{
 "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": "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\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": 1,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "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"
      ],
      "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>"
     },
     "metadata": {},
     "execution_count": 1
    }
   ],
   "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 necessary libraries\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import random\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "\n",
    "# 1 read from iris.csv\n",
    "iris_df = pd.read_csv('./iris.csv', header=0, index_col=0)\n",
    "iris_df.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "0      0\n",
       "1      0\n",
       "2      0\n",
       "3      0\n",
       "4      0\n",
       "      ..\n",
       "145    2\n",
       "146    2\n",
       "147    2\n",
       "148    2\n",
       "149    2\n",
       "Name: class, Length: 150, dtype: int64"
      ]
     },
     "metadata": {},
     "execution_count": 2
    }
   ],
   "source": [
    "# 2 label different kinds of iris to 0, 1, 2\n",
    "\n",
    "iris_df['class'].replace(['Iris-setosa', 'Iris-versicolor', 'Iris-virginica'], [0, 1, 2], inplace=True)\n",
    "iris_df['class']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "lines_to_end_of_cell_marker": 2,
    "scrolled": true
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# 2 visualize iris data\n",
    "def visualizeIris(iris_df, feature='sepal', form='ro', mark_size=5):\n",
    "    plt.plot(iris_df[feature+'-length'], iris_df[feature+'-width'], form, markersize=mark_size)\n",
    "    plt.title('original dataset')\n",
    "    plt.xlabel(feature+'-length')\n",
    "    plt.ylabel(feature+'-width')\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "visualizeIris(iris_df, feature='sepal', form='ro')\n",
    "visualizeIris(iris_df, feature='petal', form='bo')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 3 Kmeans algorithm packaging\n",
    "class KMeans():\n",
    "    \"\"\"\n",
    "        @brief: K-means clustering algorithm for analyzing iris.csv data\n",
    "        @param: data datasets\n",
    "        @param: k number of clusetr\n",
