{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# k-Means" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "根据训练样本中是否包含标签信息,机器学习可以分为 **监督学习** 和 **无监督学习**。`聚类算法`是典型的无监督学习,其训练的样本中值包含`样本的特征`,**不包含样本的标签信息**。在聚类算法中,利用样本的特征,将具有相似特征空间分布的样本划分到同一类别中。\n", "\n", "\n", "![cluster illustration](images/kmeans-illustration.jpeg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. 方法\n", "\n", "由于具有出色的速度和良好的可扩展性,K-Means聚类算法最经典的聚类方法。***k-Means算法是一个重复移动类中心点(重心,centroids)的过程***:\n", "* 移动中心点到其包含成员的平均位置;\n", "* 然后重新划分其内部成员。\n", "\n", "`k`是算法中的超参数,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。`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代价函数最小化为目标。k-Means代价函数公式如下:\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", "$$\n", "u_k = \\frac{1}{|C_k|} \\sum_{i \\in C_k} x_i\n", "$$\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。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. 算法\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", "\n", "输入:$T=\\{ x_1, x_2, ..., x_N\\}$,其中$x_i \\in R_n$,i=1,2...N\n", "\n", "输出:聚类集合$C_k$, 聚类中心$u_k$, 其中k=1,2,...K\n", "\n", "1. 初始化类的重心$u_k$,可以随机选择样本作为聚类中心\n", "2. 每次迭代的时候,把所有样本分配到离它们最近的类,即更新聚类集合$C_k$\n", "3. 然后把重心移动到该类全部成员位置的平均值那里,即更新$u_k$\n", "4. 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": "markdown", "metadata": {}, "source": [ "## 3. 计算过程演示" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "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": [ "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": 2, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "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": [ "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": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "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": [ "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": 4, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "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": [ "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": [ "## 4. Program" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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gPeAPskYpVgL3W2vT/naelpQVkWLl22+/Zfny5dSuXZshQ4YQEhIS6JCKpMt6\n9yZh0SI6Z2SwH5gXGUmnTp3Ys3gxXdPTOQDMdTpZvno1jRs3Put+9uzZQ/PGjanhchEMDMx+/n9h\nYVx0++289sYb+X4vPp+PQ4cOUbZsWUJCQvB6vVzepw9bli2jitvN5uBgnh83jjvuvPP4NS2aNKHy\n1q108vnYA3zldLJq3Trq169/2v6++uorRjz4IMmpqVSqWJGjcXGc73KxLzSUP6tXZ/X69URGRub7\nffnLNQMH4pk1i1bZxzuB35o1Y/XvvwcwKjkXFZslZb/zQz/9isk+FcaYtsAy4EJr7UpjzGvAEWvt\nyL+dZ0eO/Oup7t27071793z1LSIigXf06FHuuOUWYhYupFLFikx4/33atGnDvcOG8cPcuVQoX57x\n77xTICM9c+fO5bprriE1OZkwYwgPD6d+06bMi4khOjr69A2cBa/Xy4wZM4iPj6djx44nLS+bnJxM\nxXLlGJFdfwMwKzqah95+m3//+9957iMzM5OoyEge8niIIGsn78+ionhhyhSuuOKKAn0/hemJESP4\n/rXX6J+RQRCwMDiYyv37M/2rrwIdmpRwMTExxMTEHD9+5plnikdSMdcP/fQpPklFZeAXa2297OMu\nwGPW2v5/O08jFSIixZDH48Htdhf6fPy8staSmppKbGwsxhiaNWuGw+HHdRNP4PV6KRUZyc0ZGVQk\nqxZjYlgYU779ll69euW5nbS0NEpHR/Oo18ux8bAvo6N58v33GTx4cGGEni87duwgISGBpk2bnlRr\nlJKSwiVdurB/+3ZCgoKgdGkWL1tWIKtliZyJYjNSUYKSinzXVFhrE4DdxphG2U/1IGsqlIiIFHNj\nnnuOyIgISkdHc8lFF3H48OFAh4QxhqioKFq2bEmLFi0CllBAViH5yNGjmQTMBN4Hkt1uNv1xZl+D\nERERXNa3L7PCw9kF/BwUxIGQEHr06FEIUefP448+Sqtmzbi+b18a1K7N8uV/LfYYFRXF0hUr+GTO\nHCZ98w3rN21SQiGSG9VU/K2RrLqKiUAIEAvcbK098rdzNFIhIlKMzJo1izuuu47rXS4igbmhodS+\n9FI+nzkz0KEVKaNHj2bGM89Qy+cjGogCfqxalR3x8WfUTlpaGo8PH86ihQupUbMmr06YQIMGDQol\n5rO1aNEi/tWvHzelpuIka6nHn6tUIW7fvkCHJnKSYjNSMd8P/fT450iFMWYScDmQYK1tmeO1xlwA\n/AwMttYxUC8RAAAgAElEQVTmOo+xQPIXa+1vwAUF0ZaIiBQNSxYvppnLdXwVp46ZmXyxdGlAYyqK\nvB4PpfnrSzAB8J7h8rKQNVrx2oQJBRlagdu8eTO1reXYvt2NgS8SEnC73VrIQORsBG6fisnAG8CU\nnE4wxgQBLwJ5mqRVUPtUiIhIEZeRkcGZjBjXqFmThPBwjl2xB6hWpUqhxFacDb72WjZERLAS2ArM\ndjq57YTVoUqSZs2asQM4tjjwH0CtatWUUIgUM9baJcDp5rPeC8wADuSlTSUVIiIlXGxsLC2aNCHS\n6aRc6dLMzGX6UmZmJi+++CL9+vVjy5YthDZsyLSoKL6JjmZhVBRvf/CBHyMvHpo1a8a8hQvxXHIJ\nO9q25cFnn+XpkSNPf2Ex1LlzZ+5++GHeCQ9nUqlSLCpblhnffBPosESKL4cfHmfBGFMNGGStfRvI\n0zSyAqmpyFNHqqkQEQmIZg0bUjM2lo4+H/HADKeTX9eupWHDhied5/F46NC2LRvWraMhkAb8GRXF\na2+9hcPhoHXr1mzbtg2Hw8HFF1+c42pQqampxMXFUa1atRK9C3lGRgZbt26lVKlS1KpVK9Dh+FV8\nfDwHDhygYcOGxWofDTl3FJuaiiUF327Maoj5az9Qnpl86tWfjDG1gW9PVVNhjPkcGGut/dUYMxn4\nn7X2y9z6DdxMLhERKXRHjx4ldudO/uXzYYAaQD2Hg19//fUfScWCBQvY9vvv9AA6ZD/3bUoKK5cv\n55HHHqNz+/ZEulx4rCWkUiWWrlhB2bJl/9HG1YMGEU7WKkhvv/8+N9xww/HXV69ezZ0338ze+Hg6\nd+7Mu5Mn/6ONQEpKSmLHjh3Url2bChUq5Hjejh076NG1KxlHjpDidnPtddfxzqRJGFOk72EKTLVq\n1bSqk0hBKIQ78e7tsx7HPDP5rJppB3xmsv5RqwBcaoxxW2tn5XSBpj+JiJRgkZGRBAcHczD72A0k\nWEuVU9RGHD16FOPzceIr1YG9u3fzyP33U//gQa49epR/JycTvXs3z/5tik9aWhpXDxrEgORk7khO\n5j/p6dw9dChxcXEA7Nu3j17du1N93TquOnSIXXPmMOiyywrlfZ8pay2Dr76ayuXL07FdO2pWqcK0\nadNyPP+m666jQXw8Q5OTuTs9nbmff8706dP9GLH/ZGZmBjoEESkchhymNllr62U/6pJVV3FXbgkF\nKKkQESnRHA4H77z3Hp86nfwvMpIpUVF06d2bSy655B/ndu7cGU9wMIuAdOAoWfslXDZwIDtjY6nl\n9QJZ30A1MjOJ3bbtpOv37NlDqLXUzT6uBFQLDWXz5s1A1nKkNYFWQHmgb2Ymy1esICUlhbzYu3cv\nEyZMYMKECewr4CVMx48fzw9ffskw4D6gotfL0JtvJiEh4ZTn/7FxI82zV3gKA+qkprJ+3boCjSnQ\nVq5cSZ3q1YkID6dmlSosW7YsX+3Fx8dzw+DBdG7XjkcefJD09PQCilSkGAvQPhXGmE/IWiq2kTEm\nzhhzszHmDmPM0FOcnqf6BU1/EhEp4W648UbOb9WK2bNns23bNpo0aUJ8fDzVq1c/6byqVasyLyaG\nQZdeystHjxJkDPfecw9Dbr6ZdWvWsGDzZmqlp+MFNjid3NatG5BVQ3H/3Xczf948jqam8htwPnAE\n2JeZSb169YCsUZNka/GR9YtWKlnfVGFhYad9D1u3bqXTBRdQJyMDC4x++ml+WbmS+vXr5/vzSU5O\n5sVRozgCvANcDHQDZvl8xMbGUrly5X9c06hBAzatWUMHa3EDcZGR3Nq06UnneDweXh07lmVLltCg\nSROefPrpYlNjkpqaSr/evel2+DBDgE0JCVzepw/b4+LO6j0kJyfTuX17aiUkUM/jYd7vv7Nl0yZm\nzZlT4LGLyOlZa68/g3Nvyct5KtQWETkHrF27lou7dKFJZiY+Y9jhdLJ89Wrq1q17yvN9Ph/GmOM1\nAmlpafzriiv4ccGCrKlC11zDB1On4nA4uLJ/f3b8+CMXpqezH/gfUCM6miSPh5HPPsuDDz8MZE2j