{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# k-Means"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Method\n",
    "\n",
    "Because of the excellent speed and good expandability，K-Means cluster method is regarded as the most famous cluster method。***K-Means algorthms is a process which repeatly moves the center point，moving the center point of the class which is called centroids to the average position of all other members，and redivide the members of it.***\n",
    "\n",
    "K is the hyper-parameter which has been calculated, represents the numbers of class. K-means can distribute sample into different class automatically, without deciding the numbers of the class.\n",
    "\n",
    "K must be a positive integer smaller than the number of samples in the training set. Sometimes, the number of classes is specified by the content of the question. For example, a shoe factory has three new styles. It wants to know which potential customers each new style has, so it investigates customers and then finds out three types from the data. \n",
    "\n",
    "The parameter of K-Means is the centriod positon of class and the position of its internal observation. Similar with generalized linear models and decision tree, the optimal solution of k-means parameter is also the goal of minimizing the cost function. The cost function of K-Means is\n",
    "：\n",
    "$$\n",
    "J = \\sum_{k=1}^{K} \\sum_{i \\in C_k} | x_i - u_k|^2\n",
    "$$\n",
    "\n",
    "$u_k$is the centriod poisition of samples from type $C_k$ with the definition of：\n",
    "$$\n",
    "u_k = \\frac{1}{|C_k|} \\sum_{x \\in C_k} x\n",
    "$$\n",
    "\n",
    "Cost is the sum of each class distortions. Every class distortion equal to the sum of quare between centroids of this class and its inner members. The more compact the members inside the class are, the less the class distorts. On the contrary, the more disperse the members are more distort. \n",
    "\n",
    "The argument for minimizing the cost function is a process of repeatedly configuring the observations contained in each class and constantly moving the class's ctriod.\n",
    "1. Firstly, class centriod is a random determined poisition. In fact, the poisition of centriod equal to observed value which being determined radomly.首\n",
    "2. At each iteration, K-Means will assigns the observations to the class closest to them and move the centriod to the average value of all class members.\n",
    "3. If the maximum number of iteration steps is reached or the difference between two iterations is less than the set threshold, the algorithm is finished, otherwise repeat step 2.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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C\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "% matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "X0 = np.array([7, 5, 7, 3, 4, 1, 0, 2, 8, 6, 5, 3])\n",
    "X1 = np.array([5, 7, 7, 3, 6, 4, 0, 2, 7, 8, 5, 7])\n",
    "plt.figure()\n",
    "plt.axis([-1, 9, -1, 9])\n",
    "plt.grid(True)\n",
    "plt.plot(X0, X1, 'k.');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we intiate K-Means, set the centriod of the first class at the fifth sample and the centriod of the second class at the eleventh sample. Then we can calcualte the distance between each instance and two centriod, assigning them to the nearest class. The results are showing in the following talbe:\n",
    "![data_0](images/data_0.png)\n",
    "\n",
    "New centriod position and initial cluster result are shown in the following graph. The fist class are shown in X and the second are represented in dot. The position of centriod are indicated in a larger dot.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAEICAYAAAB/Dx7IAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4wLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvqOYd8AAAFYlJREFUeJzt3X+U3XV95/Hnm0kGCbHQ3bhpgQmD1UUpHIWE1pHanXHctayi5+w5ZW2RHM160vasgkU2qyLUVSmttVTtWntYTVlg1mwOup6CWHUnc/donbJJkF1+RM6hMGQAXbHKj4CdScJ7//je4U5CkrkDc/O9n5nn45x7Zr7f+73f+7qf3Lzudz73znwjM5EkleOYugNIkubH4pakwljcklQYi1uSCmNxS1JhLG5JKozFrY6KiDdExH01Z/hwRHyhzgwvVkRkRLyi7hzqDha3AIiI90bEjoiYiojr53G7iYh40+Guz8xvZ+bp7W7/YkXEYEQ8fFCGP8zM93TqPo+2iLg+Ij5Rdw7VZ1ndAdQ1HgU+AbwZOK7mLIcUEQFEZj5bd5ZDiYhlmbmv7hxa/DziFgCZ+ZXM/CrwDwdfFxGrIuLWiHg8In4SEd+OiGMi4kZgDXBLROyJiE2HuO1zR8CH2z4iXhcR323u//9ExOCs2zci4uqI+FvgGeDlEfHuiNgVEU9FxAMR8TvNbY8Hvg6c1Nz/nog4KSI+GhE3zdrn2yLinub9NSLi1bOum4iIyyPi/0bEExHx3yPiJYcas4h4V0T8bUT8WUT8A/DR5voNzXw/jYhvRMSpzfXR3PZHEfFkRNwVEWfOepzvOWjf3znEfW4ELgI2NR/fLc31/zEiHmmOyX0RMXyozFokMtOLl+cuVEfd1x+07hrgL4HlzcsbqI58ASaANx1hf4PAw7OWD9geOJnqxeJfUx1I/Mvm8sua1zeA3cAvU/2EuBx4C/BLQAD/gqrQzznU/TXXfRS4qfn9Pweebt7PcmATcD/QOyvf/wZOAv4JsAv43cM8tncB+4D3NbMdB7y9ub9XN9d9BPhuc/s3AzuBE5vZXw384qzH+Z6D9v2dWcsJvKL5/fXAJ2ZddzowCZzUXO4Hfqnu55KXzl084lY79gK/CJyamXuzmrdeqD9y807gtsy8LTOfzcxvATuoinzG9Zl5T2bua97/1zLz77Pyv4BvUr2YtOPfAl/LzG9l5l7gU1SF+/pZ23w2Mx/NzJ8AtwCvPcL+Hs3MP29m+xnwu8A1mbkrq2mTPwRe2zzq3gu8FHgV1Qvfrsz8QZu5j2Q/cCxwRkQsz8yJzPz7BdivupTFrXb8CdVR5DebUxMfXMB9nwr8ZnPa4vGIeBz4NaoXihmTs28QEedHxN81p20epyr5VW3e30nAQzMLWc2XT1Id+c/44azvnwFWHmF/kwctnwp8ZtZj+QnV0fXJmbkN+M/A54AfRcR1EfFzbeY+rMy8H3g/1U8WP4qILRFx0ovdr7qXxa05ZeZTmfmBzHw58DbgsllzqPM98j54+0ngxsw8cdbl+Mz8o0PdJiKOBb5MdaS8OjNPBG6jKsd28jxKVa4z+wugD3hkno/jedmaJoHfOejxHJeZ3wXIzM9m5lrgDKppm//QvN3TwIpZ+/mFedwnmfnfMvPXqB5bAn/8wh6OSmBxC6g+EdF8E64H6ImIl0TEsuZ1b42IVzRL7gmqH81nPtnx/4CXz+OuDt7+JuCCiHhzRMzc72BEnHKY2/dSTQs8BuyLiPOBf3XQ/v9pRJxwmNtvBd4SEcMRsRz4ADAFfHcej+FI/hL4UET8MkBEnBARv9n8/tyI+NXm/T4N/COtcbwT+DcRsSKqz2v/uyPcxwFjGBGnR8Qbmy9q/wj8bNZ+tQhZ3JrxEar/8B+kmnf+WXMdwCuB/wnsAcaBv8jMseZ11wAfaU4NXN7G/RywfWZOUr2h92GqMp6kOgo95HMzM58CLqEq4J8Cvw389azrvw98CXigeR8nHXT7+5qP78+BHwMXABdk5nQb2eeUmf+D6mh3S0Q8CdwNnN+8+ueA/9LM/RDVm7B/0rzuz4BpqlL+r8DIEe7mi1Tz2Y9HxFepXsj+qPl4fgj8M+BDC/F41J1mPhkgSSqER9ySVBiLW5IKY3FLUmEsbkkqTEf+yNSqVauyv7+/E7tu29NPP83xxx9fa4Zu4Vi0OBYtjkVLN4zFzp07f5yZL2tn244Ud39/Pzt27OjErtvWaDQYHBysNUO3cCxaHIsWx6KlG8YiIh6ae6uKUyWSVBiLW5IKY3FLUmEsbkkqjMUtSYWxuCWpMBa3JBXG4pakwljcklQYi1uSCmNxS1JhLG5JKozFLUmFsbglqTAWtyQVxuKWpMJY3JJUmLaKOyJ+PyLuiYi7I+JLEfGSTgeT1AGf/CSMjR24bmysWq9izFncEXEycAmwLjPPBHqAd3Q6mKQOOPdcuPDCVnmPjVXL555bby7NS7vnnFwGHBcRe4EVwKOdiySpY4aGYOtWuPBC+s8/H77+9Wp5aKjuZJqHyMy5N4q4FLga+Bnwzcy86BDbbAQ2AqxevXrtli1bFjjq/OzZs4eVK1fWmqFbOBYtjkWlf/Nm+m+8kYmLL2Ziw4a649SuG54XQ0NDOzNzXVsbZ+YRL8DPA9uAlwHLga8C7zzSbdauXZt1GxsbqztC13AsWhyLzNy2LXPVqnzw4oszV62qlpe4bnheADtyjj6eubTz5uSbgAcz87HM3At8BXj9C3hBkVS3mTntrVurI+3mtMnz3rBUV2unuHcDr4uIFRERwDCwq7OxJHXE9u0HzmnPzHlv315vLs3LnG9OZubtEXEzcAewD/gecF2ng0nqgE2bnr9uaMg3JwvT1qdKMvMPgD/ocBZJUhv8zUlJKozFLUmFsbglqTAWtyQVxuKWpMJY3JJUGItbkgpjcUtSYSxuSSqMxS1JhbG4JakwFrckFcbilqTCWNzqHM8o3uJYaAFZ3Ooczyje4lg8z/jkONd8+xrGJ8drzzGye6T2HPPR7lnepfmbdUZxfu/34POfX7pnFHcsDjA+Oc7wDcNM75+mt6eX0fWjDPQN1JZjat8UI5MjteWYL4+41VlDQ1VRffzj1dclWlSAYzFLY6LB9P5p9ud+pvdP05ho1JrjWZ6tNcd8WdzqrLGx6ujyyiurr0v5pLSOxXMG+wfp7emlJ3ro7ellsH+w1hzHcEytOebLqRJ1zqwzij93XsPZy0uJY3GAgb4BRteP0phoMNg/WNv0xEyOzWOb2TC0oYhpErC41UlHOqP4Uisrx+J5BvoGuqIoB/oGmFoz1RVZ2mVxq3M8o3iLY6EF5By3JBXG4pakwljcklQYi1uSCmNxS1JhLG5JKozFLUmFsbglqTAWtyQVxuKWpMJY3JJUGItbi9OhThV2OJ5CTIWxuLU4HXyqsMPxFGIqUFvFHREnRsTNEfH9iNgVEeX8/UMtTbNPFXa48j74b2RLhWj3iPszwN9k5quA1wC7OhdJWiAz5X3BBXDttQded+211XpLWwWa8+9xR8QJwK8D7wLIzGlgurOxpAUyNAQf+xhcfnm1fM45VWlffjl86lOWtorUzokUTgMeA/4qIl4D7AQuzcynO5pMWiiXXVZ9vfxyXnvmmXD33VVpz6yXChOZeeQNItYBfwecl5m3R8RngCcz88qDttsIbARYvXr12i1btnQocnv27NnDypUra83QLRyLymsvuYQT77qLx886izs/+9m649TO50VLN4zF0NDQzsxc19bGmXnEC/ALwMSs5TcAXzvSbdauXZt1GxsbqztC13AsMvNP/zQzIn961lmZEdXyEufzoqUbxgLYkXP08cxlzqmSzPxhRExGxOmZeR8wDNz7Ql9VpKNu1pz2neecw+Add7TmvJ0uUYHaPVnw+4CRiOgFHgDe3blI0gIaG4OrrmrNaTcarbK+6io4+2zfoFRx2iruzLwTaG/uReoWM5/TvuWW55fzZZdVpe3nuFUgf3NSi1M7v1zTzi/pSF3I4tbitH17e0fSM+W9ffvRySUtgHbnuKWybNrU/rZDQ06VqCgecUtSYSxuSSqMxS1JhbG4JakwFrckFcbilqTCWNySVBiLW5IKY3FLUmEsbkkqjMUtHSUjd43Q/+l+jvlPx9D/6X5G7hqpO5IK5d8qkY6CkbtG2HjLRp7Z+wwADz3xEBtv2QjARWddVGe02oxPjtOYaDDYP8hA30DdcYpicUtHwRWjVzxX2jOe2fsMV4xesSSLe3xynOEbhpneP01vTy+j60ct73lwqkQ6CnY/sXte6xe7xkSD6f3T7M/9TO+fpjHRqDtSUSxu6ShYc8Kaea1f7Ab7B+nt6aUneujt6WWwf7DuSEWxuKWj4Orhq1mxfMUB61YsX8HVw1fXlKheA30DjK4f5eNDH3ea5AVwjls6Cmbmsa8YvYLdT+xmzQlruHr46iU5vz1joG/Awn6BLG7pKLnorIuWdFFr4ThVIkmFsbglqTAWtyQVxuKWpMJY3JJUGItbkgpjcUtSYSxuSSqMxS1JhbG4JakwFrckFcbilqTCWNySVBiLW5IK03ZxR0RPRHwvIm7tZKBF4ZOfhLGxA9eNjVXrJelFms8R96XArk4FWVTOPRcuvLBV3mNj1fK559abS9Ki0FZxR8QpwFuAL3Q2ziIxNARbt1ZlfdVV1detW6v1kvQiRWbOvVHEzcA1wEuByzPzrYfYZiOwEWD16tVrt2zZssBR52fPnj2sXLmy1gz9mzfTf+ONTFx8MRMbNtSWoxvGols4Fi2ORUs3jMXQ0NDOzFzX1saZecQL8FbgL5rfDwK3znWbtWvXZt3GxsbqDbBtW+aqVZlXXll93battii1j0UXcSxaHIuWbhgLYEfO0a0zl3amSs4D3hYRE8AW4I0RcdP8X0+WkJk57a1b4WMfa02bHPyGpSS9AHMWd2Z+KDNPycx+4B3Atsx8Z8eTlWz79gPntGfmvLdvrzeXpEXBs7x3wqZNz183NOSbk5IWxLyKOzMbQKMjSSRJbfE3JyWpMBa3JBXG4pakwljcklQYi1uSCmNxS1JhLG5JKozFLUmFsbglqTAWtyQVxuKWpMJY3JJUGItbkgpjcUtSYSxuddz45DjXfPsaxifH644iLQqeSEEdNT45zvANw0zvn6a3p5fR9aMM9A3UHUsqmkfc6qjGRIPp/dPsz/1M75+mMdGoO5JUPItbHTXYP0hvTy890UNvTy+D/YN1R5KK51SJOmqgb4DR9aM0JhoM9g86TSItAItbHTfQN2BhSwvIqRJJKozFLUmFsbglqTAWtyQVxuKWpMJY3JJUGItbkgpjcUtSYSxuSSqMxS1JhbG4JakwFrckFcbilqTCWNySVJg5izsi+iJiLCLujYh7IuLSoxFMknRo7fw97n3ABzLzjoh4KbAzIr6Vmfd2OJsk6RDmPOLOzB9k5h3N758CdgEndzqYFsb45Dgju0c8w7q0iMxrjjsi+oGzgds7EUYLa+YM65sf3MzwDcOWt7RItH3qsohYCXwZeH9mPnmI6zcCGwFWr15No9FYqIwvyJ49e2rPULeR3SNM7ZviWZ5lat8Um8c2M7Vmqu5YtfJ50eJYtJQ2FpGZc28UsRy4FfhGZl471/br1q3LHTt2LEC8F67RaDA4OFhrhrrNHHFP7Zvi2GXHMrp+dMmf+9HnRYtj0dINYxEROzNzXTvbtvOpkgC+COxqp7TVPWbOsL7htA2WtrSItDNVch5wMXBXRNzZXPfhzLytc7G0UAb6BphaM2VpS4vInMWdmd8B4ihkkSS1wd+clKTCWNySVBiLW5IKY3FLUmEsbkkqjMUtSYWxuCWpMBa3JBXG4pakwljcklQYi1uSCmNxS1JhLG5JKozFLUmFsbglqTAWtyQVxuKWpMJY3JJUGItbkgpjcUtSYSxuSSqMxS1JhbG4JakwFrckFcbilqTCWNySVBiLW5IKY3FLUmEsbkkqjMUtSYWxuCWpMBa3JBXG4pakwljcklQYi1uSCtNWcUfEb0TEfRFxf0R8sNOhJEmHN2dxR0QP8DngfOAM4Lci4oxOB3sxxifHGdk9wvjkeN1RJGnBtXPE/SvA/Zn5QGZOA1uAt3c21gs3PjnO8A3DbH5wM8M3DFvekhadZW1sczIwOWv5YeBXD94oIjYCGwFWr15No9FYiHzzNrJ7hKl9UzzLs0ztm2Lz2Gam1kzVkqVb7Nmzp7Z/j27jWLQ4Fi2ljUU7xd2WzLwOuA5g3bp1OTg4uFC7npdjJ49lZLIq72OXHcuGoQ0M9A3UkqVbNBoN6vr36DaORYtj0VLaWLQzVfII0Ddr+ZTmuq400DfA6PpRNpy2gdH1o0u+tCUtPu0ccW8HXhkRp1EV9juA3+5oqhdpoG+AqTVTlrakRWnO4s7MfRHxXuAbQA+wOTPv6XgySdIhtTXHnZm3Abd1OIskqQ3+5qQkFcbilqTCWNySVBiLW5IKY3FLUmEsbkkqjMUtSYWxuCWpMBa3JBXG4pakwljcklQYi1uSCmNxS1JhLG5JKozFLUmFsbglqTCRmQu/04jHgIcWfMfzswr4cc0ZuoVj0eJYtDgWLd0wFqdm5sva2bAjxd0NImJHZq6rO0c3cCxaHIsWx6KltLFwqkSSCmNxS1JhFnNxX1d3gC7iWLQ4Fi2ORUtRY7Fo57glabFazEfckrQoWdySVJhFWdwR8RsRcV9E3B8RH6w7T10ioi8ixiLi3oi4JyIurTtTnSKiJyK+FxG31p2lThFxYkTcHBHfj4hdETFQd6a6RMTvN/9v3B0RX4qIl9SdqR2Lrrgjogf4HHA+cAbwWxFxRr2parMP+EBmngG8Dvj3S3gsAC4FdtUdogt8BvibzHwV8BqW6JhExMnAJcC6zDwT6AHeUW+q9iy64gZ+Bbg/Mx/IzGlgC/D2mjPVIjN/kJl3NL9/iuo/6Mn1pqpHRJwCvAX4Qt1Z6hQRJwC/DnwRIDOnM/PxelPVahlwXEQsA1YAj9acpy2LsbhPBiZnLT/MEi2r2SKiHzgbuL3eJLX5NLAJeLbuIDU7DXgM+KvmtNEXIuL4ukPVITMfAT4F7AZ+ADyRmd+sN1V7FmNx6yARsRL4MvD+zHyy7jxHW0S8FfhRZu6sO0sXWAacA3w+M88GngaW5PtAEfHzVD+NnwacBBwfEe+sN1V7FmNxPwL0zVo+pbluSYqI5VSlPZKZX6k7T03OA94WERNUU2dvjIib6o1Um4eBhzNz5ievm6mKfCl6E/BgZj6WmXuBrwCvrzlTWxZjcW8HXhkRp0VEL9WbDX9dc6ZaRERQzWXuysxr685Tl8z8UGaekpn9VM+HbZlZxJHVQsvMHwKTEXF6c9UwcG+Nkeq0G3hdRKxo/l8ZppA3apfVHWChZea+iHgv8A2qd4k3Z+Y9Nceqy3nAxcBdEXFnc92HM/O2GjOpfu8DRpoHNg8A7645Ty0y8/aIuBm4g+oTWN+jkF9991feJakwi3GqRJIWNYtbkgpjcUtSYSxuSSqMxS1JhbG4JakwFrckFeb/AyaUIWRb0bIhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "C1 = [1, 4, 5, 9, 11]\n",
