KMeans Clustering .ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data loading and Preprocessing "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Importing libraries"
   ]
  },
  {
   "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": "markdown",
   "metadata": {},
   "source": [
    "### Data loading "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "val=pd.read_csv('CANCER.txt')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Removing rows with '?' in them "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "val = val[val.g != '?']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Saurav\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:3: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    }
   ],
   "source": [
    "X = val[[ 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j']]\n",
    "y = val['output']\n",
    "X['g'] = pd.to_numeric(X['g'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " # KMeans Algorithm for different values of K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "n=10\n",
    "size = len(X.index)\n",
    "iterations = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Function for calcuating distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def euc_distance(a, b):\n",
    "    temp = (a - b)**2\n",
    "    distance = np.sum(temp)\n",
    "    return(distance**0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Function for calculating means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_means(cluster, X):\n",
    "    mean = np.zeros(len(X.columns))\n",
    "    #print(mean)\n",
    "    for item in cluster:\n",
    "        mean = mean + X.iloc[item]\n",
    "    \n",
    "    if len(cluster)!=0:\n",
    "        mean = mean/len(cluster)\n",
    "    else:\n",
    "        mean = np.asarray([1000]*len(X.columns))\n",
    "    #print(mean)\n",
    "    return(mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Iterations for different values of K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#################  K-Means ##############\n",
      "\n",
      "Means for K = 1 are : \n",
      "[[4.44216691 3.15080527 3.21522694 2.83016105 3.23426061 3.54465593\n",
      "  3.44509517 2.86969253 1.60322108]]\n",
      "\n",
      "Means for K = 2 are : \n",
      "[[7.17391304 6.8        6.73478261 5.73913043 5.47826087 7.93043478\n",
      "  6.10869565 6.03913043 2.56956522]\n",
      " [3.05518764 1.29801325 1.42825607 1.35320088 2.09492274 1.31788079\n",
      "  2.09271523 1.26048565 1.11258278]]\n",
      "\n",
      "Means for K = 3 are : \n",
      "[[7.2081448  6.93665158 6.85972851 5.88687783 5.49773756 8.03167421\n",
      "  6.18099548 6.11764706 2.6199095 ]\n",
      " [1.77692308 1.11538462 1.17692308 1.15       1.97307692 1.23076923\n",
      "  1.99615385 1.06538462 1.07692308]\n",
      " [4.84653465 1.62871287 1.85148515 1.64851485 2.38118812 1.61386139\n",
      "  2.31683168 1.63861386 1.16831683]]\n",
      "\n",
      "Means for K = 4 are : \n",
      "[[1.25274725 1.12637363 1.2032967  1.14285714 1.98351648 1.24175824\n",
      "  2.00549451 1.06593407 1.1043956 ]\n",
      " [7.125      4.75       5.         4.61538462 4.05769231 8.64423077\n",
      "  4.99038462 4.04807692 1.65384615]\n",
      " [7.19379845 8.35658915 8.07751938 6.62790698 6.55813953 7.28682171\n",
      "  6.92248062 7.56589147 3.30232558]\n",
      " [4.24253731 1.39925373 1.54850746 1.45522388 2.1641791  1.32835821\n",
      "  2.14925373 1.37686567 1.10447761]]\n",
      "\n",
      "Means for K = 5 are : \n",
      "[[6.54347826 4.7173913  4.67391304 3.39130435 4.47826087 3.02173913\n",
      "  4.43478261 5.41304348 1.67391304]\n",
      " [1.80451128 1.13157895 1.19548872 1.14661654 1.98496241 1.26691729\n",
