K_Mean_Clustering.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing all the necessary libraries\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn import preprocessing\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "from sklearn.preprocessing import StandardScaler, normalize\n",
    "from sklearn.cluster import KMeans\n",
    "from scipy.spatial.distance import cdist\n",
    "from sklearn import metrics\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>CustomerID</th>\n",
       "      <th>Genre</th>\n",
       "      <th>Age</th>\n",
       "      <th>Annual Income (k$)</th>\n",
       "      <th>Spending Score (1-100)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>Male</td>\n",
       "      <td>19</td>\n",
       "      <td>15</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>Male</td>\n",
       "      <td>21</td>\n",
       "      <td>15</td>\n",
       "      <td>81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>Female</td>\n",
       "      <td>20</td>\n",
       "      <td>16</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>Female</td>\n",
       "      <td>23</td>\n",
       "      <td>16</td>\n",
       "      <td>77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>Female</td>\n",
       "      <td>31</td>\n",
       "      <td>17</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   CustomerID   Genre  Age  Annual Income (k$)  Spending Score (1-100)\n",
       "0           1    Male   19                  15                      39\n",
       "1           2    Male   21                  15                      81\n",
       "2           3  Female   20                  16                       6\n",
       "3           4  Female   23                  16                      77\n",
       "4           5  Female   31                  17                      40"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Importing data\n",
    "data = pd.read_csv(\"~/Desktop/Desktop/Dataset/Mall_Customers_BP.csv\")\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "CustomerID                 int64\n",
       "Genre                     object\n",
       "Age                        int64\n",
       "Annual Income (k$)         int64\n",
       "Spending Score (1-100)     int64\n",
       "dtype: object"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Checking all the data types\n",
    "df.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     CustomerID   Genre  Age  Annual Income (k$)  Spending Score (1-100)\n",
      "0             1    Male   19            0.000000                0.387755\n",
      "1             2    Male   21            0.000000                0.816327\n",