    "C2 = list(set(range(12)) - set(C1))\n",
    "X0C1, X1C1 = X0[C1], X1[C1]\n",
    "X0C2, X1C2 = X0[C2], X1[C2]\n",
    "plt.figure()\n",
    "plt.title('1st iteration results')\n",
    "plt.axis([-1, 9, -1, 9])\n",
    "plt.grid(True)\n",
    "plt.plot(X0C1, X1C1, 'rx')\n",
    "plt.plot(X0C2, X1C2, 'g.')\n",
    "plt.plot(4,6,'rx',ms=12.0)\n",
    "plt.plot(5,5,'g.',ms=12.0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we recalculate the centiod of two class, move centriod to the new poisition, recalculate the distance between each sample and new centriod and reclassify the sample according the distacne.\n",
    "\n",
    "![data_1](images/data_1.png)\n",
    "\n",
    "The result of drawing are shown as follows："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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": [
    "C1 = [1, 2, 4, 8, 9, 11]\n",
    "C2 = list(set(range(12)) - set(C1))\n",
    "X0C1, X1C1 = X0[C1], X1[C1]\n",
    "X0C2, X1C2 = X0[C2], X1[C2]\n",
    "plt.figure()\n",
    "plt.title('2nd iteration results')\n",
    "plt.axis([-1, 9, -1, 9])\n",
    "plt.grid(True)\n",
    "plt.plot(X0C1, X1C1, 'rx')\n",
    "plt.plot(X0C2, X1C2, 'g.')\n",
    "plt.plot(3.8,6.4,'rx',ms=12.0)\n",
    "plt.plot(4.57,4.14,'g.',ms=12.0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, we move the center of mass to the new position, recalculate the distance between each sample and the new center of mass, and reclassify the samples according to the distance. The results are shown in the table below:\n",
    "![data_2](images/data_2.png)\n",
    "\n",
    "The result of drawing are shown as follows：\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": [
    "C1 = [0, 1, 2, 4, 8, 9, 10, 11]\n",
    "C2 = list(set(range(12)) - set(C1))\n",
    "X0C1, X1C1 = X0[C1], X1[C1]\n",
    "X0C2, X1C2 = X0[C2], X1[C2]\n",
    "plt.figure()\n",
    "plt.title('3rd iteration results')\n",
    "plt.axis([-1, 9, -1, 9])\n",
    "plt.grid(True)\n",
    "plt.plot(X0C1, X1C1, 'rx')\n",
    "plt.plot(X0C2, X1C2, 'g.')\n",
    "plt.plot(5.5,7.0,'rx',ms=12.0)\n",
    "plt.plot(2.2,2.8,'g.',ms=12.0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The centriod of class will remain the same when repeat the method, K-Means will stop cluster process when the condition are satisfied. Usually, the condition is that the difference value between two cost value of iteration are reaching the set value, or the change of the center of gravity position of the two iterations before and after reaches the limit value. If these stop conditions are small enough, k-means will find the optimal solution. But this is not necessarily the global optimal solution.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Program"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>sepal-length</th>\n",
       "      <th>sepal-width</th>\n",
       "      <th>petal-length</th>\n",
       "      <th>petal-width</th>\n",
       "      <th>class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal-length  sepal-width  petal-length  petal-width        class\n",
       "0           5.1          3.5           1.4          0.2  Iris-setosa\n",
       "1           4.9          3.0           1.4          0.2  Iris-setosa\n",
       "2           4.7          3.2           1.3          0.2  Iris-setosa\n",
       "3           4.6          3.1           1.5          0.2  Iris-setosa\n",
       "4           5.0          3.6           1.4          0.2  Iris-setosa"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This line configures matplotlib to show figures embedded in the notebook, \n",
    "# instead of opening a new window for each figure. More about that later. \n",
    "# If you are using an old version of IPython, try using '%pylab inline' instead.\n",
    "%matplotlib inline\n",
    "\n",
    "# import librarys\n",
    "from numpy import *\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import random\n",
    "\n",
    "# Load dataset\n",
    "names = ['sepal-length', 'sepal-width', 'petal-length', 'petal-width', 'class']\n",
    "dataset = pd.read_csv(\"iris.csv\", header=0, index_col=0)\n",
    "dataset.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\lenovo\\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",
      "\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",
      "C:\\Users\\lenovo\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:4: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  after removing the cwd from sys.path.\n",