      "  2.02255639 1.07894737 1.07518797]\n",
      " [4.70238095 1.35119048 1.5297619  1.50595238 2.07738095 1.26190476\n",
      "  2.02380952 1.2202381  1.05357143]\n",
      " [7.28888889 4.97777778 5.15555556 4.88888889 4.11111111 9.62222222\n",
      "  5.27777778 3.86666667 1.74444444]\n",
      " [7.14159292 8.48672566 8.33628319 6.89380531 6.69026549 7.67256637\n",
      "  7.04424779 7.7079646  3.52212389]]\n",
      "\n",
      "Means for K = 6 are : \n",
      "[[4.79032258 1.52150538 1.72043011 1.58602151 2.24193548 1.32795699\n",
      "  2.20967742 1.51612903 1.14516129]\n",
      " [1.87029289 1.13807531 1.20083682 1.14644351 2.07531381 1.28033473\n",
      "  2.0251046  1.06276151 1.0083682 ]\n",
      " [1.08       1.         1.08       1.16       1.12       1.16\n",
      "  1.84       1.08       1.72      ]\n",
      " [7.96226415 8.35849057 7.75471698 4.16981132 5.75471698 6.26415094\n",
      "  5.52830189 4.18867925 2.03773585]\n",
      " [6.79120879 8.26373626 8.16483516 7.53846154 6.6043956  7.9010989\n",
      "  7.27472527 8.54945055 3.83516484]\n",
      " [7.06741573 4.23595506 4.58426966 4.80898876 4.06741573 8.85393258\n",
      "  5.13483146 4.46067416 1.58426966]]\n",
      "\n",
      "Means for K = 7 are : \n",
      "[[   4.72121212    1.34545455    1.52727273    1.43030303    2.05454545\n",
      "     1.24242424    2.04242424    1.21818182    1.04242424]\n",
      " [   1.20792079    1.13861386    1.25742574    1.11881188    1.89108911\n",
      "     1.24752475    2.79207921    1.08910891    1.01980198]\n",
      " [1000.         1000.         1000.         1000.         1000.\n",
      "  1000.         1000.         1000.         1000.        ]\n",
      " [   6.92156863    8.45098039    8.2254902     7.41176471    6.56862745\n",
      "     7.62745098    7.17647059    8.02941176    3.76470588]\n",
      " [   2.17964072    1.13772455    1.16167665    1.19161677    2.05389222\n",
      "     1.2754491     1.53892216    1.07784431    1.11976048]\n",
      " [   6.5106383     4.63829787    4.61702128    3.53191489    4.46808511\n",
      "     3.06382979    4.38297872    5.31914894    1.65957447]\n",
      " [   7.4950495     5.3960396     5.61386139    4.58415842    4.51485149\n",
      "     9.45544554    5.33663366    3.96039604    1.69306931]]\n",
      "\n",
      "Means for K = 8 are : \n",
      "[[4.61261261 1.26126126 1.51351351 1.59459459 2.04504505 1.0990991\n",
      "  1.48648649 1.08108108 1.00900901]\n",
      " [6.23076923 6.2        6.52307692 6.47692308 5.13846154 9.13846154\n",
      "  6.64615385 8.12307692 2.04615385]\n",
      " [1.65263158 1.13684211 1.14736842 1.17894737 2.12631579 1.53684211\n",
      "  1.05263158 1.04210526 1.2       ]\n",
      " [4.78787879 1.53030303 1.66666667 1.36363636 2.18181818 1.71212121\n",
      "  3.18181818 1.5        1.09090909]\n",
      " [7.93055556 9.48611111 9.01388889 6.84722222 7.25       6.88888889\n",
      "  6.95833333 7.13888889 4.31944444]\n",
      " [1.84848485 1.12727273 1.2        1.11515152 1.90909091 1.07878788\n",
      "  2.52727273 1.1030303  1.01818182]\n",
      " [6.47619048 4.80952381 4.69047619 3.38095238 4.5        3.\n",
      "  4.42857143 5.71428571 1.73809524]\n",
      " [7.40298507 4.91044776 5.08955224 4.68656716 4.11940299 9.64179104\n",
      "  5.10447761 2.65671642 1.67164179]]\n",
      "\n",
      "Means for K = 9 are : \n",
      "[[1.25274725 1.12637363 1.2032967  1.14285714 1.98351648 1.24175824\n",
      "  2.00549451 1.06593407 1.1043956 ]\n",
      " [7.17241379 8.72413793 8.72413793 8.06896552 8.         8.27586207\n",
      "  6.75862069 8.5862069  7.89655172]\n",
      " [4.07755102 1.24489796 1.38367347 1.35510204 2.0244898  1.2244898\n",
