machinelearning_notebook/3_kmeans/1-k-means.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# k-Means"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 方法\n",
    "\n",
    "由于具有出色的速度和良好的可扩展性，K-Means聚类算法算得上是最著名的聚类方法。***K-Means算法是一个重复移动类中心点的过程，把类的中心点，也称重心（centroids），移动到其包含成员的平均位置，然后重新划分其内部成员。***\n",
    "\n",
    "K是算法计算出的超参数，表示类的数量；K-Means可以自动分配样本到不同的类，但是不能决定究竟要分几个类。\n",
    "\n",
    "K必须是一个比训练集样本数小的正整数。有时，类的数量是由问题内容指定的。例如，一个鞋厂有三种新款式，它想知道每种新款式都有哪些潜在客户，于是它调研客户，然后从数据里找出三类。也有一些问题没有指定聚类的数量，最优的聚类数量是不确定的。\n",
    "\n",
    "K-Means的参数是类的重心位置和其内部观测值的位置。与广义线性模型和决策树类似，K-Means参数的最优解也是以成本函数最小化为目标。K-Means成本函数公式如下：\n",
    "$$\n",
    "J = \\sum_{k=1}^{K} \\sum_{i \\in C_k} | x_i - u_k|^2\n",
    "$$\n",
    "\n",
    "$u_k$是第$k$个类的重心位置，定义为：\n",
    "$$\n",
    "u_k = \\frac{1}{|C_k|} \\sum_{x \\in C_k} x\n",
    "$$\n",
    "\n",
    "\n",
    "成本函数是各个类畸变程度（distortions）之和。每个类的畸变程度等于该类重心与其内部成员位置距离的平方和。若类内部的成员彼此间越紧凑则类的畸变程度越小，反之，若类内部的成员彼此间越分散则类的畸变程度越大。\n",
    "\n",
    "求解成本函数最小化的参数就是一个重复配置每个类包含的观测值，并不断移动类重心的过程。\n",
    "1. 首先，类的重心是随机确定的位置。实际上，重心位置等于随机选择的观测值的位置。\n",
    "2. 每次迭代的时候，K-Means会把观测值分配到离它们最近的类，然后把重心移动到该类全部成员位置的平均值那里。\n",
    "3. 若达到最大迭代步数或两次迭代差小于设定的阈值则算法结束，否则重复步骤2。\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Uvmi+hNYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": [
    "假设K-Means初始化时，将第一个类的重心设置在第5个样本，第二个类的重心设置在第11个样本.那么我们可以把每个实例与两个重心的距离都计算出来，将其分配到最近的类里面。计算结果如下表所示：\n",
    "![data_0](images/data_0.png)\n",
    "\n",
    "新的重心位置和初始聚类结果如下图所示。第一类用X表示，第二类用点表示。重心位置用稍大的点突出显示。\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": [
    "现在我们重新计算两个类的重心，把重心移动到新位置，并重新计算各个样本与新重心的距离，并根据距离远近为样本重新归类。结果如下表所示：\n",
    "\n",
    "![data_1](images/data_1.png)\n",
    "\n",
    "画图结果如下："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": [
    "我们再重复一次上面的做法，把重心移动到新位置，并重新计算各个样本与新重心的距离，并根据距离远近为样本重新归类。结果如下表所示：\n",
    "![data_2](images/data_2.png)\n",
    "\n",
    "画图结果如下：\n"
   ]
  },
  {
   "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": {},
     "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": [
    "再重复上面的方法就会发现类的重心不变了，K-Means会在条件满足的时候停止重复聚类过程。通常，条件是前后两次迭代的成本函数值的差达到了限定值，或者是前后两次迭代的重心位置变化达到了限定值。如果这些停止条件足够小，K-Means就能找到最优解。不过这个最优解不一定是全局最优解。\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",
    "# 导入所需库\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import random\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "\n",
    "# 1 读取鸢尾花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 对类别进行编码，3个类别分别赋值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": 3,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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naPPMoGjR0qFoKpI01rgyVLpoaYrONkZL4YxXISzFOorEOdF9SbEfVZHiey3jmJu1kKqewa3A0RHx2/zzM4HlEfHcZJEWVOlkYGZWUanqGXwIuELSbwEBzwDekSA+64Z25dVdnr2aqlA3owoxWE8U7txG0o7A3+QffxkRj7aav1t8ZdBGuwbg3EBcNRVpQHAQYrCumVDnNpJekb8eBxwNPDsfjm5oxM6qpF15dZdnr6Yq1M2oQgzWM+0qnb08f33tGMMxXYzLtle78uouz15NVaibUYUYrGdaPjOIiE/lr4vKCccmbLS8+saNT4xrLK/ebrr1xrx5sHLltuPLrJtRhRisZ4qWJvoNcA1wJXBlRNzS7cDG42cGbfiZQT1V4X59FWKwrklVtHRHYC7wUmAesD9wU0S8LlWgRTkZFNCuvLrLs1dTFepmVCEG64pUyWAy8GKyZwiHAU8hSwalFy91MjAz61yqegYbgHXAl4D/GxH3pQiuUspos76sMtyuR9CZuhyvFP1UpJCiHktZfURYca3aqhgdgGOBzwM/Ay4HTgPmF1k29dCVtonKaH+mrPZ63MZNZ+pyvFK0OZVCu+2U1Q5TXb63CqFN20Qd/RCTVTr7EHAHsKmTZVMNXUkGl1ySnUyNf2jTpmXjU63jlFO2njY6nHJK9fZlkNTleLU7f8raj3bbKRJHGX9vto12yaBdPQMAJF0s6Tay1kunAm8Bpqe9RumhMtqsL6sMt+sRdKYuxytFPxUppKjHUlYfEdaRQskA+Cywf0QcERGLI+v05s/dDKxUZbRZX1Yb/24XvzN1OV4p+qlIod12yuq7oS7fW520umwYawDO7XSZlIOfGZSwL4OkLsfLzww6i8O2QYr+DBpJuj4iDu5GYiqia0VLy2izvqwy3K5H0Jm6HK8U/VSkkKIeS1l9RNjjktQzaFrhpRHxmglHtp1cz8DMrHMTarV0LL1MBJU3MgLLlsEZZ2SvIyPp17FpEyxcCM96Vva6aVOa2K36Upxf7aQ4v3yO1lLLKwNJlwDjzhARC7oRVCuVvTJI0eZPu3Vs2gS77gpbtjyxzOTJsGED7LRTd/bLqqGMNqVSnF8+RytrolcGXwC+2GKwUSn6CWi3jkWLtv4jg+zzIjcq2/fK6Icixfnlc7S22jVh/bOyAqm9VuWejynY9UO7dVx77djLXXddp9Fa3aQ4v9pJcX75HK2topXOniNpiaRfSPrt6NDt4GqljLLTc+aMvdyLX1x8G1ZPZZSrT3F++RytraKtll4FfAr4F7JezhYBT4qIU7sb3rb8zMD3YweSnxnYBKVqwnpNRMyStC4iXtA4LmGshVQ2GUA5Zac3bcruv153Xfbf1vnn+49sUJRRrj7F+eVztJJSJYOryfoxWAKsBO4CPhcR+6cKtKhKJwMzs4pKVc/gA8DOwPuBWcCbgbe22fCTJV0r6UZJt0g6bYx5dpR0kaTbJK2WNLNgPGZmllChzm0i4joASU8C3h8RDxVY7FHgFRGxUdIOwFWSVkTENQ3zvA1YHxH7SVoInAmc0NkuFFBWZxsppOjApAr7kiKGIp0BlbGdItsoq+OiVkZvz1x7bfYgd6zbMyk6YCrj/Oqn87wKcRbRquGi0QGYTdbT2e35cCMwq8iy+fI7A9cDc5vGXwa8JH8/GfgT+a2r8YaOG6orq+GsFFI0RlaFfUkRQ5GG/crYTpFtlNUIYSuPPBIxefLWMUyenI0flaIxxTLOr346z6sQZ44UndsANwEvbfh8GFkfyO2WmwTcAGwEzhxj+s3A3g2ffwPs0WqdHSeDsjrbSCFFByZV2JcUMRTpDKiM7RTZRlkdF7Vywgljx3DCCU/Mk6IDpjLOr346z6sQZ65dMij6zGAkIq5suJq4CtjSYv7R+UYi4kBgb2COpAMKbm8rkk6SNCRpaHh4uLOFy+psI4UUHZhUYV9SxFCkM6AytlNkG2V1XNRKkcpeKTpgKuP86qfzvApxFlQ0GfxM0r9JOlzSyyX9K3CFpIMltW3OOiIeAH4KNDdydxewD4CkycBuwH1jLH9uRMyOiNkzZswoGHKurM42UkjRgUkV9iVFDEU6AypjO0W2UVbHRa0UqeyVogOmMs6vfjrPqxBnUa0uG0YHsh/y8YaV4ywzA9g9f78TcCVwTNM87wG+lr9fCHy/XSx+ZlCDffEzAz8zmIh+Os+rEGeO1J3bFCXphcAFZM8NnpT/0J8u6fQ8qKWSngx8CzgIuB9YGBEtm7nYrnoGZXW2kUKKDkyqsC8pYijSGVAZ2ymyjbI6LmqlSGWvFB0wlXF+9dN5XoU4SVfp7KnAPwFPj4gjJT2PrBTQ19OFWowrnZmZda5dMihUzwD4BnA+8I/5518BFwGlJ4OuqUtZ4EFSlTLcKeIoax0p9qVfDNK+ptDqHtLoAFyXv65tGHdDkWVTDx0/MyiiQvf1LFeV+7Ep4ihrHSn2pV8M0r4WRKJ6BlcATwGuzz8fAvysyLKph64kgwqVBbZcVcpwp4ijrHWk2Jd+MUj7WlC7ZFC0aOmHgaXAsyWtAr4JvC/Z5Umv1ags8MCoShnuFHGUtY52Buk8H6R9TaRoMng2cCRwKFkTEr+m+POG6qtTWeBBUZUy3CniKGsd7QzSeT5I+5pKq8uG0YG86QmyZih+ChwNrC6ybOrBzwwGhJ8Z+JnBRAzSvhZEinoGktZGxEGSPgusi4jvjI7rXpoaW9eKllakLLA1qEoZ7hRxlLWOFPvSLwZpXwtIVc9gGVnTEa8CDgY2AddGxItSBVqU6xmYmXUuVT2DN5C1K/SFiHhA0tOAj6UI0GxcKfoRKKuseRn9UFRlX/up/H5V6qlUQat7SFUcuvLMwKonRZtAZd03LqNNqarsaz/di6/KM6eSkKKeQZUGJ4MBkaIfgbLKmpfRD0VV9rWfyu9XpZ5KSdolg6JFS83KlaIfgbLKmpfRD0VV9rWfyu9XpZ5KRTgZWDWl6EegrLLmZfRDUZV97afy+1Wpp1IVrS4bqjj4NtGA8DMDPzPoNj8z2GroWn8G3eKipQMkRT8CZZU1L6Mfiqrsaz+V369KPZUSJKlnUCVOBmZmnUtVz8AGTRXKRqeIYeNGOOooWLcOXvACWL4cpk0rP44U26nCd2J9y8nAtjUyAkccAatXZyUfpk6FuXPhssvK+/FJEcPGjbDLLk98vvLK7PNDDxVPCGUdi3bbqcJ3Yn3NpYlsWytWZD86Gzdmjyo3bsw+r1hRrxiOOqqz8d2KI8V2qvCdWF9zMrBtVaFsdIoY1q0be/zNN5cbR4rtVOE7sb7mZGDbqkLZ6BQxvOAFY48/4IBy40ixnSp8J9bXnAxsW0cemd2PnjYNpOx17txsfJ1iWL68s/HdiiPFdqrwnVhfc9FSG1sVykaniGG0NNHNN2dXBBMpTdTr8vtV+E6stlzPwMzMXM/AKixFufmqlM13HQAbT03ODScD640U5earUjbfdQBsPDU6N/wA2XojRbn5qpTNdx0AG0+Nzg0nA+uNFOXmq1I233UAbDw1OjecDKw3UpSbr0rZfNcBsPHU6NxwMrDeSFFuvipl810HwMZTo3PDRUutd1KUm69K2XzXAbDxVOTccD0DMzNrmwx8m8jMzLpXz0DSPsA3gacCAZwbEWc1zXM48J/A7/JRP4yI07sVU18oo6JWWVJUGKvKvqQw2q3lqlUwb9623VqWoZ+Op3WmVQfJExmApwEH5+93AX4FPK9pnsOBZZ2sd9asWan6h66fFJ1rV6WD7nZxpOhEvk7adXhfhn46nrYNYCha/LZ27TZRRNwdEdfn7x8CbgX26tb2BkIZFbXKkqLCWFX2JYXFi2H9+q3HrV+fjS9LPx1P61gpzwwkzQQOAlaPMfklkm6UtELS88dZ/iRJQ5KGhoeHuxlqtZVRUassKSqMVWVfUli1auzxV19dXgz9dDytY11PBpKmARcDH4yIDU2TrweeEREvAr4K/GisdUTEuRExOyJmz5gxo6vxVloZFbXKkqLCWFX2JYV588Yef+ih5cXQT8fTOtfqHtJEB2AH4DLgwwXnvx3Yo9U8fmbgZwaV25cU/MzAuow2zwy6Vs9AkoALgPsj4oPjzLMn8MeICElzgCVkVwrjBjXw9QzKqKhVlhQVxqqyLymMlia6+ursiqCXpYn64XjaVnpW6UzSYcCVwDrgsXz0J4F9ASLia5LeC7wL2AJsIruCaHmTdOCTgZnZduhZ5zYRcRWgNvOcDZzdrRj6Uj+VA69CuXozA9y5Tb3UqKOMtjZvhj33fKI45cqVcPbZcM89TghmPeDmKOqkn8qBV6FcvZk9zsmgTvqpHHgVytWb2eOcDOqkn8qBV6FcvZk9zsmgTmrUUUZbJ58M06dvPW769Gy8mZXOD5DrZNKk7GFxP5QDnzIle1jc63L1Zga4cxszs4HQs3oGfadO5fvrEmtd4iyLj4f1kJNBEXUq31+XWOsSZ1l8PKzH/AC5iDqV769LrHWJsyw+HtZjTgZF1Kl8f11irUucZfHxsB5zMiiiTuX76xJrXeIsi4+H9ZiTQRF1Kt9fl1jrEmdZfDysx1y0tKg6tfNel1jrEmdZfDysi3rWn0G3uJ6BmVnn2iUD3yYya2fzZjj1VJg/P3vdvLnzdYyMwLJlcMYZ2evISPo4zSbA9QzMWknR74LrEFgN+MrArJUU/S64DoHVgJOBWSsp+l1wHQKrAScDs1ZS9LvgOgRWA04GZq2k6HfBdQisBvwA2ayVFP0u9FM/FNa3XM/AzGwAuJ6BmZm15WRgZmZOBmZm5mRgZmY4GZiZGU4GZmaGk4GZmeFkYGZmOBmYmRldTAaS9pH0U0m/kHSLpA+MMY8kfUXSbZJuknRwt+IZKO5Ixcw61M22ibYAH4mI6yXtAqyRdHlE/KJhniOB5+TDXOCc/NW2lztSMbPt0LUrg4i4OyKuz98/BNwK7NU027HANyNzDbC7pKd1K6aB4I5UzGw7lPLMQNJM4CBgddOkvYA7Gz7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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# 2 可视化信息\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')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 3 Kmeans算法封装\n",
    "class KMeans():\n",
    "    \"\"\"\n",
    "        @brief: 用于分析鸢尾花的 K-means 聚类算法\n",
    "        @param: data 数据集\n",
    "        @param: k 簇数\n",
    "        @param: feature 要分类的特征(默认'sepal'，可选'petal')\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, data, k=3, feature='sepal'):\n",
    "        self.color = 'rbckmyw'  # 绘图颜色\n",
    "        self.k = k  # 分成几簇\n",
