K_means_Clustering with_hyperparameter_tuning .ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reading csv file \n",
    "\n",
    "df=pd.read_csv('Customers.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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",
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       "    }\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",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>195</th>\n",
       "      <td>196</td>\n",
       "      <td>Female</td>\n",
       "      <td>35</td>\n",
       "      <td>120</td>\n",
       "      <td>79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>197</td>\n",
       "      <td>Female</td>\n",
       "      <td>45</td>\n",
       "      <td>126</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>198</td>\n",
       "      <td>Male</td>\n",
       "      <td>32</td>\n",
       "      <td>126</td>\n",
       "      <td>74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>199</td>\n",
       "      <td>Male</td>\n",
       "      <td>32</td>\n",
       "      <td>137</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>199</th>\n",
       "      <td>200</td>\n",
       "      <td>Male</td>\n",
       "      <td>30</td>\n",
       "      <td>137</td>\n",
       "      <td>83</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>200 rows × 5 columns</p>\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\n",
       "..          ...     ...  ...                 ...                     ...\n",
       "195         196  Female   35                 120                      79\n",
       "196         197  Female   45                 126                      28\n",
       "197         198    Male   32                 126                      74\n",
       "198         199    Male   32                 137                      18\n",
       "199         200    Male   30                 137                      83\n",
       "\n",
       "[200 rows x 5 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data frame contains 5 features and 200 data points\n",
    "\n",
    "This is unsupervised algorithm \n",
    "\n",
    "We need group the people on basis of their annual income and spending\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Kmeans 'K ' is hyperparameter so first we need to find the correct k value using elbow technique"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "# converting dataframe into array\n",
    "features=df.iloc[:,[3,4]].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
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       "       [137,  83]], dtype=int64)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "objective_function=[] # objective function is nothing but argmin of c sum of (|x-c|)^2   c: centroid ,x=point in data set\n",
    "for i in range(1,11):\n",
    "    clustering=KMeans(n_clusters=i, init='k-means++')\n",
    "    clustering.fit(features)\n",
    "    objective_function.append(clustering.inertia_)   # inertia is calculaing min intra distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[269981.28000000014,\n",
       " 181363.59595959607,\n",
       " 106348.37306211119,\n",
       " 73679.78903948837,\n",
       " 44448.45544793369,\n",
       " 37233.81451071002,\n",
       " 30259.657207285458,\n",
       " 25028.020475269397,\n",
       " 21913.929201194416,\n",
       " 19701.35225128174]"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "objective_function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hyper parameter tuning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# for finding optimal no of clusters we use elbow techniue \n",
    "# Elbow technique is plot between no of clusters and objective_function \n",
    "# we take k value where the objective function values decreases slowly\n",
    "plt.plot(range(1,11),objective_function)\n",
    "plt.title('The Elbow Method')\n",
    "plt.xlabel('Number of Clusters K')\n",
    "plt.ylabel('objective_function')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the above graph if we observe after k=5 objective function values decreases slowly"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Training the model with optimal no of clusters\n",
    "\n",
    "tuned_clustering=KMeans(n_clusters=5,init='k-means++',random_state=0)\n",
    "labels=tuned_clustering.fit_predict(features)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[55.2962963 , 49.51851852],\n",
       "       [25.72727273, 79.36363636],\n",
       "       [86.53846154, 82.12820513],\n",
       "       [26.30434783, 20.91304348],\n",
       "       [88.2       , 17.11428571]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# x and y  coordinates of all clusters\n",
    "# Centroids of clusters\n",
    "tuned_clustering.cluster_centers_[:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1,\n",
       "       3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 0,\n",
       "       3, 1, 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, 2, 4, 2, 0, 2, 4, 2, 4, 2,\n",
       "       0, 2, 4, 2, 4, 2, 4, 2, 4, 2, 0, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2,\n",
       "       4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2,\n",
       "       4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2,\n",
       "       4, 2])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# array of clusters of each point (predicted clusters for points)\n",
    "labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([39, 40, 40, 40, 40, 42, 42, 43, 43, 43, 43, 44, 44, 46, 46, 46, 46,\n",
       "       47, 47, 48, 48, 48, 48, 48, 48, 49, 49, 50, 50, 54, 54, 54, 54, 54,\n",
       "       54, 54, 54, 54, 54, 54, 54, 57, 57, 58, 58, 59, 59, 60, 60, 60, 60,\n",
       "       60, 60, 61, 61, 62, 62, 62, 62, 62, 62, 63, 63, 63, 63, 63, 63, 64,\n",
       "       64, 65, 65, 65, 65, 67, 67, 67, 67, 69, 71, 72, 76], dtype=int64)"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# coordinates of cluster1 with respective x axis(income)\n",
    "features[labels==0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([61, 55, 47, 42, 42, 52, 60, 54, 60, 45, 41, 50, 46, 51, 46, 56, 55,\n",
       "       52, 59, 51, 59, 50, 48, 59, 47, 55, 42, 49, 56, 47, 54, 53, 48, 52,\n",
       "       42, 51, 55, 41, 44, 57, 46, 58, 55, 60, 46, 55, 41, 49, 40, 42, 52,\n",
       "       47, 50, 42, 49, 41, 48, 59, 55, 56, 42, 50, 46, 43, 48, 52, 54, 42,\n",
       "       46, 48, 50, 43, 59, 43, 57, 56, 40, 58, 35, 34, 40], dtype=int64)"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# coordinates of cluster1 with respective y axis(spending)\n",
    "features[labels==0,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualizing the clusters\n",
    "\n",
    "plt.scatter(features[labels==0,0],features[labels==0,1],c='green',label='cluster1')\n",
    "plt.scatter(features[labels==1,0],features[labels==1,1],c='yellow',label='cluster2')\n",
    "plt.scatter(features[labels==2,0],features[labels==2,1],c='red',label='cluster3')\n",
    "plt.scatter(features[labels==3,0],features[labels==3,1],c='orange',label='cluster4')\n",
    "plt.scatter(features[labels==4,0],features[labels==4,1],c='blue',label='cluster5')\n",
    "\n",
    "\n",
    "plt.scatter(tuned_clustering.cluster_centers_[:,0],tuned_clustering.cluster_centers_[:,1],s=300,c='black',label='centroid')\n",
    "\n",
    "\n",
    "plt.title('Clusters of customers')\n",
    "plt.xlabel('Annual Income(K$)')\n",
    "plt.ylabel('Spending Score(1-100)')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import davies_bouldin_score "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5725628995597086\n"
     ]
    }
   ],
   "source": [
    "print(davies_bouldin_score(features, tuned_clustering.labels_)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    " from sklearn import metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.553931997444648"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metrics.silhouette_score(features, tuned_clustering.labels_, metric='euclidean')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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