      "2             3  Female   20            0.008197                0.051020\n",
      "3             4  Female   23            0.008197                0.775510\n",
      "4             5  Female   31            0.016393                0.397959\n",
      "..          ...     ...  ...                 ...                     ...\n",
      "195         196  Female   35            0.860656                0.795918\n",
      "196         197  Female   45            0.909836                0.275510\n",
      "197         198    Male   32            0.909836                0.744898\n",
      "198         199    Male   32            1.000000                0.173469\n",
      "199         200    Male   30            1.000000                0.836735\n",
      "\n",
      "[200 rows x 5 columns]\n"
     ]
    }
   ],
   "source": [
    "# Performing Standard Scaling while pre-processing data\n",
    "scaler = StandardScaler()\n",
    "df[['Annual Income (k$)', 'Spending Score (1-100)']] = scaler.fit_transform(df[['Annual Income (k$)', 'Spending Score (1-100)']])\n",
    "print(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Optimum number of clusters using elbow method -\n",
    "\n",
    "distortions = []\n",
    "inertias = []\n",
    "mapping1 = {}\n",
    "mapping2 = {}\n",
    "K = range(1, 15)\n",
    "\n",
    "# Making a seperate array file having data for Annual income and spending score\n",
    "\n",
    "array1 = df['Annual Income (k$)'].to_numpy()\n",
    "array2 = df['Spending Score (1-100)'].to_numpy()\n",
    "array = np.array(list(zip(array1, array2))).reshape(len(array1), 2)\n",
    "\n",
    "for k in K:\n",
    "    # Building and fitting the model\n",
    "    kmeanModel = KMeans(n_clusters=k)\n",
    "    kmeanModel.fit(array)\n",
    "\n",
    "    distortions.append(sum(np.min(cdist(array, kmeanModel.cluster_centers_,\n",
    "                                        'euclidean'), axis=1)) / array.shape[0])\n",
    "    inertias.append(kmeanModel.inertia_)\n",
    "\n",
    "    mapping1[k] = sum(np.min(cdist(array, kmeanModel.cluster_centers_,\n",
    "                                   'euclidean'), axis=1)) / array.shape[0]\n",
    "    mapping2[k] = kmeanModel.inertia_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 : 0.28732920189537803\n",
      "2 : 0.24292656691665446\n",
      "3 : 0.17933377150541488\n",
      "4 : 0.15082836340613298\n",
      "5 : 0.11815479432710524\n",
      "6 : 0.11112000368540828\n",
      "7 : 0.1044359606420634\n",
      "8 : 0.09393611512914361\n",
      "9 : 0.08643992903159538\n",
      "10 : 0.08059377195989027\n",
      "11 : 0.07540293005035847\n",