      "  2.00408163 1.15510204 1.02857143]\n",
      " [8.09375    8.125      7.59375    4.125      5.375      3.375\n",
      "  6.09375    8.84375    1.9375    ]\n",
      " [7.58823529 9.44117647 9.         6.91176471 7.41176471 9.44117647\n",
      "  7.17647059 5.         1.76470588]\n",
      " [7.19402985 4.65671642 4.92537313 4.73134328 3.92537313 9.52238806\n",
      "  5.08955224 2.8358209  1.67164179]\n",
      " [6.08333333 7.91666667 6.91666667 8.33333333 6.08333333 2.58333333\n",
      "  5.5        2.91666667 1.91666667]\n",
      " [6.24242424 3.15151515 3.57575758 2.57575758 3.66666667 3.12121212\n",
      "  3.81818182 4.15151515 1.90909091]\n",
      " [6.55102041 6.06122449 6.2244898  5.91836735 4.87755102 9.26530612\n",
      "  6.71428571 8.55102041 1.89795918]]\n",
      "\n",
      "Means for K = 10 are : \n",
      "[[6.93548387 9.         8.41935484 5.41935484 7.03225806 8.90322581\n",
      "  7.03225806 2.58064516 2.32258065]\n",
      " [1.24719101 1.08988764 1.18539326 1.12921348 1.98876404 1.23595506\n",
      "  1.92696629 1.0505618  1.1011236 ]\n",
      " [7.015625   4.21875    4.578125   5.09375    3.921875   9.578125\n",
      "  4.984375   3.265625   1.515625  ]\n",
      " [5.92857143 8.0952381  8.21428571 9.07142857 6.         9.5952381\n",
      "  7.11904762 8.54761905 2.69047619]\n",
      " [6.27272727 7.36363636 6.63636364 8.72727273 6.27272727 1.63636364\n",
      "  5.27272727 3.90909091 2.        ]\n",
      " [4.         1.5505618  1.57303371 1.48314607 2.14606742 1.53932584\n",
      "  3.23595506 1.65168539 1.06741573]\n",
      " [8.         7.10169492 6.89830508 3.89830508 5.16949153 6.25423729\n",
      "  6.3559322  8.79661017 2.08474576]\n",
      " [8.13333333 9.13333333 8.53333333 7.46666667 8.8        6.93333333\n",
      "  6.33333333 9.06666667 9.46666667]\n",
      " [7.76       3.64       4.4        2.28       3.84       3.56\n",
      "  3.96       3.84       2.48      ]\n",
      " [4.0591716  1.20118343 1.34911243 1.36094675 2.01775148 1.13609467\n",
      "  1.53254438 1.0887574  1.02366864]]\n"
     ]
    }
   ],
   "source": [
    "print(\"#################  K-Means ##############\")\n",
    "saved_means = []\n",
    "saved_clusters = []\n",
    "sum_sq_dis=[]\n",
    "for K in range(1, n+1):\n",
    "    initial_index=np.random.choice(size, K)\n",
    "    #print(initial_index)\n",
    "    \n",
    "    means = []\n",
    "    for i in range(K):\n",
    "        means.append(X.iloc[initial_index[i]])\n",
    "        \n",
    "    for it in range(iterations):\n",
    "        cluster=[]\n",
    "        for i in range(K):\n",
    "            cluster.append([])\n",
    "            \n",
    "        for i in range(size):\n",
    "            distance = 1000000000 \n",
    "            index = 0\n",
    "            for j in range(K):\n",
    "                temp = euc_distance(X.iloc[i], means[j])\n",
    "                if temp<distance:\n",
    "                    distance = temp\n",
    "                    index = j\n",
    "            cluster[index].append(i)\n",
    "\n",
    "        means=[]\n",
    "        for i in range(K):\n",
    "            means.append(get_means(cluster[i], X))\n",
    "    saved_means.append(means)\n",
    "    saved_clusters.append(cluster)\n",
    "        \n",
    "    print('\\nMeans for K =', K, 'are : ')\n",
    "    print(np.asarray(means))\n",
    "    #print(cluster)\n",
    "\n",
    "#print(sum_sq_dis)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Elbow Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def elbow_method(means, cluster, X, K):\n",
    "    sum1 = 0.0\n",
    "    for i in range(K):\n",
    "        for item in cluster[i]:\n",