    "        self.data = data  # 保存数据\n",
    "        self.feature = feature  # 要分类的特征\n",
    "        self.feature_points = np.array([iris_df[feature+'-length'], iris_df[feature+'-width']]).T # 特征\n",
    "        self.clusters = {key: [] for key in range(self.k)}  # k类分类点(空集，待填充)\n",
    "        self.centroids = random.sample(list(self.feature_points), k)  # 随机重心\n",
    "        self.count = 0  # 用于记录迭代了几次\n",
    "\n",
    "    # 欧式距离\n",
    "    def __distance(self, point1, point2):\n",
    "        return np.sqrt(np.square(np.array(point1) - np.array(point2)).sum())\n",
    "\n",
    "    # 计算重心\n",
    "    def __calc_centroids(self, points):\n",
    "        np_points = np.array(points)\n",
    "        return np_points.mean(axis=0)\n",
    "\n",
    "    # 可视化绘图\n",
    "    def __drawPoints(self, index, cluster, props='ro'):\n",
    "        # 绘制重心\n",
    "        plt.plot(self.centroids[index][0], self.centroids[index][1], '^', c=self.color[index], ms=14)\n",
    "        np_cluster = np.array(cluster)  # 转成numpy数组，方便绘图\n",
    "        plt.plot(np_cluster[:, 0], np_cluster[:, 1], props)  # 绘图\n",
    "        plt.xlabel(self.feature+'-length')\n",
    "        plt.ylabel(self.feature+'-width')\n",
    "        plt.grid(True)\n",
    "\n",
    "    # 计算是否满足停止条件\n",
    "    def __stopable(self, index_list, index_list_his):\n",
    "        self.count = self.count+1  # 做一次检查，说明迭代了一次\n",
    "        # 初次无历史索引，忽略\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",
    "    # 生成簇\n",
    "    def __cluster(self):\n",
    "        min_index_list = []\n",
    "        while True:\n",
    "            # 清空点集，重新归类\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",
    "                # 计算所有点和重心距离，存入distance_array\n",
    "                dis = np.array([])\n",
    "                for i in range(self.k):\n",
    "                    dis = np.append(dis, self.__distance(self.centroids[i], point))\n",
    "\n",
    "                # 找出最小值的索引\n",
    "                min_index = np.argmin(dis)\n",
    "                min_index_list.append(min_index)\n",
    "                # 按最小索引分类\n",
    "                self.clusters[min_index].append(point)\n",
    "\n",
    "            # 清空当前重心\n",
    "            self.centroids.clear()\n",
    "            # 重新计算新的重心\n",
    "            for i in range(self.k):\n",
    "                self.centroids.append(self.__calc_centroids(self.clusters[i]))\n",
    "                # 绘图，可视化\n",
    "                self.__drawPoints(i, self.clusters[i], props=self.color[i]+'.')\n",
    "            plt.show()\n",
    "\n",
    "            # 若无点的索引变化，则退出聚类循环\n",
    "            if self.__stopable(min_index_list, min_index_list_his):\n",
    "                return\n",