      "12 : 0.07245081781913605\n",
      "13 : 0.06855406127413047\n",
      "14 : 0.06588949103132469\n"
     ]
    },
    {
     "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": [
    "# Using Distortion -\n",
    "# Tabulating the results -\n",
    "\n",
    "for key,val in mapping1.items():\n",
    "    print(str(key)+' : '+str(val))\n",
    "\n",
    "# Visualizing the result -\n",
    "\n",
    "plt.plot(K, distortions, 'bx-')\n",
    "plt.xlabel('Values of K')\n",
    "plt.ylabel('Distortion')\n",
    "plt.title('The Elbow Method using Distortion')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 : 23.040720326039906\n",
      "2 : 13.993505283127979\n",
      "3 : 9.058985215159455\n",
      "4 : 6.110312266413655\n",
      "5 : 3.583117905952559\n",
      "6 : 3.0987079488159965\n",
      "7 : 2.6260623772655123\n",
      "8 : 2.2191023969247357\n",
      "9 : 1.8826909978439232\n",
      "10 : 1.6412663266849248\n",
      "11 : 1.4553320984391274\n",
      "12 : 1.3229025293309493\n",
      "13 : 1.165437147535807\n",
      "14 : 1.0636880892948428\n"
     ]
    },
    {
     "data": {
      "image/png": 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wLFkSmnWuWhWS/tixYbmISEunxJ+D4cPhuutgyxb47ndD0p84MSwXEWnplPhz9KMfwc47w8MPw9lnK+mLSPFQ4s/RjBmwfn14/qc/qZ9+ESkeSvw5SNX0H3gAhg0LbftPOUXJX0SKgxJ/DmbODDX9ESPgN7+BlSvhpJPCchGRli7rG7jM7DhgH6Btapm7X5WPoFq6iy+ueT5kCJxwAkyaBAsWxBeTiEi2sjriN7ObgW8APwYMOAXYLY9xFZVrroHVq9WOX0SKQ7alnqHufhqw0t2vBIYAffIXVnHZd1/49rfDRd7q6rijERFpWLaJP2q/wjoz6wVsAnbPT0jF6corQ3fNv/513JGIiDQs28T/iJl1Bm4AZhN61vx7voIqRv37w/e/D7feCu++G3c0IiL1M3dv2gfM2gBt3X1VfkLaWnl5uc+aNatQm8tZdXXYAZx8Mtx1V9zRiEjSmdlL7l5ed3mDR/xmNiJ6PDk1AccBI6PnkmaXXeC88+Cee+DVV+OORkQks8ZKPcOixxMyTMfnMa6idckl0KkTXHpp3JGIiGTWYDt+d/9V9PQqd1+Y/pqZ6eJuBl26hHb+l14K//43DB0ad0QiIrVle3H3/gzLJjVnIKXk/POhZ0/45S/D8IwiIi1Jg0f8ZrYX4W7dHevU9DuRdgev1Na+PVx2Gfz4xzB1Khx7bNwRiYjUaOyIfyChlt+Z2vX9g4Dv5ze04nb22dCvXzjq37Il7mhERGo0VuN/yMweAS5x92sLFFNJ2H77cFPX6afD/feH3jtFRFqCRmv87v4FMKoAsZScU0+FffaByy+HzZvjjkZEJMj24u6/zewvZnaEmR2UmvIaWQkoK4Orr4a33oIJE+KORkQkyOrOXTPLNMSIu/uI5g9pa8Vy524m7qHr5g8/hPnzoa0uiYtIgdR3525W/fG7u0aUzZEZXHstjBwJf/0r/OQncUckIkmXbX/8Pc1snJk9Hs0PMrOz8hta6RgxAo4+OuwAVq+OOxoRSbpsa/zjgSlAr2j+beCCfARUqq69Fj75BH7/+7gjEZGkyzbxd3P3icAWAHffDHyRt6hK0ODBodfO3/0Oli2LOxoRSbJsE/9aM9sJcAAzOxQoWLfMpeLqq2HdujBAu4hIXLJN/D8BJgP9zexZ4A7C+LvSBHvvDaedFi7yLloUdzQiklRZJX53n03oonko8ANgH3efm8/AStUVV4QmnldeGXckIpJU2R7xAxwC7E/op+dbZnZafkIqbbvtBj/8Idx+e7ixS0Sk0LJtznkn8FvgcGBwNG11U4Bk55e/hHbtQlcOIiKFltUNXIQkP8ibOkCvZNSjR7iR69e/htmz4SB1fiEiBZRtqec1YOd8BpI0F10EXbuGo38RkULKuh0/8IaZTTGzyakpn4GVuh13hF/8AqZMgRkz4o5GRJIk207ahmVa7u71piwzu40wiMvH7v7laFlX4D6gH/AeMNbdVza2/WLupK0h69fDgAHQty88+2zo10dEpLnU10lbts05Z2SaGvnYeGB0nWU/B6a7+wBgejSfWO3awX/9Fzz3HDzySNzRiEhSNJj4zWyNma3OMK0xswa7G3P3p4EVdRaPAVI9008ATso58hJx5pmw555w6aUaolFECqPBxO/uHd29U4apo7t3ymF7Pd29Olp3NdAjl6BLSevWoXXPq6/CvffGHY2IJEFTbuAqKDM728xmmdmsZSXeq9nYsXDAAaHss3Fj3NGISKkrdOJfama7AESPH9f3Rne/xd3L3b28e/fuBQswDq1awTXXwIIFMG5c3NGISKkrdOKfDJwePT8deKjA22+xKirg8MND2WfdurijEZFSlrfEb2b3As8BA81scTRi13XAKDObD4yK5oXQlPM3v4Hqavjzn+OORkRKWVbt+ONWqu34MznuuNC8c8EC6Nw57mhEpJhtUzt+KZwBA2DlSrjhhpplVVVw/fXxxSQipUWJv4UZMwbatAlDNH70UUj6Y8eGoRtFRJqDEn8LM3w43HorbNgQLviOHQsTJ4blIiLNQYm/Bfrud2HIEHjlldBls5K+iDQnJf4WqKoK5s+HgQNh6lQN0ygizUuJv4VJ1fQnToSXX4ZBg8I4vWriKSLNRYm/hZk5s6am365d6Ku/d2+45BKYNy/u6ESkFCjxtzAXX1y7pt+tW0j+HTuGi70ffRRfbCJSGpT4i8Aee8Cjj8LHH4cbvD77LO6IRKSYKfEXifJy+Mc/YM4cOOUU2LQp7ohEpFgp8ReRykq46SZ44gn44Q+hCHrbEJEWaLu4A5Cm+f73YdGi0Itn376hD38RkaZQ4i9CV14JH3wAv/oV9OkThm8UEcmWEn8RMgvdOixZEs4AevWCY4+NOyoRKRaq8Rep1q1h0iTYd1/4+tdh9uy4IxKRYqHEX8Q6dQrNPLt2Dc0833sv7ohEpBgo8Re5Xr3g8cfh88/DDV4rVsQdkYi0dEr8JWDQIHjooTBq15gxYScgIlIfJf4SceSRcOed8MwzoVvnLVvijkhEWiol/hIydmwYuWvSJPjpT+OORkRaKjXnLDEXXhja+N94Y2jjf+GFcUckIi2NEn+JMQtH/YsXw0UXhS6dTzkl7qhEpCVR4i9BZWWh3v/RR6Hev/POcMQRcUclIi2Favwlql270NKnX7/Q0ufNN+OOSERaCiX+ErbTTqGN//bbhzb+1dVxRyQiLYESf4nbffdwd+/y5eHu3jVr4o5IROKmxJ8ABx8cBnGZO1eDuIiIEn9iVFTASSfBlCnwgx/UDOJSVQXXXx9vbCJSWGrVkyDnnhtq/rffHgZxGTYs3PQ1cWLckYlIISnxJ8jw4fDww2EIxyuvhPbtw/zw4XFHJiKFpFJPwowYEW7sAli7NvTtIyLJosSfMFVVcMstcOml0KZNGLP3sss0cLtIkijxJ0hVVU1N/+qrQzPPtm3hmmvgZz9T8hdJCiX+BJk5MyT9VE1/5Eh45BEYOjT073PeeerOWSQJdHE3QS6+eOtlI0eGuv/PfhaS/4YNcPPN0EqHBCIlS4lfMIMbbqgp+2zcCOPGhc7eRKT0xJL4zew9YA3wBbDZ3cvjiENqmIW6f+qC74YNcMcd0Lp13JGJSHOL84h/uLsvj3H7ksHll4fkf8kl4cj/3ntDJ28iUjpUyZWtXHwx/OEP8MADcPLJGrxdpNTElfgdmGpmL5nZ2THFIA04/3y46abQ5HPMGFi3Lu6IRKS5xFXqOczdl5hZD2Camc1z96fT3xDtEM4G6Nu3bxwxJt4554Syz1lnwfHHw+TJ0KFD3FGJyLaK5Yjf3ZdEjx8DDwKHZHjPLe5e7u7l3bt3L3SIEjnzzDCM44wZMHo0rF4dd0Qisq0KnvjNrL2ZdUw9B44BXit0HJK9U0+Fv/8dXngBRo2ClSvjjkhEtkUcpZ6ewINmltr+Pe7+RAxxSBOcckoo+5xySrjpa9q0MLSjiBSfgid+d18A7F/o7cq2O/HEMID7V78aun2YNg169ow7KhFpKjXnlCYZPTr07/POO3DUUbBkSdwRiUhTKfFLk40cCU88AYsXh1G8Fi2KOyIRaQolfsnJkUeGUs+yZeH5woVxRyQi2VLil5wdeihMnw6rVoXkP39+3BGJSDaU+GWbHHxwGODl88/hoINg/Pjar1dVwfXXxxKaiNRDiV+22f77hxu8WreG730P/va3sDw14tfgwfHGJyK1KfFLsxg0CJ5/PrTtP/vs0MXDySfDXXfVjPglIi2DBmKRZvOlL4W7e8vLQ+duAMcdB3vvHc4KDjggTPvvD+qFQyQ+SvzSrN5/P4zcde65YSCXE0+ETz+Fp56Cu++ueV+vXjU7gdQOoX9/jfolUghK/NJsUjX91IDuX/ta7fnly2HOHHjllZrHqVNh8+bw+R12gP32q71D2HdfaN8+XCAePLh22aiqKgwgn2ksYRGpn7l73DE0qry83GfNmhV3GNKIXJLzhg3wxhthJ5C+Q1i1KrxuBgMGhDOEF1+Eyy6D006Dt96Cb3yjZqciIlszs5cyDW2rxC8tjnsoGdU9O0i/ScwsnBUcdVQ4S9h//3CBuW3b2MIWaXHqS/wq9UiLYwb9+oVpzJia5atWhZHBJkwIZaDttoP/+