    "            temp = (means[i] - X.iloc[item])**2\n",
    "            sum1 += np.sum(temp)\n",
    "    #print(sum1)\n",
    "    return(sum1)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(n):\n",
    "    sum_sq_dis.append(elbow_method(saved_means[i], saved_clusters[i], X, i+1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Elbow Plot')"
      ]
     },
     "execution_count": 11,
     "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.figure()\n",
    "plt.plot(range(1, n+1), sum_sq_dis)\n",
    "plt.xlabel('number of clusters (K)')\n",
    "plt.ylabel('Sum of squared Distance')\n",
    "plt.title('Elbow Plot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clearly from the plot it can be seen that K=2 gives the best cluster according to Elbow method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Silhouette Score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "############## Shilloute Score ###############\n",
      "For no of clusters = 2  The average silhouette_score is : 0.6381806308198421\n",
      "For no of clusters = 3  The average silhouette_score is : 0.40151424562324856\n",
      "For no of clusters = 4  The average silhouette_score is : 0.37832789525749877\n",
      "For no of clusters = 5  The average silhouette_score is : 0.36434969264731987\n",
      "For no of clusters = 6  The average silhouette_score is : 0.25027038458286377\n",
      "For no of clusters = 7  The average silhouette_score is : 0.31336192511316274\n",
      "For no of clusters = 8  The average silhouette_score is : 0.2520195584288289\n",
      "For no of clusters = 9  The average silhouette_score is : 0.33316654303508986\n",
      "For no of clusters = 10  The average silhouette_score is : 0.3269499948482584\n"
     ]
    }
   ],
   "source": [
    "print(\"############## Shilloute Score ###############\")\n",
    "saved_s=[]\n",
    "for t in range(1, n):\n",
    "    s_avg = 0\n",
    "    left = 0\n",
    "    for i in range(t+1):\n",
    "        if len(saved_clusters[t][i]) ==0:\n",
    "            left=left+1\n",
    "            continue\n",
    "        min1 = 100000000\n",
    "        cluster_index = -1\n",
    "        for j in range(t+1):\n",
    "            if i!=j:\n",
    "                dist = euc_distance(saved_means[t][i], saved_means[t][j])\n",
    "                if dist< min1:\n",
    "                    min1 = dist\n",
    "                    cluster_index = j\n",
    "                    \n",
    "        sum1 = 0.0\n",
    "        for item in saved_clusters[t][i]:\n",
    "            sum1 += euc_distance(saved_means[t][i], X.iloc[item])\n",
    "        a = sum1/len(saved_clusters[t][i]) \n",
    "        \n",
    "        sum1 = 0.0\n",
    "        j= cluster_index\n",
    "        for item in saved_clusters[t][j]:\n",
    "            sum1 += euc_distance(saved_means[t][i], X.iloc[item])\n",
    "        b = sum1/len(saved_clusters[t][j])\n",
    "        \n",
    "        s = (b - a)/max(a, b)   \n",
    "        s_avg = s_avg + s\n",
    "    s_avg = s_avg/(t+1-left) \n",
    "    saved_s.append(s_avg)\n",
    "    print(\"For no of clusters =\", t+1, \" The average silhouette_score is :\", s_avg) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Silhouette Plot')"
      ]
     },
     "execution_count": 13,
     "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.figure()\n",
    "plt.plot( range(2, n+1), saved_s)\n",
    "plt.xlabel('number of clusters (K)')\n",
    "plt.ylabel('Silhouette Corfficient')\n",
    "plt.title('Silhouette Plot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clearly from the plot it can be seen that K=2 gives the best cluster according to Silhouette Score"
   ]
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}