      "C:\\Users\\lenovo\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:5: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n",
      "  \"\"\"\n"
     ]
    }
   ],
   "source": [
    "#Fixme-解决赋值的问题，参考https://www.jb51.net/article/138045.htm\n",
    "#Coding the class and assign value 0, 1, 2 to each class.\n",
    "dataset['class'][dataset['class']=='Iris-setosa']=0\n",
    "dataset['class'][dataset['class']=='Iris-versicolor']=1\n",
    "dataset['class'][dataset['class']=='Iris-virginica']=2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "def originalDatashow(dataSet):\n",
    "    #Draw original sample point.\n",
    "    num,dim=shape(dataSet)\n",
    "    marksamples=['ob'] #Sample graphic marking\n",
    "    for i in range(num):\n",
    "        plt.plot(datamat.iat[i,0],datamat.iat[i,1],marksamples[0],markersize=5)\n",
    "    plt.title('original dataset')\n",
    "    plt.xlabel('sepal length')\n",
    "    plt.ylabel('sepal width') \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "lines_to_end_of_cell_marker": 2,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Get sample data\n",
    "datamat = dataset.loc[:, ['sepal-length', 'sepal-width']]\n",
    "#True label\n",
    "labels = dataset.loc[:, ['class']]\n",
    "#Show original data\n",
    "originalDatashow(datamat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "\n",
    "def randChosenCent(dataSet,k):\n",
    "    \"\"\"Initialize cluster center:By randomly generating a value over the interval as a new central point \"\"\"\n",
    "\n",
    "    # Sample numb\n",
    "    m=shape(dataSet)[0]\n",
    "    # initialize list\n",
    "    centroidsIndex=[]\n",
    "    \n",
    "    #Generate a list similar to the sample index\n",
    "    dataIndex=list(range(m))\n",
    "    if False:\n",
    "        for i in range(k):\n",
    "            #Generate random number\n",
    "            randIndex=random.randint(0,len(dataIndex))\n",
    "            #Put the sample index that generate randomly into centroidsIndex\n",
    "            centroidsIndex.append(dataIndex[randIndex])\n",
    "            #Delete the sample that has been choosen\n",
    "            del dataIndex[randIndex]\n",
    "    else:\n",
    "        random.shuffle(dataIndex)\n",
    "        centroidsIndex = dataIndex[:k]\n",
    "    \n",
    "    #Get the sample by index\n",
    "    centroids = dataSet.iloc[centroidsIndex]\n",
    "    return mat(centroids)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def distEclud(vecA, vecB):\n",
    "    \"\"\"Calculate the Euclidean distance between two vector\"\"\"\n",
    "    return sqrt(sum(power(vecA - vecB, 2))) #la.norm(vecA-vecB)\n",
    "\n",
    "\n",
    "def kMeans(dataSet, k):\n",
    "    # The total number of sample\n",
    "    m = shape(dataSet)[0]\n",
    "    # Allocate sample to the nearest culster: save as [cluster number, square of distance](m_row x 2_column)\n",
    "    clusterAssment = mat(zeros((m, 2)))\n",
    "\n",
    "    # step1: Initialize cluster center by the sample point that generate randomly\n",
    "    centroids = randChosenCent(dataSet, k)\n",
    "    print('Original centers=', centroids)\n",
    "\n",
    "    # Flag bit，if the result of sample classification before and after iteration has changed, the value is True\n",
    "    clusterChanged = True\n",
    "    # View the number of iterations\n",
    "    iterTime = 0\n",
    "    \n",
    "    # All sample assignment results are no longer changed and the iteration terminates\n",
    "    while clusterChanged:\n",
    "        clusterChanged = False\n",
    "        \n",
    "        # step2: Allocate to the nearest cluster corresponding to the nearest cluster center\n",
    "        for i in range(m):\n",
    "            # Initially define distance as infinite\n",
    "            minDist = inf;\n",
    "            # Initialize index value\n",
    "            minIndex = -1\n",
    "            # Calculate the distance of each sample and k centriods\n",
    "            for j in range(k):\n",
    "                # Calculate the distance between the ith smaple and jth centriods\n",
    "                distJI = distEclud(centroids[j, :], dataSet.values[i, :])\n",
    "                # Judeg if the distance if the minimum\n",
    "                if distJI < minDist:\n",
    "                    # Update to get the minimum distance\n",
    "                    minDist = distJI\n",
    "                    # Get corresponding cluster numbers\n",
    "                    minIndex = j\n",
    "            # If the result of sample classification is not the same，mark clusterChanged to True\n",
    "            if clusterAssment[i, 0] != minIndex:\n",
    "                clusterChanged = True\n",
    "            clusterAssment[i, :] = minIndex, minDist ** 2  # Allocate smaple to nearest cluster\n",
    "            \n",
    "        iterTime += 1\n",
    "        sse = sum(clusterAssment[:, 1])\n",
    "        print('the SSE of %d' % iterTime + 'th iteration is %f' % sse)\n",
    "        \n",
    "        # step3:Update cluster center\n",
    "        for cent in range(k):  # When finished sample classification ,recalculate cluster center\n",
    "            # Get all sample point of this cluster，nonzero[0] represent the column of A == cent \n",