\n6dqxIykbN1IlPZ0/IiMZ+tBDjBo9+rTx/+uKK4j95huaWUsN4NegIKpcfTXTCmDK0X+uu461n3/O\nAJ+PVLIWba8DbAwKInbv3lNOFdu8eTOXXHQRoRkZHPV46N2vHx9Pn05Q0F8TAK67+mpWz5nDeS4X\ncWFheOrVY/maNXlKogJtzZo1DOzenVuPHj3+3EelSvHJ3Ll07NjxjNubPXs2D193HdclJwPgAcaF\nhrJ3//4iVVMjJUexKdRe64d+Wp26ULugaaRCROQc8NSjj9IpNZVjtXsxHg9jRo/m/cmnruA78eYY\nsjZm+/b77/nzzz9xOBxER0cD4PV6+d+cOQz3egkFKgO7IiK4eOhQ7r777pOSltDQUBYuXcp7773H\n7l27uPuii7jiiitOG3tqaio//vADwdZyEEgGOvt8HNy//8w/iFP4aeFC+vt8hABlgDZADPDMs8+e\nMqEAaNy4MVt27GD9+vWUKlWKpk2bnlSkfejQIWZ9+y0PZGYSCrTMyOCjPXtYunTpKaeeFTWVKlXi\ncEYGKWTtEO4CEjMzTzlqkxcOhwMvWSNTBvCRVcfy9//PRKT4UlIhInIOSDp0iBMnCpX1+Ug8eDDH\n83NSpkyZk46DgoIICQ4mNTupsEBaUBBt2rQ55ShIREQE999//xn1Ofbll6mWkcFVZE2bigEWBQXx\nbB4SkryoVLky+xISqEhW/PscDobddRdPPPFErtdFRkbm+Ku91+vFYczxJeINEGIMHo+nQGIubNWr\nV+eRRx/lzXHjqAvsBO6+554cR7ZOp1u3bgRXrMj3GRnUzMxkvdPJoH79is10MJFCc5b7SBRF+olA\nROQcMOiaa1jqdJJE1taoy51OBl1zTb7bNcYwctQopjud/AzMCg2FqlUZOHBgvts+ZsvGjdTzeI5/\nYTUAQiIiuOKqqwqk/QnvvcfCqCi+dTr5LCqKoAYNGDNmTI7n+3w+vv32W9566y1WrFhxynMqVapE\n+/bt+V94ODuAhcHBuKOj6dSpU75i3bdvH5d06UJkeDj1a9YkJiYmX+3lZuTo0Xw9bx63vfYaM77/\nnjEvvXTWbUVERLB0xQra33YbaT17ctPjjzP1008LMFoRCTTVVIiInAN8Ph9PPPYYk95/H4fDwUPD\nhzP8sccKbF+Fr7/+mvnz5lG1enXuve8+SpUqleO5brebca+8klXA3LgxT40c+Y8RkBO9MX48rz/x\nBP9yuQgGZgLxwcG4w8L4/Kuv6N27d77j37VrF/PnzycyMpIBAwbkuLGftZbBV17J8h9/pKrXyxZj\neGHcOO64886TzvN6vWzevJlXX36Z31avpl6DBrz6xhv/KI4/U+3OP5/IP/6gicfDTrKSw9/++IPa\ntWufdJ7b7WbMc8+xZMECatevz/MvvXTWU5dEiqNiU1Ox0Q/9NPVPTYWSChER8avrrr6aNdkFzLvD\nwkivU4cVv/2WYwGz1+tlyA03MGPGDKzHQxXgOsgqCi9ThgNJSX7bdC4mJoZ/9+/PLSkpBAOJwMTQ\nUI6kpBASEgJkLa3bu3t3Evb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Iz6dOJbp0aZ4cNeq0IwszZ87kfzNnUrFyZR58+GEqVap0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "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", "import numpy as np\n", "from sklearn.datasets import make_blobs\n", "import matplotlib.pyplot as plt\n", "import random\n", "\n", "# 生成数据\n", "centers = [(7, 0), (0, 0), (5, 5)]\n", "n_samples = 500\n", "\n", "X, y = make_blobs(n_samples=n_samples, n_features=2, \n", " cluster_std=1.0, centers=centers, \n", " shuffle=True, random_state=42)\n", "\n", "# 画出数据\n", "plt.figure(figsize=(15, 9))\n", "plt.scatter(X[:, 0], X[:, 1], c=y)\n", "plt.colorbar()\n", "plt.savefig(\"k-means_data.pdf\")\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# k-means\n", "\n", "def calc_distance(v1, v2):\n", " \"\"\"\n", " 计算两个向量的距离\n", " \n", " v1 - 特征1\n", " v2 - 特征2\n", " \"\"\"\n", " return np.sum(np.square(v1-v2))\n", "\n", "def rand_cluster_cents(X, k):\n", " \"\"\"\n", " 初始化聚类中心:通过在区间范围随机产生的值作为新的中心点\n", " \n", " X - 数据样本\n", " k - 聚类个数\n", " \"\"\"\n", "\n", " # 样本数\n", " n=np.shape(X)[0]\n", " \n", " # 生成随机下标列表\n", " dataIndex=list(range(n))\n", " random.shuffle(dataIndex)\n", " centroidsIndex = dataIndex[:k]\n", " \n", " # 返回随机的聚类中心\n", " return X[centroidsIndex, :]\n", "\n", "def kmeans(X, k):\n", " \"\"\"\n", " kMeans算法\n", " \n", " X - 数据样本\n", " k - 聚类个数\n", " \"\"\"\n", " # 样本总数\n", " n = np.shape(X)[0]\n", " \n", " # 分配样本到最近的簇:存[簇序号,距离的平方] (n行 x 2列)\n", " clusterAssment = np.zeros((n, 2))\n", "\n", " # step1: 通过随机产生的样本点初始化聚类中心\n", " centroids = rand_cluster_cents(X, k)\n", " print('最初的中心=', centroids)\n", "\n", " iterN = 0\n", " \n", " while True: \n", " clusterChanged = False\n", " \n", " # step2:分配到最近的聚类中心对应的簇中\n", " for i in range(n):\n", " minDist = np.inf;\n", " minIndex = -1\n", " for j in range(k):\n", " # 计算第i个样本到第j个中心点的距离\n", " distJI = calc_distance(centroids[j, :], X[i, :])\n", " if distJI < minDist:\n", " minDist = distJI\n", " minIndex = j\n", " \n", " # 样本上次分配结果跟本次不一样,标志位clusterChanged置True\n", " if clusterAssment[i, 0] != minIndex:\n", " clusterChanged = True\n", " clusterAssment[i, :] = minIndex, minDist ** 2 # 分配样本到最近的簇\n", " \n", " iterN += 1\n", " sse = sum(clusterAssment[:, 1])\n", " print('the SSE of %d' % iterN + 'th iteration is %f' % sse)\n", " \n", " # step3:更新聚类中心\n", " for cent in range(k): # 样本分配结束后,重新计算聚类中心\n", " ptsInClust = X[clusterAssment[:, 0] == cent, :]\n", " centroids[cent, :] = np.mean(ptsInClust, axis=0)\n", " \n", " # 如果聚类重心没有发生改变,则退出迭代\n", " if not clusterChanged:\n", " break\n", " \n", " return centroids, clusterAssment\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "最初的中心= [[-0.66262376 0.57059867]\n", " [ 4.95053629 5.67481949]\n", " [-0.3357847 1.66902153]]\n", "the SSE of 1th iteration is 263177.945774\n", "the SSE of 2th iteration is 40707.497266\n", "the SSE of 3th iteration is 40405.518386\n", "the SSE of 4th iteration is 40348.918515\n", "the SSE of 5th iteration is 40256.192636\n", "the SSE of 6th iteration is 40226.957376\n", "the SSE of 7th iteration is 40226.925909\n", "the SSE of 8th iteration is 40224.485426\n", "the SSE of 9th iteration is 40225.152890\n", "the SSE of 10th iteration is 40226.135748\n" ] } ], "source": [ "# 进行k-means聚类\n", "k = 3 # 用户定义聚类数\n", "mycentroids, clusterAssment = kmeans(X, k)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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CkSNH2PvSS2SG0HbeF1+weuHCDunDmz179rB69Wq2b99OSkoKSUlJJCcns2HD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\nniNLgC5KGcAXgW4AvSjlm55wB/w5KfsHYwoXgh9sbsdRUV0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/H6dxGjpf03+qP26lsfT6pWz+zGYGpg4Yh+8xgtVQvRr05IXez0j7RWJVjY1G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\nXfvoV8A5SqlZwJ+BG4AbMyuSu9M23pI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def datashow(dataSet, k, centroids, clusterAssment, fnFig=None): # 二维空间显示聚类结果\n", " from matplotlib import pyplot as plt\n", " num, dim = np.shape(dataSet) # 样本数num ,维数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', ' len(marksamples):\n", " print('sorry,your k is too large,please add length of the marksample!')