    "        @param: feature feature for clustering(default is 'sepal'，'petal' is optional)\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, data, k=3, feature='sepal'):\n",
    "        self.color = 'rbckmyw'  # colors for graphics\n",
    "        self.k = k  # how many clusters\n",
    "        self.data = data  # save data\n",
    "        self.feature = feature  # feature for clustring\n",
    "        self.feature_points = np.array([iris_df[feature+'-length'], iris_df[feature+'-width']]).T # feature\n",
    "        self.clusters = {key: [] for key in range(self.k)}  # k clusters(null，need to be filled)\n",
    "        self.centroids = random.sample(list(self.feature_points), k)  # random centroids\n",
    "        self.count = 0  # record several iterations\n",
    "\n",
    "    # euclid distance\n",
    "    def __distance(self, point1, point2):\n",
    "        return np.sqrt(np.square(np.array(point1) - np.array(point2)).sum())\n",
    "\n",
    "    # calculate centroids of points\n",
    "    def __calc_centroids(self, points):\n",
    "        np_points = np.array(points)\n",
    "        return np_points.mean(axis=0)\n",
    "\n",
    "    # visualize data\n",
    "    def __drawPoints(self, index, cluster, props='ro'):\n",
    "        # plot centroids\n",
    "        plt.plot(self.centroids[index][0], self.centroids[index][1], '^', c=self.color[index], ms=14)\n",
    "        np_cluster = np.array(cluster)  # transfer to numpy array for convenient plotting\n",
    "        plt.plot(np_cluster[:, 0], np_cluster[:, 1], props)  # plot\n",
    "        plt.xlabel(self.feature+'-length')\n",
    "        plt.ylabel(self.feature+'-width')\n",
    "        plt.grid(True)\n",
    "\n",
    "    # is programme should stop?\n",
    "    def __stopable(self, index_list, index_list_his):\n",
    "        self.count = self.count+1  # count once if checked\n",
    "        # ignore first time\n",
    "        if len(index_list) != len(index_list_his):\n",
    "            return False\n",
    "        np_index_list = np.array(index_list)\n",
    "        np_index_list_his = np.array(index_list_his)\n",
    "        return not np.any(np_index_list-np_index_list_his)\n",
    "\n",
    "    # generate clusters\n",
    "    def __cluster(self):\n",
    "        min_index_list = []\n",