    "            #Without [0], column will also be shown\n",
    "            ptsInClust = dataSet.iloc[nonzero(clusterAssment[:, 0].A == cent)[0]]\n",
    "            # Update cluster center: calculate average value according to column direction, axis=0.\n",
    "            centroids[cent, :] = mean(ptsInClust, axis=0)\n",
    "    return centroids, clusterAssment\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "最初的中心= [[4.8 3.4]\n",
      " [5.5 2.4]\n",
      " [5.3 3.7]]\n",
      "the SSE of 1th iteration is 136.220000\n",
      "the SSE of 2th iteration is 58.811902\n",
      "the SSE of 3th iteration is 53.100129\n",
      "the SSE of 4th iteration is 49.715722\n",
      "the SSE of 5th iteration is 47.874761\n",
      "the SSE of 6th iteration is 46.133064\n",
      "the SSE of 7th iteration is 44.593439\n",
      "the SSE of 8th iteration is 44.384855\n",
      "the SSE of 9th iteration is 43.591498\n",
      "the SSE of 10th iteration is 41.904928\n",
      "the SSE of 11th iteration is 39.066514\n",
      "the SSE of 12th iteration is 38.316500\n",
      "the SSE of 13th iteration is 37.912536\n",
      "the SSE of 14th iteration is 37.423306\n",
      "the SSE of 15th iteration is 37.136261\n",
      "the SSE of 16th iteration is 37.123702\n"
     ]
    }
   ],
   "source": [
    "# Perform k-means clustering\n",
    "k = 3  # Cluster numbers designed by customer\n",
    "mycentroids, clusterAssment = kMeans(datamat, k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def datashow(dataSet, k, centroids, clusterAssment):  # Show cluster result in two dimensional space\n",
    "    from matplotlib import pyplot as plt\n",
    "    num, dim = shape(dataSet)  # sample numbers:num ,dimension: dim\n",
    "\n",
    "    if dim != 2:\n",
    "        print('sorry,the dimension of your dataset is not 2!')\n",
    "        return 1\n",
    "    marksamples = ['or', 'ob', 'og', 'ok', '^r', '^b', '<g']  # Sample graphic marking\n",
    "    if k > len(marksamples):\n",
    "        print('sorry,your k is too large,please add length of the marksample!')\n",
    "        return 1\n",
    "        # Draw all sample\n",
    "    for i in range(num):\n",
    "        markindex = int(clusterAssment[i, 0])  # Change value to int form, cluster number\n",
    "        # The characteristic dimension corresponds to x,y; Sample graphic marking and size\n",
    "        plt.plot(dataSet.iat[i, 0], dataSet.iat[i, 1], marksamples[markindex], markersize=6)\n",
    "\n",
    "    # Draw center point\n",
    "    markcentroids = ['o', '*', '^']  # Cluster center graphic marking\n",
    "    label = ['0', '1', '2']\n",
    "    c = ['yellow', 'pink', 'red']\n",
    "    for i in range(k):\n",
    "        plt.plot(centroids[i, 0], centroids[i, 1], markcentroids[i], markersize=15, label=label[i], c=c[i])\n",
    "        plt.legend(loc='upper left')\n",
    "    plt.xlabel('sepal length')\n",
    "    plt.ylabel('sepal width')\n",
    "\n",
    "    plt.title('k-means cluster result')  # Title\n",
    "    plt.show()\n",
    "    \n",
    "    \n",
    "# Draw real graphic\n",
    "def trgartshow(dataSet, k, labels):\n",
    "    from matplotlib import pyplot as plt\n",
    "\n",
    "    num, dim = shape(dataSet)\n",
    "    label = ['0', '1', '2']\n",
    "    marksamples = ['ob', 'or', 'og', 'ok', '^r', '^b', '<g']\n",
    "    # Finishing the draw of scatter point by circulation\n",
    "    for i in range(num):\n",
    "        plt.plot(datamat.iat[i, 0], datamat.iat[i, 1], marksamples[int(labels.iat[i, 0])], markersize=6)\n",
    "    for i in range(0, num, 50):\n",
    "        plt.plot(datamat.iat[i, 0], datamat.iat[i, 1], marksamples[int(labels.iat[i, 0])], markersize=6,\n",
    "                 label=label[int(labels.iat[i, 0])])\n",
    "    plt.legend(loc='upper left')\n",
    "    \n",
    "    # Add axis lable and title\n",
    "    plt.xlabel('sepal length')\n",
    "    plt.ylabel('sepal width')\n",
    "    plt.title('iris true result')  # Title\n",
    "\n",
    "    # Show graphic\n",
    "    plt.show()\n",
    "    # label=labels.iat[i,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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"
    },
    {
     "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": [
    "# The drawing shows\n",
    "datashow(datamat, k, mycentroids, clusterAssment)\n",
    "trgartshow(datamat, 3, labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How to use sklearn to do the classifiction\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "import matplotlib.pyplot as plt \n",
    "from sklearn.cluster import KMeans\n",
    "\n",
    "# load digital data\n",
    "digits, dig_label = load_digits(return_X_y=True)\n",
    "\n",
    "# draw one digital\n",
    "plt.gray() \n",
    "plt.matshow(digits[0].reshape([8, 8])) \n",
    "plt.show() \n",
    "\n",
    "# calculate train/test data number\n",
    "N = len(digits)\n",
    "N_train = int(N*0.8)\n",
    "N_test = N - N_train\n",
    "\n",
    "# split train/test data\n",
    "x_train = digits[:N_train, :]\n",
    "y_train = dig_label[:N_train]\n",
    "x_test  = digits[N_train:, :]\n",
    "y_test  = dig_label[N_train:]\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# do kmeans\n",