R9Yvz68XlYGAwfW7AhSj716hXWKSKDEL0Vj9uzQWujyy8OwkBMnhjuG33kH5s4N05w58NxzYfyAlJ12CjuB9B3CPvvUPjvQNQRJEiV+KQp1LxwPH157fuDAMFZAyqefwquv1uwM5s6FW2+tGTu4rCw0P03tCAC+/nX4xz9gxIja2xMpNUr8UhRmzqx9IXf48DA/c2bmi7udO8MRR4Qp5YsvYMGCmh3BnDnhprP0s4Ojj4bevUPnc2ecEXYU774byk5qaiqlQhd3JfFWrao5Oxg3LpSUdtih5uwAYPvtwxnCXnvVngYO1AD00nLp4q5IPXbcEQ4/HDZtgg8+qLmGcM890KMHzJtXM82dCw8+GM4eUnr33nqHsNdeNReVdf1AWholfhEavoZw5pm137txYyj/pO8Q5s0LrY3WrKl5X4cOYQfQuTNceWVI8l/9ahi45owzdP1A4qNSjwjNc1TuDh99tPUOYd68cCaRrlOnUDraYw/Yfffa0267hdKSyLbSDVwiMfrsM7jwwtBl9YgR4W7kBQvCTWnvvx/KTClmsOuutXcG6TuIXr2gVdSvrspI0hDV+EViNHMm/POfNdcPLrusJll/8UUYtH7hwq2n6dPDa+nHZ9tvH84Kdt89PL/qKvjJT+CEE8Jnzj1XZSRpmI74RfKs7vWDuvON2bAhnBVk2jEsXAiffLL1Z7p2hZ13rpl69sz8vFu3hpup6oyiuOmIXyQmTb0Hoa42bcL1gC99KfPrq1fDz34Gt9wSxj845JBwrWHp0vD4/PPhMb15akqrVmFshPp2EmVloZfV228PXWw/9VTz3dimnUp8dMQvUuRSZxA//GFNVxaZdiiffRZ2AOk7hUzzS5eGlkt1pfo72nVX6NMnnFWkpp12yvy8a9fQXDZTX0nbeiYkjdMRv0gJaqwri3QdOsCee4apIe6hy4v0HcFtt8G0aXDwwWHAnBUroLoaXn89lJrSm7HWVVYGXbpk3ikcf3w4kxg1KlzPuOKK0OLp7behY8cwtW+fWyd7OqOonxK/SBHb1jJSJmYhUXfpEobNrKqCl1+uuTB9ww1br3vTJli5MuwEVqyomTLNp3YYK1aEMhWEm+IgXKTOFE+HDjU7gvSpU6fMyzt2DDuwk08O8Y4aFW6++973VKYClXpEpAH5LsdMmwbf+lYYVOeee8LOZc89wxlEpmn16vpf27Ahu2126hRuqttxx4Yf63utbdv8/y7NtWNRqUdEmiwfZxQpVVXw7W+HHlGHDw+9o6aS54knNn19mzZl3iHceitMmhSO+ocMCX0zffppzeOHH4YzkNT8li0Nb6dNm5odwDHHhC47liyBoUPhzjvh/vtDX0+5TG3ahDOcwYPr37E0Bx3xi0gsClEuyfbCd4o7rF1be8fQ0OPMmaH7jp13DjuDdetqptQAQU1hBu3ahZ1Aq1ahNPad74RxKHI5m9CduyKSKPkuxzS2U9myBT7/vPbOoKnTiy/Cm2+GEthVVzU9RpV6RCRR8l2maqw1VatWNSWcXLeRPuJcajvNQUf8IiJNlO8yVXOdrajUIyJSJPLdqkeJX0SkRNWX+FvFEYyIiMQnlsRvZqPN7C0ze8fMfh5HDCIiSVXwxG9mZcB/AxXAIOBbZjao0HGIiCRVHEf8hwDvuPsCd98I/B0YE0McIiKJFEfi3xVYlDa/OFpWi5mdbWazzGzWsmXLChaciEipi+MGrkwdrG7VtMjdbwFuATCzZWb2fr4Dy1E3YHncQeSgWOMGxR4XxR6PbYl9t0wL40j8i4E+afO9gSUNfcDdu+c1om1gZrMyNZdq6Yo1blDscVHs8chH7HGUemYCA8xsdzPbHvgmMDmGOEREEqngR/zuvtnMfgRMAcqA29z99ULHISKSVLF00ubujwGPxbHtPLgl7gByVKxxg2KPi2KPR7PHXhRdNoiISPNRlw0iIgmjxC8ikjBK/Dkwsz5mVmVmb5rZ62Z2ftwxNZWZlZnZy2b2SNyxNIWZdTazSZRSfIIAAAWiSURBVGY2L/r9h8QdUzbM7MLob+U1M7vXzNrGHVNDzOw2M/vYzF5LW9bVzKaZ2fzosUucMWZST9w3RH8vc83sQTPrHGeM9ckUe9prPzUzN7NuzbEtJf7cbAYucve9gUOBc4uwv6HzgTfjDiIHfwSecPe9gP0pgu9gZrsC5wHl7v5lQmu2b8YbVaPGA6PrLPs5MN3dBwDTo/mWZjxbxz0N+LK77we8Dfyi0EFlaTxbx46Z9QFGAR8014aU+HPg7tXuPjt6voaQfLbqdqKlMrPewHHA3+KOpSnMrBNwJDAOwN03uvun8UaVte2Adma2HbADjdy0GDd3fxpYUWfxGGBC9HwCcFJBg8pCprjdfaq7b45mnyfcNNri1PObA9wIXEyGHg5ypcS/jcysH3Ag8EK8kTTJHwh/SFviDqSJ9gCWAbdHZaq/mVn7uINqjLt/CPyWcMRWDaxy96nxRpWTnu5eDeHgB+gRczy5+B7weNxBZMvMTgQ+dPc5zbleJf5tYGYdgPuBC9x9ddzxZMPMjgc+dveX4o4lB9sBBwE3ufuBwFpaZrmhlqgWPgbYHegFtDez78QbVfKY2aWEMu3dcceSDTPbAbgU+K/mXrcSf47MrDUh6d/t7g/EHU8THAacaGbvEbrEHmFmd