K-means.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.cluster import KMeans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'>\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": [
    "X= -2 * np.random.rand(100,2)\n",
    "#X1 = 1 + 2 * np.random.rand(50,2)\n",
    "#X[50:100, :] = X1\n",
    "X1 = np.array([[2,3],[3,5],[4,2],[4,6],[4,9],[5,5],[6,8],[7,7],[7,9],[8,8],[8,12],[9,5],[10,10],[10,13],[11,8]])\n",
    "\n",
    "print(type(X1))\n",
    "\n",
    "plt.scatter(X1[ : , 0], X1[ :, 1], s = 50, c = 'b')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "from sklearn.cluster import KMeans\n",
    "Kmean = KMeans(n_clusters=2)\n",
    "Kmean.fit(X1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "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": [
    "from sklearn.cluster import KMeans\n",
    "Kmean = KMeans(n_clusters=3)\n",
    "Kmean.fit(X1)\n",
    "\n",
    "Kmean.cluster_centers_\n",
    "plt.scatter(X1[ : , 0], X1[ : , 1], s =50, c='b')\n",
    "plt.scatter(3.6, 4.2, s=200, c='g', marker='s')\n",
    "plt.scatter(6.83333333, 7.66666667, s=200, c='r', marker='s')\n",
    "plt.scatter(9.75, 10.75, s=200, c='y', marker='s')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "from sklearn.cluster import KMeans \n",
    "from sklearn import metrics \n",
    "from scipy.spatial.distance import cdist \n",
    "import numpy as np \n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "distortions = [] \n",
    "inertias = [] \n",
    "mapping1 = {} \n",
    "mapping2 = {} \n",
    "K = range(1,10) \n",
    "  \n",
    "for k in K: \n",
    "    #Building and fitting the model \n",
    "    kmeanModel = KMeans(n_clusters=k).fit(X1) \n",
    "    kmeanModel.fit(X1)     \n",
    "      \n",
    "    distortions.append(sum(np.min(cdist(X1, kmeanModel.cluster_centers_, \n",
    "                      'euclidean'),axis=1)) / X.shape[0]) \n",
    "    inertias.append(kmeanModel.inertia_) \n",
    "  \n",
    "    mapping1[k] = sum(np.min(cdist(X, kmeanModel.cluster_centers_, \n",
    "                 'euclidean'),axis=1)) / X.shape[0] \n",
    "    mapping2[k] = kmeanModel.inertia_ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 : 11.27646614693777\n",
      "2 : 6.996635882221785\n",
      "3 : 6.996635882221785\n",
      "4 : 6.996635882221785\n",
      "5 : 6.996635882221785\n",
      "6 : 5.376227712930047\n",
      "7 : 5.376227712930047\n",
      "8 : 5.066009200763859\n",
      "9 : 5.376227712930047\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": [
    "for key,val in mapping1.items(): \n",
    "    print(str(key)+' : '+str(val))\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": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 : 243.06666666666663\n",
      "2 : 104.89999999999999\n",
      "3 : 61.66666666666667\n",
      "4 : 43.416666666666664\n",
      "5 : 33.0\n",
      "6 : 22.166666666666668\n",
      "7 : 14.166666666666666\n",
      "8 : 11.666666666666666\n",
      "9 : 9.166666666666666\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": [
    "for key,val in mapping2.items(): \n",
    "    print(str(key)+' : '+str(val)) \n",
    "    \n",
    "    \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": []
  }
 ],
 "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}