    "        while True:\n",
    "            # clear clusters for new iteration\n",
    "            del self.clusters\n",
    "            self.clusters = {key: [] for key in range(self.k)}\n",
    "\n",
    "            min_index_list_his = min_index_list\n",
    "            min_index_list = []\n",
    "            for point in self.feature_points:\n",
    "                # calculate all distance from a point to all centroids and save results to dis\n",
    "                dis = np.array([])\n",
    "                for i in range(self.k):\n",
    "                    dis = np.append(dis, self.__distance(self.centroids[i], point))\n",
    "\n",
    "                # find min value's index\n",
    "                min_index = np.argmin(dis)\n",
    "                min_index_list.append(min_index)\n",
    "                # clustering\n",
    "                self.clusters[min_index].append(point)\n",
    "\n",
    "            # clear old centroids\n",
    "            self.centroids.clear()\n",
    "            # calculate new centroids\n",
    "            for i in range(self.k):\n",
    "                self.centroids.append(self.__calc_centroids(self.clusters[i]))\n",
    "                # plot, visualize\n",
    "                self.__drawPoints(i, self.clusters[i], props=self.color[i]+'.')\n",
    "            plt.show()\n",
    "\n",
    "            # if there's no points' index has been changed, then return\n",
    "            if self.__stopable(min_index_list, min_index_list_his):\n",
    "                return\n",
    "\n",
    "    # return final result\n",
    "    def result(self):\n",
    "        self.__cluster()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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XvvZM0YyYtRsWFKvqPySrXRtSsxvwlU4/k+StyDWQi6YssSrOZGUe55497sceG5zHWLz48ILbEbRNk5XFOYP65PGGxDOSiJRX/QWyVDSjtNo2E5nZFwmuTtqUu5+feEQiUh6Nl81tLKknpRF1zuDPM4miiyRxzZ+oeVx9NWzeDBdcAOvXzz9WKaEsLirVyQ7W7LK5c3Nw7rkwM6OdtETaJgN335JVIN1gchLWrAn+OZpvnYCoeVx9NXz0o8Hj2r2+az0iiR0sSic7WKtiGrOzsGNHvHlIYcS9hPXpZnaLmT1oZt+p3dIOrmyyGKuweXP759LFsuhX38kOFreYhnbSUoh7AvlG4FPAIeAs4B+Az6UVVFllMVbhggvaP5culkW/+rg7WCcl9rSTlkLccQaL3f1OMzN3fwT4X2a2Dbg2xdhKJ4uxCrWjbZ0z6EFZ9KuPu4PFPSo480ztpCURNxlUzKwP+E8z+z1gN3B8emGVVxJ1AqLmsX69vl89K4tCFFE7WCdHBd/6VjAqWT2LCi9uM9GVwLOAK4DVwNuA304rKBEpsE4Kb2vcQWnEvTbR/3P3GYIiN1e4+wXu/o12nzGzY83sm2a208weMLMPNZnmGDO72cweNrO7zWzFvNZCRLLRyVEBPDPuYN++dOOSBYvbm+hVZnYfcC9wX/gDvzriYxXg9e5+BnAm8AYze03DNO8ADrj7i4G/ANT4IVJknRwV1OjooBTiNhONAJe7+wp3XwG8m6CHUUvh5TBmwqdHh7fG0cxvBj4bPr4FWGNmFjOmjsSstVGIOhkx6pfEWpe8i9sksT037NnDOTt3smHPntbLSaAwTdRyJg8eZDS8X0isqbv6al59ySXBeIFWFlKBaXIy/lFBzewsTEx09pk4ccadJm1liTNKuwsX1W7A9iav3RPjc/3ADmAGWN/k/fuBU+qefxs4od0853Ohug5qbSyouE0SYtYvibUueRa36aTuSKttev3u3c7Y2NO363fvPnI5MQvTtBO1nNoy+tosI06sqbvqKnfwam3nueqqI6dJogJTgkVlWn6fkvzSJqD0cXr0heri9ibaYmbXA58n+O/+LcC4mb0yTCj3tEg0c8CZZjYA/LOZvczd7+80YZnZMDAMsGzZMsY7HGwzOrqcSmUl1apRqVQZGZmiUnm042kAZmZmOl5+JzZufDnwXMAAZ+PGA6xadW8q65KmTmJotU03Nj7ftYtVu3YdvhyC9sgqUKlWGdm+nUqHsUYtJ84y4sSatlePjrKY2p4DPxkd5ZvnnnvYNMtHR1lZqWDVKtVKhamRER6tPLM2L9+4sW7vgwMbN3LvqlUdzaMTrf72cZaRZBzdHmcs7TJF7QaMtbndFXMe1wLva3jtdmAwfHwU8ARg7eajI4NOjgzmdGQQg44M6ujIoDvj9Ogjg9TqDgBLgYHw8WLg34HzGqZ5N/Dp8PHFwBei5jvfegYTE+4f+Uj7v0OcabK4rvn117uffXbrGslx1+Wd7/x2rvWP48Tp3n6bXr97t5+9Y0fbH9eJ6Wn/yNTUvBJB3OVMTE/7O8fG2i4jTqypu+oq//HJJzdPBDVRf5ioHTDOPGJq+31K6kubgG6IM5FkACwDPgN8OXz+UuAdEZ95ObCdoAfS/cC14esfBs4PHx8L/BPwMPBN4LSoWFTcJr6yxKo4k1WWON3LE2s3xBmVDOKeM/h7gt5D/zN8vgu4OUwQrZqf7gVe0eT1a+se/xT4jZgxiIhISuJ2LT3B3b9AcA4Ndz8EzKUWlYiIZCpuMvixmT2fcJxAOHhs/p26C6oMXYF7TZwxBEmMM4gTR9Q4g6g4ElmXJHbSXtrRe2ldFyhuM9F7gVuBF5nZ1wlODl+UWlQ5yKJuiHRm8uBB1uzcyWy1yqK+Pu484wwGlyzpeJqk4qgAozt3ziuORNYli+pJ3aSX1jUBcY8MXgScC/wCQXfQ/yR+IimFLOqGSGfGp6eZrVaZA2arVcanp+c1TVJxVBcQRyLrkkX1pG7SS+uagLjJ4IPu/kOC0VBnAX9HUOyma2RRN0Q6MzQwwKK+PvqBRX19DA0MzGuapOLoW0AciaxLFtWTukkvrWsC4v53XztZ/CZgo7v/q5n9SUox5SKLuiHSmcElS7jzjDMYn55maGCgafNPnGmSimNk+3bWtmiGioojkXXJonpSN+mldU1A3GSwO7wcxa8C683sGOIfVZRGFnVDpDODS5ZE/sDHmSaJOCrh/XzjSGRdsqie1E16aV0XKO4P+m8SnCs4x92ngecB708rKBERyVasIwN3fwrYXPd8L7A3raBERCRbXdfUI90lTt/8OLUI0h6HkFQcUdNE1kyYnGT56Gj6/eq7qf9+FutSgu3VVd1DpbvE6Zu/Yc8eLgsvFX3HgQMADJ90UkfzSEIScURNE7WMWr/6lZUKjI6m16++m/rvZ7EuJdleOjKQworTN3/T/v1tn2cxDiGpOKKmiVpGrV+9Vavp9qvvpv77WaxLSbaXkoEUVpy++RcuXdr2eat57K1UeN327exLqMjIfOPoZJqoZdT61Vf7+tLtV99N/fezWJeSbC81E0lhxembX2sm2bR/PxcuXXp4s0mbeaybmuJrBw+y7pFH+GRDJa/5mG8cnUwTtYxav/qpkRFOW7s2vaaIbuq/n8W6lGR7KRlIocXpmz980klH/jC2mcfeSoUbv/99qsCN+/bxwVNP5QXHHLPgWDuNYz7TRC2DwUEerVQ4Le0fnG7qv5/FupRge6mZSHrOuqkpqkFxJebcWffIIzlHJJI/JQPpKbWjgtkwGcy6c+O+fYmdOxApKzUTSUuTBw+mes2frGK45MEH+fKTT3Lu857Hc/r7nz4qqKkdHbQ7d1CrZ3DMwYOpbouo9S3C30S6k5KBNJVV//y0Y7jkwQcZffxxAEYff5w+wnJ9dWpHB63OHcSpZ5CEJGoiiMyXmomkqaz656cdw5effPKw542JoKbduYM49QySkERNBJH5UjKQprKoE5BFDOc+73mxpmt37iBOPYMkJFETQWS+1EwkTWVRJyCLGD730pcCcMv+/cy6422mbXXuIE49gyQkURNBZL6UDKSlLOoEZBHDx170IjY98QTu7VJB+3MHceoZJCGJmggi86FmIul69eMKomjcgfQqJQPpao3jCqJo3IH0KiUDyVWt//5Cag20qwGwbmqKQ9VWfYiam+/RQVZ1E6SEVM9ApLUk+u9H9b3/vwcOcKjDuGbdmejwB11jAKSlktQzUDKQ3DTrv9/pD2izvvf183j7iSfywe9+lzmgH1i3ciXXnHpqkqsRKw7pYc3qGRQwGaiZSHKTRP/9ovTN1xgAaUn1DETaS6L/flH65msMgLSkegYi0ZLov1+UvvkaAyAtqZ6BiIiUQWrJwMxeaGZjZvagmT1gZlc2mWbIzA6a2Y7wdm1a8YiISGtpNhMdAv7A3e8xs2cD28zsq+7+YMN0/+7u56UYh4iIREjtyMDd97r7PeHjHwEPASentbxeksT4laIMkIoadBYnzqKsSxI27NnDOTt3smHPnvyCKMEAKUleJieQzWwF8Arg7iZvD5rZTmAP8D53fyCLmMoqifErRRkgFTXoLE6cRVmXJGzYs4fLdu0C4I4DBwAYPumkbIMoyQApSV7qycDMjgc2Ae9x9x82vH0PcKq7z5jZG4F/AU5vMo9hYBhg2bJljI+PpxpzOzMzM7kuf3R0OZXKSqpVo1KpMjIyRaXyaNNpW8U6ClQICr1UqlVGtm8njyvxRMURJ84s1yXtv/3Gxue7drEqTA6dWEicy0dHWVmpYNUq1UqFqZERHk3xOk15f5/i6ok43T21G3A0cDvw3pjTTwEntJtm9erVnqexsbFclz8x4b54sXt/f3A/MdF62laxTkxP++ItW7x/bMwXb9niE9PT6QQboRZHX4s44sSZ5bqk/be/fvduZ2zs6dv1u3fPaz4LirOTHSwBeX+f4uqGOIGt3ua3NbUjAzMz4DPAQ+7+iRbTvAD4vru7mb2a4BzGD9KKqRskMX6lKAOkogadxYmzKOuShFqT0Kb9+7lw6dLsm4igNAOkJHlpNhO9FngbcJ+Z7Qhf+yNgOYC7fxq4CPhdMzsE/AS4OMxg0kYS41eKMkAqatBZnDiLsi5JGD7ppHySQL0SDJCS5KWWDNz9a4BFTPO3wN+mFYOIiMSjEcgiIqJkUEbd1A18w549vD+8F5H86EJ1JdNN3cDr+9VvDe9zby8X6VE6MiiZZnUyymrT/v1tn4tIdpQMSqYkdTJiuXDp0rbPRSQ7aiYqmW7qBl5rEtq4axfvWrVKTUQiOVIyKKFu6gY+fNJJrNq1iyElApFcqZlIRESUDERERMmgI5OTwVVDy9C/P6pOQFGUJc6sdFNtBikXJYOYav37R0ZWsmZNsQd81a7xPwKs2bmzsD8sZYkzK7Xt8cHvflfbQzKnZBBTrX9/tWqF798/Pj3NbLVKFZitVhmfns47pKbKEmdWattjDm0PyZ6SQUy1/v19fdXC9+8fGhhgUV8ffcCivj6GBgbyDqmpssSZldr26EfbQ7KnZBBTrX//2rVThb8ERO0a/2uh0GUgyxJnVmrbY93KldoekjmNM+jA4CBUKo8yOHha3qFEiqoTUBRliTMr3VSbQcpFRwYiIqJkICIiSgYisSRRd0FjCKTIdM5AJEISdRdqYwhmq1UW9fXpBLEUjo4MRCIkUXdBYwik6JQMRCIkUXdBYwik6NRMJBIhiboLtTEE49PTDA0MqIlICkfJQCSGJOouaAyBFJmaiURERMlARESUDEREBCUDERFByUBERFAyEBERlAxERAQlAxERQclARERIMRmY2QvNbMzMHjSzB8zsyibTmJn9tZk9bGb3mtkr04pHRERaS/NyFIeAP3D3e8zs2cA2M/uquz9YN825wOnh7eeBT4X3IiKSodSODNx9r7vfEz7+EfAQcHLDZG8G/sED3wAGzOzEtGLqJZMHDzIa3ouIRMnknIGZrQBeAdz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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "iterated 11 times\n"
     ]
    }
   ],
   "source": [
    "k = 3\n",