8UbUtYWA4vdPXV2NYmwI2jpjgYWuvsyd98EPAAMjTmmXCw1s10AosePY44na2Z2OnA8cKoXz81L/QkHC3Oi/6+9gdlmtvO2rliJPwdmZoQ685vu/vu442kKd/+Fu/d2936EC4xPuntRHH26+0fAIjMbGC0aCbwRY0jZ+gA41Mx2iP52RlIEF6UzmAycHj0/HXgoxliyZmajgUuAE919XdzxZMvdX3X3Hu7eL/r/uhg4KPp/sE2U+HNzGPBdwtHyK9FUGXdQCfFj4G4zmwscAFwbczyNis5QJgGzgVcJ/+9adBcCZnYv8Bww0MwWm9lZwHXAKDObT2hlcl2cMWZST9x/AToC06L/qzfHGmQ96ok9P9sqnrMeERFpDjriFxFJGCV+EZGEUeIXEUkYJX4RkYRR4hcRSRglfik5ZvaUmR1bZ9kFZvbXRj5T8MG4zey8qJfRu+ssPyq951Qzu9rMpphZm0LHKKVHiV9K0b1s3fvlN6PlLc1/ApXufmp9b4i6GjgMOMndNxQsMilZSvxSiiYBx6eOjqOO9HoBz5jZTWY2K+ob/8pMHzazz9Kef93MxkfPu5vZ/WY2M5oOi5YPS7uR72Uz65hhnT+J+uJ/zcwuiJbdTOh4brKZXVhPLBcBlcAJ7r4+1x9EJF0sg62L5JO7f2JmLxL6Nn+IcLR/n7u7mV3q7ivMrAyYbmb7ufvcLFf9R+BGd3/GzPoCU4C9gZ8C57r7s1HHfZ+nf8jMDgbOBL4CGPCCmc1w93Oi7gSGu/vyDNs7DBgIHOzun2V4XSQnOuKXUpVe7kkv84w1s9nAy8A+QFMG0Dka+IuZvULot6ZTdHT/LPB7MzsP6JzW93vK4cCD7r42SuAPAEdksb13CDuKY5oQo0ijdMQvpeqfhGR8ENDO3Web2e6Eo/PB7r4yKuFkGgIxvR+T9NdbAUMylFyuM7NHCSWZ583saHefl/a65fgdlgKnEs5MPnH3qhzXI1KLjvilJEVH1k8Bt1FztN+J0If/KjPrCVTU8/GlZra3mbUCvpq2fCrwo9SMmR0QPfaPelL8f8AsYK8663saOCnqnbN9tM5/Zfk93gZOBu5KbU9kWynxSym7lzAu798BolGMXgZeJ+wQnq3ncz8HHgGeJIyYlXIeUB4N2v0GcE60/ILoou0cYD11RniKhukcD7xIGKntb+7+crZfwt1nEq4RTDaz/tl+TqQ+6p1TRCRhdMQvIpIwSvwiIgmjxC8ikjBK/CIiCaPELyKSMEr8IiIJo8QvIpIw/x9y9GH0kxOVcAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Using Inertias -\n",
    "# Tabulating the results -\n",
    "\n",
    "for key,val in mapping2.items():\n",
    "    print(str(key)+' : '+str(val))\n",
    "\n",
    "# Visualizing the result -\n",
    "\n",
    "plt.plot(K, inertias, 'bx-')\n",
    "plt.xlabel('Values of K')\n",
    "plt.ylabel('Inertia')\n",
    "plt.title('The Elbow Method using Inertia')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# From the two graphs it can be concluded that 5 is the optimum number of cluster for our dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.08792846 0.79962894]\n",
      " [0.6        0.16443149]\n",
      " [0.58638083 0.82783883]\n",
      " [0.09265859 0.20319432]\n",
      " [0.33029751 0.49508692]]\n"
     ]
    },
    {
     "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": [
    "# Finding Centroids -\n",
    "data = pd.DataFrame(array, columns=('Annual Income (k$)', 'Spending Score (1-100)'))\n",
    "data.head()\n",
    "\n",
    "kmeans = KMeans(n_clusters=5).fit(data)\n",
    "centroids = kmeans.cluster_centers_\n",
    "print(centroids)\n",
    "\n",
    "plt.scatter(data['Annual Income (k$)'], data['Spending Score (1-100)'], c= kmeans.labels_.astype(float))\n",
    "plt.scatter(centroids[:, 0], centroids[:, 1], c='red')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}