\n", " return 1\n", " # 绘所有样本\n", " for i in range(num):\n", " markindex = int(clusterAssment[i, 0]) # 矩阵形式转为int值, 簇序号\n", " # 特征维对应坐标轴x,y;样本图形标记及大小\n", " plt.plot(dataSet[i, 0], dataSet[i, 1], marksamples[markindex], markersize=6)\n", "\n", " # 绘中心点\n", " markcentroids = ['o', '*', '^'] # 聚类中心图形标记\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') #图例\n", " plt.xlabel('feature 1')\n", " plt.ylabel('feature 2')\n", "\n", " plt.title('k-means cluster result') # 标题\n", " if fnFig != None: plt.savefig(fnFig)\n", " plt.show()\n", " \n", " \n", "# 画出实际图像\n", "def trgartshow(dataSet, k, labels, fnFig=None):\n", " from matplotlib import pyplot as plt\n", "\n", " num, dim = np.shape(dataSet)\n", " label = ['0', '1', '2']\n", " marksamples = ['ob', 'or', 'og', 'ok', '^r', '^b', '" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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" ] }, "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": 13, "metadata": {}, "outputs": [ { "data": { "image/png": "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" ] }, "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": [ "## 6. 深入思考\n", "\n", "1. 如何计算聚类的精度?\n", "2. 如何匹配聚类的类别和真实类别?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 7. 评估聚类性能\n", "\n", "### 7.1 方法1 - ARI\n", "\n", "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)对聚类结果进行评估,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": 14, "metadata": { "scrolled": true }, "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": [ "contingency表的定义:\n", "\n", "![ARI_ct](images/ARI_ct.png)\n", "其中$X$为真实类别,$Y$为聚类的簇\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 7.1.1 RI\n", "为了方便理解ARI,先讨论一下RI,也就是rand index,是ARI的基础方法。\n", "\n", "假如有两类,那么针对这两类的的RI评价指标为:\n", "\n", "$$\n", "R = \\frac{a + b}{a+b+c+d}\n", "$$\n", "\n", "a,b,c,d分别代表的含义为:\n", "* a : 应该在一类,最后聚类到一类的数量,\n", "* b : 不应该在一类,最后聚类结果也没把他们聚类在一起的数量。\n", "* c和d那么就是应该在一起而被分开的和不应该在一起而被迫在一起的。毕竟强扭的瓜不甜,c和d固然是错误的。\n", "\n", "所以从R的表达式中可以看出,a和b是对的,这样能够保证R在0到1之间,而且,聚类越准确,指标越接近于1.\n", "\n", "这里有一个关键性的问题,就是什么叫数量?怎么去计算?准确的说,是配对的数量。比如说a是应该在一起而真的幸福的在一起了的数量,这显然就应该像人类一样按照小夫妻数量计算,但是我们的样本可不管一夫一妻制,任意选两个就是一个配对,所以,就是 $n(n-1)/2$ 这样来计算,也就是组合数,n个当中选两个的选法。同时我们看到,分母其实是所有配对的总和,所以,我们最后可以写成这样:\n", "\n", "$$\n", "R = \\frac{a + b}{a+b+c+d} = \\frac{a + b}{\\binom{n}{2}}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 7.1.2 ARI\n", "\n", "有了先前RI的感性理解之后,接下来解释一下ARI。\n", "\n", "RI有一个缺点,就是惩罚力度不够,换句话说,大家普遍得分比较高,没什么区分度,遍地80分。这样的话,往往是考试的制度不合适,于是就诞生出了ARI,这个指标相对于RI就很有区分度了。