    "# iris = KMeans(data=iris_df, k=k, feature='petal') # cluster by petal\n",
    "iris = KMeans(data=iris_df, k=k, feature='sepal')  # clusetr by sepal\n",
    "iris.result()\n",
    "print('iterated', iris.count, 'times')"
   ]
  },
  {
   "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": "iVBORw0KGgoAAAANSUhEUgAAAP4AAAECCAYAAADesWqHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAC9pJREFUeJzt3V+IXPUZxvHn6Zr4L5HEakUSMV0pARFq/hAqAWmTKLFKelNDAgqVluSiFUMLGntTvPNK7EURQtQKxoiJBoq01gQVEVptNsYaTSwaIm6irpJIjIUE49uLOSkxpO7Z7f5+OzPv9wNLZndn5/ntbp45Z2bPnNcRIQC5fGuyFwCgPooPJETxgYQoPpAQxQcSovhAQl1RfNvLbb9j+13b6wtnPWJ7xPaekjmn5V1h+0Xbe22/Zfuuwnnn2X7N9htN3n0l85rMAduv2362dFaTd8D2m7Z3295ZOGuG7a229zW/w+sKZs1tvqdTb0dtrysSFhGT+iZpQNJ7kgYlTZX0hqSrC+ZdL2m+pD2Vvr/LJc1vLk+X9K/C358lTWsuT5H0qqQfFP4efy3pCUnPVvqZHpB0SaWsxyT9ork8VdKMSrkDkj6SdGWJ2++GLf4iSe9GxP6IOCHpSUk/KRUWES9LOlzq9s+S92FE7Goufy5pr6RZBfMiIo41705p3oodpWV7tqSbJW0slTFZbF+kzobiYUmKiBMR8Vml+KWS3ouI90vceDcUf5akD057f1gFizGZbM+RNE+drXDJnAHbuyWNSNoeESXzHpR0t6SvCmacKSQ9b3vI9pqCOYOSPpH0aPNQZqPtCwvmnW6VpM2lbrwbiu+zfKzvjiO2PU3S05LWRcTRklkRcTIirpU0W9Ii29eUyLF9i6SRiBgqcfvfYHFEzJd0k6Rf2r6+UM456jwsfCgi5kn6QlLR56AkyfZUSSskbSmV0Q3FH5Z0xWnvz5Z0aJLWUoTtKeqUflNEPFMrt9ktfUnS8kIRiyWtsH1AnYdoS2w/XijrvyLiUPPviKRt6jxcLGFY0vBpe0xb1bkjKO0mSbsi4uNSAd1Q/H9I+p7t7zb3dKsk/WmS1zRhbFudx4h7I+KBCnmX2p7RXD5f0jJJ+0pkRcS9ETE7Iuao83t7ISJuK5F1iu0LbU8/dVnSjZKK/IUmIj6S9IHtuc2Hlkp6u0TWGVar4G6+1NmVmVQR8aXtX0n6qzrPZD4SEW+VyrO9WdIPJV1ie1jS7yLi4VJ56mwVb5f0ZvO4W5J+GxF/LpR3uaTHbA+oc8f+VERU+TNbJZdJ2ta5P9U5kp6IiOcK5t0paVOzUdov6Y6CWbJ9gaQbJK0tmtP86QBAIt2wqw+gMooPJETxgYQoPpAQxQcS6qriFz78ctKyyCOv2/K6qviSav5wq/4iySOvm/K6rfgAKihyAI/tvj4qaObMmWP+muPHj+vcc88dV96sWWN/seLhw4d18cUXjyvv6NGxv4bo2LFjmjZt2rjyDh48OOaviQg1R++N2cmTJ8f1db0iIkb9wUz6Ibu9aNmyZVXz7r///qp5O3bsqJq3fn3xF7x9zZEjR6rmdSN29YGEKD6QEMUHEqL4QEIUH0iI4gMJUXwgIYoPJNSq+DVHXAEob9TiNydt/IM6p/y9WtJq21eXXhiActps8auOuAJQXpvipxlxBWTR5kU6rUZcNScOqP2aZQDj0Kb4rUZcRcQGSRuk/n9ZLtDr2uzq9/WIKyCjUbf4tUdcASiv1Yk4mjlvpWa9AaiMI/eAhCg+kBDFBxKi+EBCFB9IiOIDCVF8ICGKDyTEJJ1xqD3ZZnBwsGreeEaE/T8OHz5cNW/lypVV87Zs2VI1rw22+EBCFB9IiOIDCVF8ICGKDyRE8YGEKD6QEMUHEqL4QEIUH0iozQitR2yP2N5TY0EAymuzxf+jpOWF1wGgolGLHxEvS6r7KgoARfEYH0howl6Wy+w8oHdMWPGZnQf0Dnb1gYTa/Dlvs6S/SZpre9j2z8svC0BJbYZmrq6xEAD1sKsPJETxgYQoPpAQxQcSovhAQhQfSIjiAwlRfCChvpidt2DBgqp5tWfZXXXVVVXz9u/fXzVv+/btVfNq/39hdh6ArkDxgYQoPpAQxQcSovhAQhQfSIjiAwlRfCAhig8kRPGBhNqcbPMK2y/a3mv7Ldt31VgYgHLaHKv/paTfRMQu29MlDdneHhFvF14bgELazM77MCJ2NZc/l7RX0qzSCwNQzpge49ueI2mepFdLLAZAHa1flmt7mqSnJa2LiKNn+Tyz84Ae0ar4tqeoU/pNEfHM2a7D7Dygd7R5Vt+SHpa0NyIeKL8kAKW1eYy/WNLtkpbY3t28/bjwugAU1GZ23iuSXGEtACrhyD0gIYoPJETxgYQoPpAQxQcSovhAQhQfSIjiAwn1xey8mTNnVs0bGhqqmld7ll1ttX+eYIsPpETxgYQoPpAQxQcSovhAQhQfSIjiAwlRfCAhig8kRPGBhNqcZfc826/ZfqOZnXdfjYUBKKfNsfrHJS2JiGPN+fVfsf2XiPh74bUBKKTNWXZD0rHm3SnNGwMzgB7W6jG+7QHbuyWNSNoeEczOA3pYq+JHxMmIuFbSbEmLbF9z5nVsr7G90/bOiV4kgIk1pmf1I+IzSS9JWn6Wz22IiIURsXCC1gagkDbP6l9qe0Zz+XxJyyTtK70wAOW0eVb/ckmP2R5Q547iqYh4tuyyAJTU5ln9f0qaV2EtACrhyD0gIYoPJETxgYQoPpAQxQcSovhAQhQfSIjiAwkxO28cduzYUTWv39X+/R05cqRqXjdiiw8kRPGBhCg+kBDFBxKi+EBCFB9IiOIDCVF8ICGKDyRE8YGEWhe/Garxum1OtAn0uLFs8e+StLfUQgDU03aE1mxJN0vaWHY5AGpou8V/UNLdkr4quBYAlbSZpHOLpJGIGBrleszOA3pEmy3+YkkrbB+Q9KSkJbYfP/NKzM4DeseoxY+IeyNidkTMkbRK0gsRcVvxlQEohr/jAwmN6dRbEfGSOmOyAfQwtvhAQhQfSIjiAwlRfCAhig8kRPGBhCg+kBDFBxLqi9l5tWehLViwoGpebbVn2dX+eW7ZsqVqXjdiiw8kRPGBhCg+kBDFBxKi+EBCFB9IiOIDCVF8ICGKDyRE8YGEWh2y25xa+3NJJyV9ySm0gd42lmP1fxQRnxZbCYBq2NUHEmpb/JD0vO0h22tKLghAeW139RdHxCHb35G03fa+iHj59Cs0dwjcKQA9oNUWPyIONf+OSNomadFZrsPsPKBHtJmWe6Ht6acuS7pR0p7SCwNQTptd/cskbbN96vpPRMRzRVcFoKhRix8R+yV9v8JaAFTCn/OAhCg+kBDFBxKi+EBCFB9IiOIDCVF8ICGKDyTkiJj4G7Un/ka/weDgYM047dy5s2re2rVrq+bdeuutVfNq//4WLuzvl5NEhEe7Dlt8ICGKDyRE8YGEKD6QEMUHEqL4QEIUH0iI4gMJUXwgIYoPJNSq+LZn2N5qe5/tvbavK70wAOW0Hajxe0nPRcRPbU+VdEHBNQEobNTi275I0vWSfiZJEXFC0omyywJQUptd/UFJn0h61Pbrtjc2gzW+xvYa2ztt133pGoAxa1P8cyTNl/RQRMyT9IWk9WdeiRFaQO9oU/xhScMR8Wrz/lZ17ggA9KhRix8RH0n6wPbc5kNLJb1ddFUAimr7rP6dkjY1z+jvl3RHuSUBKK1V8SNityQeuwN9giP3gIQoPpAQxQcSovhAQhQfSIjiAwlRfCAhig8k1Bez82pbs2ZN1bx77rmnat7Q0FDVvJUrV1bN63fMzgNwVhQfSIjiAwlRfCAhig8kRPGBhCg+kBDFBxKi+EBCoxbf9lzbu097O2p7XY3FAShj1HPuRcQ7kq6VJNsDkg5K2lZ4XQAKGuuu/lJJ70XE+yUWA6COsRZ/laTNJRYCoJ7WxW/Oqb9C0pb/8Xlm5wE9ou1ADUm6SdKuiPj4bJ+MiA2SNkj9/7JcoNeNZVd/tdjNB/pCq+LbvkDSDZKeKbscADW0HaH1b0nfLrwWAJVw5B6QEMUHEqL4QEIUH0iI4gMJUXwgIYoPJETxgYQoPpBQqdl5n0gaz2v2L5H06QQvpxuyyCOvVt6VEXHpaFcqUvzxsr0zIhb2WxZ55HVbHrv6QEIUH0io24q/oU+zyCOvq/K66jE+gDq6bYsPoAKKDyRE8YGEKD6QEMUHEvoPF72a45tCHDcAAAAASUVORK5CYII=\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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\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-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}