    "kmeans = KMeans(n_clusters=10, random_state=0).fit(x_train)\n",
    "\n",
    "# kmeans.labels_ - output label\n",
    "# kmeans.cluster_centers_ - cluster centers\n",
    "\n",
    "# draw cluster centers\n",
    "fig, axes = plt.subplots(nrows=1, ncols=10)\n",
    "for i in range(10):\n",
    "    img = kmeans.cluster_centers_[i].reshape(8, 8)\n",
    "    axes[i].imshow(img)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exerciese - How to caluate the accuracy?\n",
    "\n",
    "1. How to match cluster label to groundtruth label\n",
    "2. How to solve the uncertainty of some digital"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Value the performance of cluster\n",
    "\n",
    "Mehtod 1: If the data that has been valued have correct categories data, then use Adjusted Rand Index(ARI), ARI is similar to the method for accuracy calculating which considered the problem that the class cluster cannot correspond to the classification tag.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ari_train = 0.687021\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import adjusted_rand_score\n",
    "\n",
    "ari_train = adjusted_rand_score(y_train, kmeans.labels_)\n",
    "print(\"ari_train = %f\" % ari_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given the contingency table:\n",
    "![ARI_ct](images/ARI_ct.png)\n",
    "\n",
    "the adjusted index is:\n",
    "![ARI_define](images/ARI_define.png)\n",
    "\n",
    "* [ARI reference](https://davetang.org/muse/2017/09/21/adjusted-rand-index/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Method 2: if the value that has been evaluated do not have categories, Silhouette Coefficient will be used to evaluate the performance of cluster result. **Silhouette Coefficient take into account both the cohesion and the separation of the clusters, the value range is [-1,1], the higher Silhouette Coefficient represent the better clustering effect will be** \n",
    "\n",
    "Detailed steps for calculating Silhouette Coefficient\n",
    "1. For the ith smapel in the clusterded data$x_i$, calculate the average value between $x_i$ and all the other smaple in the same cluster, written as $a_i$, used to quantify the cohesion within a cluster\n",
    "2. Choose a cluster $b$ outside of $x_i$, calculate the average distance between $x_i$ and all samples in cluster $b$, traverse all other cluster, find the closest average distance and noted as $b_i$, which can be used to quantify the degree of separation between clusters.\n",
    "3. For sample $x_i$, Silhouette Coefficient is $sc_i = \\frac{b_i−a_i}{max(b_i,a_i)}$ \n",
    "4. Finally, calculate average value for all sample $\\mathbf{X}$, which will be the Silhouette Coefficient for current cluster result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.metrics import silhouette_score\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.rcParams['figure.figsize']=(10,10)\n",
    "plt.subplot(3,2,1)\n",
    "\n",
    "x1=np.array([1,2,3,1,5,6,5,5,6,7,8,9,7,9])   #Initialize original data\n",
    "x2=np.array([1,3,2,2,8,6,7,6,7,1,2,1,1,3])\n",
    "X=np.array(list(zip(x1,x2))).reshape(len(x1),2)\n",
    "\n",
    "plt.xlim([0,10])\n",
    "plt.ylim([0,10])\n",
    "plt.title('Instances')\n",
    "plt.scatter(x1,x2)\n",
    "\n",
    "colors=['b','g','r','c','m','y','k','b']\n",
    "markers=['o','s','D','v','^','p','*','+']\n",
    "\n",
    "clusters=[2,3,4,5,8]\n",
    "subplot_counter=1\n",
    "sc_scores=[]\n",
    "for t in clusters:\n",
    "    subplot_counter +=1\n",
    "    plt.subplot(3,2,subplot_counter)\n",
    "    kmeans_model=KMeans(n_clusters=t).fit(X)   #KMeans modeling\n",
    "\n",
    "    for i,l in enumerate(kmeans_model.labels_):\n",
    "        plt.plot(x1[i],x2[i],color=colors[l],marker=markers[l],ls='None')\n",
    "\n",
    "    plt.xlim([0,10])\n",
    "    plt.ylim([0,10])\n",
    "\n",
    "    sc_score=silhouette_score(X,kmeans_model.labels_,metric='euclidean')   #Calculate Silhouette Coefficient\n",
    "    sc_scores.append(sc_score)\n",
    "\n",
    "    plt.title('k=%s,silhouette coefficient=%0.03f'%(t,sc_score))\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(clusters,sc_scores,'*-')   #Draw the relationship between cluster numbers and corresponding Silhouette Coefficient\n",
    "plt.xlabel('Number of Clusters')\n",
    "plt.ylabel('Silhouette Coefficient Score')\n",
    "\n",
    "plt.show()   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How to determin the 'k'?\n",
    "\n",
    "Using \"Elbow observation\" can cursely determine the relatively reasonable numbers of cluster. K-means modeling are ultimately expecting that the sum of squares between all data points and their class clusters to be stable, so we could find best cluster numbers by observing this value. Under ideal condition, this broken line has an inflection point of slope as it falls and flattens out, this represents that from the K value that this inflection point represents, the increase of cluster center will not extremely broken the cluster inner structure.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from sklearn.cluster import KMeans\n",
    "from scipy.spatial.distance import cdist\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "cluster1=np.random.uniform(0.5,1.5,(2,10))\n",
