EastWestAirlines(K-Means clustering).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pylab as plt\n",
    "from sklearn.cluster import KMeans\n",
    "from scipy.spatial.distance import cdist \n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "Airlines = pd.read_csv(\"E:/DataScience/Assignments/Clustering/EastWestAirlines.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ID#</th>\n",
       "      <th>Balance</th>\n",
       "      <th>Qual_miles</th>\n",
       "      <th>cc1_miles</th>\n",
       "      <th>cc2_miles</th>\n",
       "      <th>cc3_miles</th>\n",
       "      <th>Bonus_miles</th>\n",
       "      <th>Bonus_trans</th>\n",
       "      <th>Flight_miles_12mo</th>\n",
       "      <th>Flight_trans_12</th>\n",
       "      <th>Days_since_enroll</th>\n",
       "      <th>Award?</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>28143</td>\n",
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       "      <td>215</td>\n",
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       "      <td>0</td>\n",
       "      <td>6968</td>\n",
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       "      <th>2</th>\n",
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       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4123</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7034</td>\n",
       "      <td>0</td>\n",
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       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>14776</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>500</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>6952</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>97752</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>43300</td>\n",
       "      <td>26</td>\n",
       "      <td>2077</td>\n",
       "      <td>4</td>\n",
       "      <td>6935</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   ID#  Balance  Qual_miles  cc1_miles  cc2_miles  cc3_miles  Bonus_miles  \\\n",
       "0    1    28143           0          1          1          1          174   \n",
       "1    2    19244           0          1          1          1          215   \n",
       "2    3    41354           0          1          1          1         4123   \n",
       "3    4    14776           0          1          1          1          500   \n",
       "4    5    97752           0          4          1          1        43300   \n",
       "\n",
       "   Bonus_trans  Flight_miles_12mo  Flight_trans_12  Days_since_enroll  Award?  \n",
       "0            1                  0                0               7000       0  \n",
       "1            2                  0                0               6968       0  \n",
       "2            4                  0                0               7034       0  \n",
       "3            1                  0                0               6952       0  \n",
       "4           26               2077                4               6935       1  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Airlines.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def norm_func(i):\n",
    "    x = (i-i.min())/(i.max()-i.min())\n",
    "    return (x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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>Balance</th>\n",
       "      <th>Qual_miles</th>\n",
       "      <th>cc1_miles</th>\n",
       "      <th>cc2_miles</th>\n",
       "      <th>cc3_miles</th>\n",
       "      <th>Bonus_miles</th>\n",
       "      <th>Bonus_trans</th>\n",
       "      <th>Flight_miles_12mo</th>\n",
       "      <th>Flight_trans_12</th>\n",
       "      <th>Days_since_enroll</th>\n",
       "      <th>Award?</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>0.016508</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000660</td>\n",
       "      <td>0.011628</td>\n",
       "      <td>0.000000</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.011288</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000815</td>\n",
       "      <td>0.023256</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.839884</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.024257</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.015636</td>\n",
       "      <td>0.046512</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.847842</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.008667</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.001896</td>\n",
       "      <td>0.011628</td>\n",
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       "      <td>0.000000</td>\n",
       "      <td>0.837955</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.057338</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.75</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.164211</td>\n",
       "      <td>0.302326</td>\n",
       "      <td>0.067398</td>\n",
       "      <td>0.075472</td>\n",
       "      <td>0.835905</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Balance  Qual_miles  cc1_miles  cc2_miles  cc3_miles  Bonus_miles  \\\n",
       "0  0.016508         0.0       0.00        0.0        0.0     0.000660   \n",
       "1  0.011288         0.0       0.00        0.0        0.0     0.000815   \n",
       "2  0.024257         0.0       0.00        0.0        0.0     0.015636   \n",
       "3  0.008667         0.0       0.00        0.0        0.0     0.001896   \n",
       "4  0.057338         0.0       0.75        0.0        0.0     0.164211   \n",
       "\n",
       "   Bonus_trans  Flight_miles_12mo  Flight_trans_12  Days_since_enroll  Award?  \n",
       "0     0.011628           0.000000         0.000000           0.843742     0.0  \n",
       "1     0.023256           0.000000         0.000000           0.839884     0.0  \n",
       "2     0.046512           0.000000         0.000000           0.847842     0.0  \n",
       "3     0.011628           0.000000         0.000000           0.837955     0.0  \n",
       "4     0.302326           0.067398         0.075472           0.835905     1.0  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_Airlines = norm_func(Airlines.iloc[:,1:])\n",
    "df_Airlines.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6, 6, 6, ..., 5, 2, 2])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cluster=KMeans(n_clusters=8)\n",
    "cluster.fit(df_Airlines)\n",
    "cluster.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([1657.66572161]),\n",
       " array([1392.12408309]),\n",
       " array([1170.237473]),\n",
       " array([1002.45329086]),\n",
       " array([953.5500114]),\n",
       " array([907.38540997])]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = list(range(2,8))\n",
    "c\n",
    "TWSS = [] # variable for storing total within sum of squares for each kmeans \n",
    "for i in c:\n",
    "    kmeans = KMeans(n_clusters = i)\n",
    "    kmeans.fit(df_Airlines)\n",
    "    WSS = [] # variable for storing within sum of squares for each cluster \n",
    "    for j in range(i):\n",
    "        WSS.append(sum(cdist(df_Airlines.iloc[kmeans.labels_==j,:],kmeans.cluster_centers_[j].reshape(1,df_Airlines.shape[1]),\"euclidean\")))\n",
    "    TWSS.append(sum(WSS))\n",
    "    \n",
    "TWSS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([<matplotlib.axis.XTick at 0x230f94ff7c0>,\n",
       "  <matplotlib.axis.XTick at 0x230f94ff790>,\n",
       "  <matplotlib.axis.XTick at 0x230f94e2460>,\n",
       "  <matplotlib.axis.XTick at 0x230f95441c0>,\n",
       "  <matplotlib.axis.XTick at 0x230f95446d0>,\n",
       "  <matplotlib.axis.XTick at 0x230f9544be0>],\n",
       " <a list of 6 Text major ticklabel objects>)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(c,TWSS, 'ro-');plt.xlabel(\"No_of_Clusters\");plt.ylabel(\"Total_within_SS\");plt.xticks(c)"
   ]
  },
  {
   "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
}