupby('labels').count()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "SmQyHhmFhpB3"
   },
   "source": [
    "## Hierarchical Clustering "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "_zAMRDe_hpB5"
   },
   "source": [
    "### 8. Variable creation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "VESIKt49hpB6"
   },
   "source": [
    "For Hierarchical clustering, we will create datasets using multivariate normal distribution to visually observe how the clusters are formed at the end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "qpUh49bKhpB8"
   },
   "outputs": [],
   "source": [
    "np.random.seed(101)  # for repeatability of this dataset\n",
    "a = np.random.multivariate_normal([10, 0], [[3, 1], [1, 4]], size=[100,])\n",
    "b = np.random.multivariate_normal([0, 20], [[3, 1], [1, 4]], size=[50,])\n",
    "c = np.random.multivariate_normal([10, 20], [[3, 1], [1, 4]], size=[100,])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://docs.scipy.org/doc/numpy-1.15.1/reference/generated/numpy.random.multivariate_normal.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Eui7Qgc8hpCH"
   },
   "source": [
    "### 9. Combine all three arrays a,b,c into a dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Nle34XhhhpCI"
   },
   "outputs": [],
   "source": [
    "a_df = pd.DataFrame(a)\n",
    "ab_df = a_df.append(pd.DataFrame(b))\n",
    "abc = ab_df.append(pd.DataFrame(c))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "lov1nQqAhpCa"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(250, 2)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abc.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "v6JlILlihpCe"
   },
   "source": [
    "### 10. Use scatter matrix to print all the 3 distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "i6Nf9LznhpCg"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1a0d99ce4e0>"
      ]
     },
     "execution_count": 52,
     "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(x=abc[0], y=abc[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Ufj36K5NhpCo"
   },
   "source": [
    "### 11. Find out the linkage matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "rXJAOAilhpCp"
   },
   "source": [
    "https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.cluster.hierarchy.linkage.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "EOxwi5gshpCt"
   },
   "source": [
    "Use ward as linkage metric and distance as Eucledian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "xJsL16lqhpCu"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ward 0.9536963071171022\n"
     ]
    }
   ],
   "source": [
    "Z = linkage(abc, 'ward')\n",
    "cen, coph_dists = cophenet(Z , pdist(abc))\n",
    "print(\"Ward\", cen)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "UnVS8VYMhpC9"
   },
   "source": [
    "### 12. Plot the dendrogram for the consolidated dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "oeLtemVqhpC_"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 7))  \n",
    "plt.title(\"Dendrograms\")  \n",
    "dend = sch.dendrogram(sch.linkage(abc, method='ward'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "TMfqcHfuhpDH"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0], dtype=int64)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cluster = AgglomerativeClustering(n_clusters=3, affinity='euclidean', linkage='ward')  \n",
    "cluster.fit_predict(abc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "PJhBRBIwhpDM"
   },
   "outputs": [],
   "source": [
    "abc['labels'] = cluster.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>labels</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>101</td>\n",
       "      <td>101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>49</td>\n",
       "      <td>49</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0    1\n",
       "labels          \n",
       "0       101  101\n",
       "1       100  100\n",
       "2        49   49"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abc.groupby('labels').count()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "QXE-T9cHhpDS"
   },
   "source": [
    "### 13. Recreate the dendrogram for last 12 merged clusters "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.cluster.hierarchy.dendrogram.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "4PKR3o5QhpDX"
   },
   "source": [
    "Hint: Use truncate_mode='lastp' attribute in dendrogram function to arrive at dendrogram "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "GDri9xtAhpDY"
   },
   "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": [
    "dend = sch.dendrogram(sch.linkage(abc, method='ward'), p=12, truncate_mode='lastp')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zjFjCWL5hpDr"
   },
   "source": [
    "### 14. From the truncated dendrogram, find out the optimal distance between clusters which u want to use an input for clustering data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "DQ5m6orQhpDt"
   },
   "source": [
    "https://docs.scipy.org/doc/scipy-0.15.1/reference/generated/scipy.cluster.hierarchy.fcluster.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "5-yUhkgMhpDx"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "owSZBbSUhpEC"
   },
   "source": [
    "### 15. Using this distance measure and fcluster function to cluster the data into 3 different groups"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "HLVorGUEhpEE"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Rgty9iOlhpEL"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "642Ur5TWhpEX"
   },
   "source": [
    "### Use matplotlib to visually observe the clusters in 2D space "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "YHHSylfQhpEX"
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [
    "n2kFVi2GhpBn",
    "Ufj36K5NhpCo",
    "zjFjCWL5hpDr",
    "owSZBbSUhpEC",
    "642Ur5TWhpEX"
   ],
   "name": "R4_Internal_Lab_Clustering.ipynb",
   "provenance": [],
   "version": "0.3.2"
  },
  "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}