    "cluster2=np.random.uniform(5.5,6.5,(2,10))\n",
    "cluster3=np.random.uniform(3,4,(2,10))\n",
    "\n",
    "X=np.hstack((cluster1,cluster2,cluster3)).T\n",
    "plt.scatter(X[:,0],X[:,1])\n",
    "plt.xlabel('x1')\n",
    "plt.ylabel('x2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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rPy0WBeAO4CrSIaMeJxT4zGfga1+D669PRyL16ZN3IjOz9lFI89HyiLgyIp6OiKm1U9GTlbiaGli6FO66K+8kZmbtp5Ci8AdJ35LUT9IGtVPRk5W43XaDrbbypTrNrHMppCh8ndSn8AQwNZvyO3usRNQOe/HoozB7dt5pzMzaR4tFISK2aGTasiPClboRI9LtmDH55jAzay8tFgVJ3SV9R9Kd2XRmNvppxdtyS9hrr3QUUpmNFmJm1qhCmo+uBHYBfptNu1Cil83MQ00NzJwJUyu+693MOoNCisLgiPh6RPwlm04GBhc7WLk49th0iKo7nM2sMyikKKyQ9NnaGUlb4vMV6qy/Phx2GIwdC8uW5Z3GzGzNFFIUzgMmSHpU0kTgL8C5xY1VXkaOhIUL4cEH805iZrZmWjyjOSL+LOlzwDbZopcj4uPixiovBx0EffumDufDDss7jZlZ2zVZFCTtGxF/kXRUg4e2kkQT11yuSN27w3HHwejR8O67sN56eScyM2ub5pqP9sluD2tkOrTIucrOyJHw8cdwxx15JzEzaztfjrOdRMDnPw8bbQSPPZZ3GjOz1bXb5TglnSWpj5JrJE2TdED7xOw8pLS3MGkSvPZa3mnMzNqmkKOP/jUiFgMHABsCNcDFRU1Vpk48Md3ecku+OczM2qqQoqDs9hDgpoiYXm+Z1bP55rDPPh72wszKVyFFYaqkh0lF4SFJ6wArixurfI0cCX//Ozz1VN5JzMxar9miIEnAD4DzScNdfAj0AE7ugGxl6ZhjYK210t6CmVm5abYoRDo0aXxETIuId7NliyLi+Q5JV4b69IEjj4TbboNPPsk7jZlZ6xTSfDRNkgfAa4WaGnj7bRg/Pu8kZmatU0hR+BLwpKRXJT0v6QVJ3lNoxgEHpPMV3IRkZuWmxbGPgAOLnqKT6dYNTjgBfvObtMewQcVf0drMykUhl+OcDQwE9s3uf1jI8ypdTU0aSnvcuLyTmJkVrpAzmn8IfBe4IFvUHfDpWS3YaSfYfntffMfMykshv/i/ChwOfAAQEf8E1ilmqM5ASnsLf/sbvPJK3mnMzApTSFH4JDs0NQAk9S5upM7jxBNTcXCHs5mVi0KKwjhJvwPWk/RvwJ+A0cWN1TkMGAD77pvGQvKwF2ZWDgrpaP4lcCdwF7A18IOIuKKl50m6TtJ8SS828fgQSe9JejabftDa8OWgpgZmzYInnsg7iZlZywo9iugFYBLwWHa/EDcAB7WwzqSI+GI2/aTA1y0rRx0FvXq5w9nMykMhRx+dCjwNHAUcQzqR7V9bel5EPAa8vcYJy9w668BXv5oOTV26NO80ZmbNK2RP4Txgp4g4KSK+DuxCOkS1Pewu6TlJf5S0fVMrSTpN0hRJUxYsWNBOm+44I0emazfff3/eSczMmldIUVgELKk3vyRbtqamAZtHxBeAK4B7mloxIq6OiOqIqK6qqmqHTXesYcOgXz8fhWRmpa+QovAK8JSkH2Unsj0J/J+kf5f0723dcEQsjoj3s/vjge6S+rb19UpZ165p2Ivx42HhwrzTmJk1rZCi8CrpV3ztQZX3Aq+RTmBr80lskjbJrteApF2zLO2xB1KSRo6E5cvTkNpmZqWqxQHxIuLHtfcldQHWzq7Z3CxJY4EhQF9Jc4AfkobIICKuInVaf1PScuAj4LjsJLlOaccd03TzzXDmmXmnMTNrXItFQdKtwOnACmAy0EfSZRHxi+aeFxHHt/D4r4FftyJr2Rs5Ev7jP+Dll2GbbfJOY2b2aYU0H22X7RkcCfwR2AKoKWqqTuqEE6BLF3c4m1npKqQodJfUnVQU7ouIZazqX7BW6NcP9tsvDXuxcmXeaczMPq2QovA74HWgN/CYpM2BFvsUrHEjR8Ls2TBpUt5JzMw+rZCxjy6PiP4RcUgks4GhHZCtUzrySOjd201IZlaamuxoljQiIm5p5lyEXxUpU6fWuzcccwzccQdccQX07Jl3IjOzVZrbU6i9bsI6TUzWRjU1sHgx3Hdf3knMzFancjs1oLq6OqZMmZJ3jDWyYgUMGpTOW3jggbzTmFklkDQ1IqpbWq/ZPgVJQyXdJWl6Nt0paUi7paxQXbumq7I99BDMm5d3GjOzVZosCpK+AlwH3A+cAJwIjAeuk3RIx8TrvGpq0h6Dh70ws1LS3J7CecCREXF9RDwXEc9GxHWk8xXaa+jsirX99rDzzr74jpmVluaKwiYR8VzDhRHxPLBx8SJVjpoamDYNpk/PO4mZWdJcUfigjY9ZAS65BAYOTP0LtecsTJiQlpuZ5aW5AfE+K6mxgyYFbFmkPBVj8GAYPhyqq2HMGNh/fzjuuHTZTjOzvDRXFI5o5rFftneQSjN0aCoARxwBS5bAUUfBPfek5WZmeWmyKETExI4MUomGDoVvfxt+9jNYZx0YMiTvRGZW6QoZEM+KZMIEuPpqOOggePNNuOyyvBOZWaVzUcjJhAmpT2HcOLj7blhvPRg1Ki03M8tLwUVBUq9iBqk0kyengjB0aBoU7/zzYdmyVCDMzPLSYlGQtIekl4CZ2fwXJP226Mk6uVGjVu9U/uY3097CnDn5ZTIzK2RP4X+AA4FFANkJbXsXM1Ql6tMndTrfc49PZjOz/BTUfBQRbzRYtKIIWSred74DvXrBxRfnncTMKlUhReENSXsAIam7pP8AZhQ5V0Xq2xdOPx3GjoVZs/JOY2aVqJCicDpwBtAfeBP4YjZvRXDuuWnoCw93YWZ5KOQazQsj4sSI2DgiNoqIERGxqCPCVaJNN4WTT4brr4d//jPvNGZWaZob5gIASZc3svg9YEpE3Nv+kWzUKBg9Gi69NE1mZh2lkOajtUhNRn/Pph2BAcApkv63iNkq1pZbwvHHw1VXwSLvk5lZByqkKOwIDI2IKyLiCmA/YFvgq8ABxQxXyS64AD780ENfmFnHKqQorA+sXW++N7BBRKwAPi5KKmP77eHII+GKK2Dx4rzTmFmlKKQoXAI8K+l6STcAzwC/kNQb+FMxw1W6Cy+Ed99NzUhmZh1BEdHySlI/YNdsdnJE5HZcTHV1dUyZMiWvzXe4Aw6A55+H115LYySZmbWFpKkRUd3SeoUOiLcUmAu8A2wlycNcdJALL4R58+C66/JOYmaVoJAB8U4FHgMeAn6c3f6ouLGs1j77wB57pJPZli3LO42ZdXaF7CmcBQwGZkfEUGAn4N2iprI6Utpb+Mc/0rWczcyKqZCisDQilgJI+kxEzAS2aelJkq6TNF/Si008LkmXS3pF0vOSdm5d9MpxyCHwhS+kgfJWeChCMyuiQorCHEnrAfcAj0i6F5hdwPNuAA5q5vGDgc9l02nAlQW8ZkWq3Vt4+WVfhMfMiqugo4/qVpb2AdYFHoyITwpYfxBwf0Ts0MhjvwMejYix2fzLwJCImNvca1ba0Ue1VqyA7bZLQ2tPm5YKhZlZodrl6CNJXSXNrJ2PiIkRcV8hBaEA/YH612mYky1rLMdpkqZImrJgwYJ22HT56do1XbLz2WfhwQfzTmNmnVWzRSE7a/llSZt1UJ6mclwdEdURUV1VVZVnlFydeCIMHAgXXQSt2MEzMytYocNcTJf0Z0n31U7tsO03gYH15gdky6wJPXqkEVT/+leYNCnvNGbWGbU4dDbw/SJt+z7gTEm3AV8C3mupP8HglFPgpz9Newt7+xRCM2tnhVxkZyLwOtA9uz8ZmNbS8ySNBf4GbCNpjqRTJJ0u6fRslfHALOAVYDTwrba9hcrSsyeccw48/DBUYH+7mRVZi0cfSfo30iGjG0TEZyV9DrgqIoZ1RMCGKvXoo/oWL4bNNoNhw+Cuu/JOY2bloD3HPjoD2BNYDBARfwc2WrN4tib69IFvfzuds/DSS3mnMbPOpJCi8HH9Q1AldQN87EvOzjornbNw8cV5JzGzzqSQojBR0oVAT0n7A3cAfyhuLGtJ377wjW/ArbfCrFl5pzGzzqKQonA+sAB4AfgGqYP4P4sZygpz7rnppLZf/CLvJGbWWRRSFI4EboqIYyPimIgYHa0ZG8OKpn9/OOmkdK2FuT6Y18zaQSFF4TDg/yTdLOnQrE/BSsSoUbB8OVx6ad5JzKwzKOQ8hZOBrUh9CccDr0q6ptjBrDCf/Swcf3y6jvOiRXmnMbNyV9DlOCNiGfBH4DZgKqlJyUrE+efDBx/AFVfkncTMyl0hl+M8WNINwN+Bo4FrgE2KnMtaYYcd4Igj4PLLYcmSvNOYWTkrZE9hJOkCO9tExEkRMT4ilhc5l7XShRfCO++kZiQzs7YqpE/h+Ii4JyI+BpC0l6TfFD+atcauu8J++6UO548+yjuNmZWrgvoUJO0k6ReSXgd+Csxs4SmWgwsvhHnz4Prr805iZuWqyaIgaWtJP8yuvHYF8A/SAHpDI8JdmiVoyBDYfXe45BJYtizvNGZWjprbU5gJ7AscGhF7ZYVgRcfEsraQ0t7C7Nlp+Aszs9ZqrigcBcwFJkgaLWkY4MvFl7ivfAV23BF+/nNY4RJuZq3UZFHIOpePA7YFJgBnAxtJulLSAR0V0Fqndm/h5Zfh97/PO42ZlZtCjj76ICJujYjDSNdRfgb4btGTWZsdcwx87nPws5+BR6kys9Yo6OijWhHxTkRcnddV16wwXbums5yfeQYeeijvNGZWTlpVFKx8jBgBAwfCRRflncTMyomLQifVowecdx48/jhMmpR3GjMrFy4Kndgpp0BVVepbMDMrhItCJ9arF5xzDjz4IEydmncaMysHLgqd3Le+Beuum85bMDNriYtCJ7fuunDmmXD33TBjRt5pzKzUuShUgLPPhp494eKL805iZqXORaEC9O0Lp50GY8bA66/nncbMSpmLQoU491zo0iWNoGpm1hQXhQoxYACcdBJcdx3MnZt3GjMrVS4KFWTUqHSdhV/9Ku8