\n", "\n", "$$\n", "ARI = \\frac{Index - ExpctedIndex}{MaxIndex - ExpectedIndex}\n", "$$\n", "\n", "具体的公式是:\n", "$$\n", "ARI = \\frac{ \\sum_{ij} \\binom{n_{ij}}{2} - \\left[ \\sum_i \\binom{a_i}{2} \\sum_j \\binom{b_j}{2} \\right] / \\binom{n}{2} }{ \\frac{1}{2} \\left[ \\sum_i \\binom{a_i}{2} + \\sum_j \\binom{b_j}{2} \\right] - \\left[ \\sum_i \\binom{a_i}{2} \\sum_j \\binom{b_j}{2} \\right] / \\binom{n}{2} }\n", "$$\n", "\n", "ARI取值范围为[-1,1],值越大越好,反映两种划分的重叠程度,使用该度量指标需要数据本身有类别标记。\n", "\n", "* $ \\sum_{ij} \\binom{n_{ij}}{2}$ : $n_{ij}$代表的是聚类之后在$i$类,应该在$j$类的样本数量,很显然,这一求和,就是RI中的a,应该在一起而真的在一起的数量。\n", "\n", "* $\\frac{1}{2} \\left[ \\sum_i \\binom{a_i}{2} + \\sum_j \\binom{b_j}{2} \\right]$ : 是如果聚类是完全对的,那么就应该是$a$, $b$的所有组合可能之和,所以在表达式里面叫做MaxIndex。\n", "\n", "* $\\left[ \\sum_i \\binom{a_i}{2} \\sum_j \\binom{b_j}{2} \\right] / \\binom{n}{2}$ 是a的期望\n", "$$\n", "E(\\sum_{ij} \\binom{n_{ij}}{2}) = \\sum_i \\binom{n_i}{2} \\sum_j \\binom{n_j}{2} / \\binom{n}{2}\n", "$$\n", "\n", "假设配对矩阵是这样的,共有n(n-1)/2个配对方法。在行方向计算出可能取到的配对数,在列方向计算可能取到的配对数,相乘以后,除以总的配对数,这就是a的期望了。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "* [ARI聚类效果评价指标](https://blog.csdn.net/qtlyx/article/details/52678895)\n", "* [ARI reference](https://davetang.org/muse/2017/09/21/adjusted-rand-index/)\n", "* [聚类性能评估-ARI(调兰德指数)](https://zhuanlan.zhihu.com/p/145856959)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "### 7.2 方法2 - 轮廓系数\n", "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": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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QES9GxM4Kh1WqA4CpkiYCBwI9FY6naBHxY2BbQee3A9en768H3jGmQZWHc1gV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\nsnjx0YyMXMjAwPVMTEyycOE8SiUXn3cC/3btkesw34wGmON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1kqEawZ13wpZbwkorFZ1Ealybbw6XXALDhsELLxSdRpLKp8NDAhHRGbg0pXRQ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\n53pqNtCSUvpiSmn7SmaVJGl+unaFK66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"text/plain": [ "" ] }, "metadata": {}, "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", "plt.savefig('k-means_silhouette_coef.pdf')\n", "plt.show() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 8. 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": 17, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", 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" ] }, "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": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "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'),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。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 参考资料\n", "* [机器学习聚类算法之K-Means](https://www.biaodianfu.com/k-means.html)" ] } ], "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": "3.5.4" } }, "nbformat": 4, "nbformat_minor": 2 }