    "\n",
    "    # 返回最终结果\n",
    "    def result(self):\n",
    "        self.__cluster()\n"
   ]
  },
  {
   "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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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "迭代了 7 次\n"
     ]
    }
   ],
   "source": [
    "k = 3\n",
    "# iris = KMeans(data=iris_df, k=k, feature='petal') # 根据花瓣分类\n",
    "iris = KMeans(data=iris_df, k=k, feature='sepal')  # 根据萼片分类\n",
    "iris.result()\n",
    "print('迭代了', iris.count, '次')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 利用sklearn进行分类\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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": {
      "needs_background": "light"
     },
     "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": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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)"
   ]
  },
  {
   "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": "markdown",
   "metadata": {},
   "source": [
    "## 评估聚类性能\n",
    "\n",
    "方法1： 如果被用来评估的数据本身带有正确的类别信息，则利用Adjusted Rand Index(ARI)，ARI与分类问题中计算准确性的方法类似，兼顾了类簇无法和分类标记一一对应的问题。\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": [
    "\n",
    "\n",
    "方法2： 如果被用来评估的数据没有所属类别，则使用轮廓系数(Silhouette Coefficient)来度量聚类结果的质量，评估聚类的效果。**轮廓系数同时兼顾了聚类的凝聚度和分离度，取值范围是[-1,1]，轮廓系数越大，表示聚类效果越好。** \n",
    "\n",
    "轮廓系数的具体计算步骤： \n",
    "1. 对于已聚类数据中第i个样本$x_i$，计算$x_i$与其同一类簇内的所有其他样本距离的平均值，记作$a_i$，用于量化簇内的凝聚度 \n",
    "2. 选取$x_i$外的一个簇$b$，计算$x_i$与簇$b$中所有样本的平均距离，遍历所有其他簇，找到最近的这个平均距离，记作$b_i$，用于量化簇之间分离度 \n",
    "3. 对于样本$x_i$，轮廓系数为$sc_i = \\frac{b_i−a_i}{max(b_i,a_i)}$ \n",
    "4. 最后，对所有样本集合$\\mathbf{X}$求出平均值，即为当前聚类结果的整体轮廓系数。"
   ]
  },
  {
   "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])   #初始化原始数据\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建模\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')   #计算轮廓系数\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,'*-')   #绘制类簇数量与对应轮廓系数关系\n",
    "plt.xlabel('Number of Clusters')\n",
    "plt.ylabel('Silhouette Coefficient Score')\n",
    "\n",
    "plt.show()   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 如何确定K\n",
    "\n",
    "利用“肘部观察法”可以粗略地估计相对合理的聚类个数。K-means模型最终期望*所有数据点到其所属的类簇距离的平方和趋于稳定，所以可以通过观察这个值随着K的走势来找出最佳的类簇数量。理想条件下，这个折线在不断下降并且趋于平缓的过程中会有斜率的拐点，这表示从这个拐点对应的K值开始，类簇中心的增加不会过于破坏数据聚类的结构*。\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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'),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": [
    "从上图可见，类簇数量从1降到2再降到3的过程，更改K值让整体聚类结构有很大改变，这意味着新的聚类数量让算法有更大的收敛空间，这样的K值不能反映真实的类簇数量。而当K=3以后再增大K，平均距离的下降速度显著变缓慢，这意味着进一步增加K值不再会有利于算法的收敛，同时也暗示着K=3是相对最佳的类簇数量。"
   ]
  }
 ],
 "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
}