kZlaqXBQqyFZbwXHHwZVXwttv553GzEqRi0KFOf98+OADuMLXzjOzRrgoVJh/+Rc4/HC47DJYsiTvNGZWaopaFCQdJOllSa9IOr+Rx0+StEDSs9l0ajHzWHLhhfDOO/C73+WdxMxKTdGKgqSuwG+Ag4HtgOMlbdfIqrdHxBez6Zpi5bFVvvQlGDYMLr0Uli7NO42ZlZJi7insCrwSEbMi4hPgNuCIIm7PWuF734O33oLrr887iZmVkmIWhf7AG/Xm52TLGjpa0vOS7pQ0sLEXknSapCmSpixYsKAYWSvOkCGw227pZLZly/JOY2alIu+O5j8AgyJiR+AR4MbGVsouAVodEdVVVVUdGrCzklLfwuuvw9ixeacxs1JRzKLwJlD/l/+AbFmdiFgUER9ns9cAuxQxjzVw6KGw445pWO2VK/NOY2aloJhFYTLwOUlbSOoBHAfcV38FSf3qzR4OeHDnDiTBBRfAzJlwzz15pzGzUlC0ohARy4EzgYdIX/bjImK6pJ9IOjxb7TuSpkt6DvgOcFKx8ljjjj02nel80UUQkXcaM8ubosy+Caqrq2PKlCl5x+hUrr0WTj01XbbzwAPzTmNmxSBpakRUt7Re3h3NVgJqatIoqhddlHcSM8ubi4LRowecdx5MmpQmM6tcLgoGpOajqqp0JJKZVS4XBQOgVy845xz44x9h2rS805hZXlwUrM63vgV9+nhvwaySuShYnXXXhTPPhLvuSucumFnlcVGw1Zx9Nqy1Flx8cd5JzCwPLgq2mqoq2HlnuPnmNC5SrQkT0uB5Zta5uSjYp3znO2kspLPPTvMTJsDw4TB4cL65zKz4uuUdwErP8OFw441w771QXQ0zZsApp8CCBalAVFWlacMNoZv/BZl1Kh7mwho1ezbsuSe8+WbT60iwwQarisRGG62633B+o43WvIhccknaWxk6dNWyCRNg8mQYNartr2tWCQod5sK/86xRs2bBxx/D978PV14JV10F22yT9hbmz0+39af58+Gll9L9RYuaHlyvtog0V0Bq5/v2Xb2IDB6c9mLGjUuFobZZa9y4jvlMzCqBi4J9Sv0v26FD01R/viUrVqTC0LBoNJyfOTMNq7FoUdPXc1h//dULxm67petAfPnL8MQT8JOfQL9+8O676ZBaqX0/C7NK4+Yj+5SObqZZsQLefrvxvY/G5ufPb/x1evSAjTdVqbAxAAAIBklEQVQubNpgAxcQqyyFNh+5KFhZqd2LGTkSrr8evvc92GQTmDev8Wn+fFi+/NOv061b2gNprGBsssnq8xtuCF2aOU7PfR1WDtynYJ1Ow2atQw9dNX/iiY0/Z+VKeOedTxeLt95aff7FF9PtsmWffo2uXVPTVVN7HQBHHw2jR8MRR6QmMfd1WLnynoKVjWL/Io9IfRON7XE0LCLz5qWO+MZI0L8/bL756p3nVVWp87zhsrXWWvPsZi1x85FZEUXA4sWrF4lrr01Xr6uuhi22SP0fCxeuul2xovHXWnvtpgtGY8vXWaew/hA3a1l9bj4yKyIpHe207rqw9dbpy3bKlFWH8F5yyepfxitXpr2Q2k7z2mLRcHrrLXjhhXR/6dLGt92jR/N7HvUP6z32WLj9dhg2rHQO4XWxKm0uCmZrqJBDeLt0SUc8bbBBOt+jJRHwwQctF5GFC+G119L9xYsbf6399oPu3VOH+0YbwRlnQM+e6Roa7X3bvXvL783nm5Q2FwWzNTR58uoFYOjQND95cmHndTRGSs1Ka6+dmqIK8fHHqUg0LCB33pk6v3fZBXbYAT78ED76KN0uWZKO0Kq/7KOP0tQWXbum4tBSARk8GA45BHbaCZ57DkaMgOnTU4GrfX7D16k/rbVW+x9S7D2YxH0KZp1Y7a/wb34zNWsVegLiypWpyDQsFh9+2PiyQm/r31+0qOnO+kI0LBaNFY/WLJs+HS64AH7729Tc9vTTcNJJhX9mxdJexcp9CmYVbk3OTO/SJX1R9uxZ3GyjRqVideON6YuvtnA0LCStWVbb7NZweVN9NA0df/zq8/vvnz6HtdZa/baxZa1Zp6Xn1w7x0tHNbS4KZp1UMZq12sOaDqPSVitXpsLQUlG59Va4//7UF7P33uk5H3306dva+4sWNb1OU8O3FKJbt1UFokuXVJz23Reeeaa4n5Wbj8ysQ5Vy231bm9saE5FOhmyqYDQsLi2tM3lyGnTy+99PY361ls9TMDNrhYZ7MA3nSyHbmhSrQouCr7xmZkbzzW15ql+cfvKTdDt8eFpeDN5TMDMrYR199JGLgplZBXDzkZmZtZqLgpmZ1XFRMDOzOi4KZmZWx0XBzMzqlN3RR5IWALPb+PS+wMJ2jNNeSjUXlG4252od52qdzphr84ioammlsisKa0LSlEIOyepopZoLSjebc7WOc7VOJedy85GZmdVxUTAzszqVVhSuzjtAE0o1F5RuNudqHedqnYrNVVF9CmZm1rxK21MwM7NmuCiYmVmdiigKkq6TNF/Si3lnqU/SQEkTJL0kabqks/LOBCBpLUlPS3ouy/XjvDPVJ6mrpGck3Z93llqSXpf0gqRnJZXMML6S1pN0p6SZkmZI2r0EMm2TfU6102JJZ+edC0DSOdm/+RcljZW0Vt6ZACSdlWWaXuzPqiL6FCTtDbwP3BQRO+Sdp5akfkC/iJgmaR1gKnBkRLyUcy4BvSPifUndgceBsyLiyTxz1ZL070A10CciDs07D6SiAFRHREmd8CTpRmBSRFwjqQfQKyLezTtXLUldgTeBL0VEW09Kba8s/Un/1reLiI8kjQPGR8QNOefaAbgN2BX4BHgQOD0iXinG9ipiTyEiHgPezjtHQxExNyKmZfeXADOA/vmmgkjez2a7Z1NJ/HqQNAD4CnBN3llKnaR1gb2BawEi4pNSKgiZYcCreReEeroBPSV1A3oB/8w5D8Dngaci4sOIWA5MBI4q1sYqoiiUA0mDgJ2Ap/JNkmRNNM8C84FHIqIkcgH/C4wCVuYdpIEAHpY0VdJpeYfJbAEsAK7PmtuukdQ771ANHAeMzTsEQES8CfwS+AcwF3gvIh7ONxUALwJflrShpF7AIcDAYm3MRaEESFobuAs4OyIW550HICJWRMQXgQHArtkubK4kHQrMj4ipeWdpxF4RsTNwMHBG1mSZt27AzsCVEbET8AFwfr6RVsmasw4H7sg7C4Ck9YEjSMV0U6C3pBH5poKImAH8N/AwqenoWWBFsbbnopCzrM3+LmBMRNydd56GsuaGCcBBeWcB9gQOz9rvbwP2lXRLvpGS7FcmETEf+D2p/Tdvc4A59fby7iQViVJxMDAtIublHSSzH/BaRCyIiGXA3cAeOWcCICKujYhdImJv4B3g/4q1LReFHGUdutcCMyLiV3nnqSWpStJ62f2ewP7AzHxTQURcEBEDImIQqdnhLxGR+y85Sb2zAwXImmcOIO3y5yoi3gLekLRNtmgYkOtBDA0cT4k0HWX+AewmqVf2f3MYqZ8vd5I2ym43I/Un3FqsbXUr1guXEkljgSFAX0lzgB9GxLX5pgLSL98a4IWs/R7gwogYn2MmgH7AjdmRIV2AcRFRMod/lqCNgd+n7xG6AbdGxIP5RqrzbWBM1lQzCzg55zxAXfHcH/hG3llqRcRTku4EpgHLgWconeEu7pK0IbAMOKOYBwxUxCGpZmZWGDcfmZlZHRcFMzOr46JgZmZ1XBTMzKyOi4KZmdVxUTBrB5IGldoovGZt4aJgZmZ1XBTM2pmkLbMB6AbnncWstSrijGazjpINKXEbcFJEPJd3HrPWclEwaz9VwL3AUXlfKMmsrdx8ZNZ+3iMNqrZX3kHM2sp7Cmbt5xPgq8BDkt6PiKKNZGlWLC4KZu0oIj7ILgb0SFYY7ss7k1lreJRUMzOr4z4FMzOr46JgZmZ1XBTMzKyOi4KZmdVxUTAzszouCmZmVsdFwczM6vw/q9uciIjZDX0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "K=range(1,10)\n",
    "meandistortions=[]\n",
    "\n",
    "for k in K:\n",
    "    kmeans=KMeans(n_clusters=k)\n",
    "    kmeans.fit(X)\n",
    "    meandistortions.append(\\\n",
    "            sum(np.min(cdist(X,kmeans.cluster_centers_,'euclidean'),\\\n",
    "                       axis=1))/X.shape[0])\n",
    "\n",
    "plt.plot(K,meandistortions,'bx-')\n",
    "plt.xlabel('k')\n",
    "plt.ylabel('Average Dispersion')\n",
    "plt.title('Selecting k with the Elbow Method')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As can be seen from the figure above, in the process that cluster number decrease from 1 to 2 and 3, the change of K value can make a big difference to the whole cluster structure, which means new cluster number make algorithm have larger convergence space and this K means can not represent real cluster members. When K=3, if we increase K, the decrease speed of average distance are slow down obviously, which means that a further increase in K is no longer conducive to the convergence of the algorithm, at the same time, it also mplies that K=3 is the relative optimal number of class clusters\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "jupytext_formats": "ipynb,py",
  "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}