{ "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", "## 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)***:\n", "* 移动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", "$$\n", "u_k = \\frac{1}{|C_k|} \\sum_{i \\in C_k} x_i\n", "$$\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。\n", "\n", "## 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", "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": "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": "iVBORw0KGgoAAAANSUhEUgAAAWoAAAEICAYAAAB25L6yAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAVAklEQVR4nO3df3Dcd33n8ec7cmRwzCVtnRMXR0ZhoPRy5CCx0yJy9KSKOUhJ4K9LU4Jd8HR81zmaQOLLUdKkLdRNJ01ToNNyQ6nLJNHg8wSGaUL4dbK2w7UiYzvkLiQmM7lEsYKhDdD8UMJJtvy+P3bFyo4srWytvx9Jz8eMRvr+2O++9+31Sx99vrv7jcxEklSuM6ouQJI0N4NakgpnUEtS4QxqSSqcQS1JhTOoJalwBrXaKiLeFhGPVVzDRyPis1XWcCoioi8inq66DlXHoBYAEfHBiNgXERMR8bkF3G40It5+ou2Z+c3MfEOr+5+q2UItM/8oM3+zXfd5urW7hyrPqqoLUDEOAX8IvAN4ZcW1zCoiAojMPFp1LbOJiFWZeaTqOrT8OKIWAJn5xcz8EvCj47dFxLqIuC8ino2IH0fENyPijIi4C9gA3BsR4xFx4yy3/ekI90T7R8RbIuIfGsf/3xHRN+P2tYjYERF/D7wEvDYiPhARByLihYh4IiL+U2Pfs4CvAOc1jj8eEedFxO9HxN0zjvnuiHikcX+1iPjXM7aNRsT2iPg/EfFcRPyPiHjFbD2LiPdHxN9HxJ9FxI+A34+I1RFxe0QcjIh/jIj/HhGvnKuPjW0ZEa+bcezPRcQfznKfL+thRLwiIu6OiB81jr03Irpm/YfWkmRQqxU3AE8D5wJdwEeBzMzNwEHgysxcm5m3zXWQ2faPiPXAl6mP5n8W2A58ISLOnXHTzcA24FXAU8A/AVcA/wL4APBnEXFJZr4IXA4cahx/bWYemllDRPw88HngQ43Hcz/10OucsdtVwDuBC4B/C7x/jof1S8ATjb7sAP4Y+HngzcDrgPXALY19Z+3jXD073gl6/hvA2UA38HPAfwZ+spDjqmwGtVpxGPhXwGsy83Bj3nmxPiTmfcD9mXl/Zh7NzG8A+4BfnbHP5zLzkcw80rj/L2fm/826vwO+Drytxfv7NeDLmfmNzDwM3E59quetM/b5VGYeyswfA/dSD90TOZSZf96Y8vh/1H+hfDgzf5yZLwB/BFzd2LddfTxMPaBfl5lTmbk/M59fhOOqEAa1WvEnwOPA1xtTDR9ZxGO/BviPjT/Zn42IZ4F/Rz3Qpo3NvEFEXB4R32pMHzxLPdTXtXh/51EflQPQmO8eoz7ynfaDGT+/BKyd43gzazsXWAPsn/FYvtpYD+3r413A14BdEXEoIm6LiDMX6dgqgEGteWXmC5l5Q2a+Fng3cH1EDExvXujhjlseA+7KzHNmfJ2VmX88220iYjXwBeoj4a7MPIf69EW0WM8h6r8cpo8X1KcMvrfAx/Gy2oAfUp9y+DczHsvZmbkW5u3jS9RDftqrW7xPGqPzP8jMC6n/ZXAFsOUkH48KZFALqL9ioXHSrAPoaJygWtXYdkVEvK4Ras8BU8D0Ky/+EXjtAu7q+P3vBq6MiHdExPT99kXE+Se4fSewGngGOBIRlwP/4bjj/1xEnH2C2+8G3hURA41R5w3ABPAPC3gMs2qMzv+K+pz5vwSIiPUR8Y7Gz3P18SHgvY0evBP493Pc1TE9jIj+iLgoIjqA56lPhRT5yhidHINa036X+mjwI9TnjX/SWAfweuB/AuPACPCXmTnc2HYr8LuNP/W3t3A/x+yfmWPAe6ifWHuG+gj7v3KC52Zj3vda6oH7z8B7gb+dsf271E8WPtG4j/OOu/1jjcf359RHwFdSPzE32ULtrfhv1Kc3vhURz1Pv2/TryOfq43WNWp4FrgG+NMd9HN/zVwP3UA/pA8DfUZ8O0TIRXjhAksrmiFqSCmdQS1LhDGpJKpxBLUmFa8uHMq1bty57enraceiWvfjii5x11lmV1lAKe9FkL5rsRVMJvdi/f/8PM/Pc2ba1Jah7enrYt29fOw7dslqtRl9fX6U1lMJeNNmLJnvRVEIvIuKpE21z6kOSCmdQS1LhDGpJKpxBLUmFM6glqXAGtSQVzqCWpMIZ1JJUOINakgpnUEtS4QxqSSqcQS1JhTOoJalwBrUkFc6glqTCGdSSVDiDWpIK11JQR8SHI+KRiPhORHw+Il7R7sIktcFtt8Hw8LHrhofr61WseYM6ItYD1wKbMvONQAdwdbsLk9QGl14KV13VDOvh4frypZdWW5fm1Oo1E1cBr4yIw8Aa4FD7SpLUNv39sHs3XHUVPZdfDl/5Sn25v7/qyjSHyMz5d4q4DtgB/AT4emZeM8s+24BtAF1dXRt37dq1yKUuzPj4OGvXrq20hlLYiyZ7Udezcyc9d93F6ObNjG7dWnU5lSvhedHf378/MzfNujEz5/wCfgbYA5wLnAl8CXjfXLfZuHFjVm14eLjqEophL5rsRWbu2ZO5bl0+uXlz5rp19eUVroTnBbAvT5CprZxMfDvwZGY+k5mHgS8Cbz313x+STrvpOendu+sj6cY0yMtOMKoorQT1QeAtEbEmIgIYAA60tyxJbbF377Fz0tNz1nv3VluX5jTvycTMfCAi7gEeBI4A3wY+0+7CJLXBjTe+fF1/vycTC9fSqz4y8/eA32tzLZKkWfjOREkqnEEtSYUzqCWpcAa1JBXOoJakwhnUklQ4g1qSCmdQS1LhDGpJKpxBLUmFM6glqXAGtSQVzqCWpMIZ1Gofr3jdZC90CgxqtY9XvG6yFy8zMjbCrd+8lZGxkcrrGDw4WHkdc2n1KuTSws244jW/9Vvw6U+v3Cte24tjjIyNMHDnAJNTk3R2dDK0ZYje7t7K6pg4MsHg2GBldczHEbXaq7+/Hkwf/3j9+woNJsBezFAbrTE5NclUTjE5NUlttFZpHUc5Wmkd8zGo1V7Dw/XR480317+v5Iuo2ouf6uvpo7Ojk47ooLOjk76evkrrOIMzKq1jPk59qH1mXPH6p9flm7m8ktiLY/R29zK0ZYjaaI2+nr7Kphum69g5vJOt/VuLnPYAg1rtNNcVr1daONmLl+nt7i0iGHu7e5nYMFFELSdiUKt9vOJ1k73QKXCOWpIKZ1BLUuEMakkqnEEtSYUzqCWpcAa1JBXOoJakwhnUklQ4g1qSCmdQS1LhDGpJKpxBreVptktfnYiXxFLhDGotT8df+upEvCSWloCWgjoizomIeyLiuxFxICLK/TxACY699NWJwvr4z4iWCtXqiPqTwFcz8xeANwEH2leStEimw/rKK+GOO47ddscd9fWGtJaAeT+POiLOBn4ZeD9AZk4Ck+0tS1ok/f3wsY/B9u315UsuqYf09u1w++2GtJaEVi4ccAHwDPA3EfEmYD9wXWa+2NbKpMVy/fX179u38+Y3vhG+8516SE+vlwoXmTn3DhGbgG8Bl2XmAxHxSeD5zLz5uP22AdsAurq6Nu7atatNJbdmfHyctWvXVlpDKexF3ZuvvZZzHn6YZy+6iIc+9amqy6mcz4umEnrR39+/PzM3zboxM+f8Al4NjM5Yfhvw5blus3Hjxqza8PBw1SUUw15k5p/+aWZE/vNFF2VG1JdXOJ8XTSX0AtiXJ8jUeac+MvMHETEWEW/IzMeAAeDRxfotIrXdjDnphy65hL4HH2zOWTv9oSWg1Yvb/jYwGBGdwBPAB9pXkrSIhofhlluac9K1WjOcb7kFLr7YE4oqXktBnZkPAbPPnUilmn6d9L33vjyMr7++HtK+jlpLgO9M1PLUyptZWnlTjFQAg1rL0969rY2Up8N6797TU5d0Elqdo5aWlhtvbH3f/n6nPlQ0R9SSVDiDWpIKZ1BLUuEMakkqnEEtSYUzqCWpcAa1JBXOoJakwhnUklQ4g1qSCmdQS6fJ4MOD9HyihzP+4Ax6PtHD4MODVZekJcLP+pBOg8GHB9l27zZeOvwSAE899xTb7t0GwDUXXVNlaZUZGRuhNlqjr6eP3u7eqsspmkEtnQY3Dd3005Ce9tLhl7hp6KYVGdQjYyMM3DnA5NQknR2dDG0ZMqzn4NSHdBocfO7ggtYvd7XRGpNTk0zlFJNTk9RGa1WXVDSDWjoNNpy9YUHrl7u+nj46OzrpiA46Ozrp6+mruqSiGdTSabBjYAdrzlxzzLo1Z65hx8COiiqqVm93L0Nbhvh4/8ed9miBc9TSaTA9D33T0E0cfO4gG87ewI6BHStyfnpab3evAd0ig1o6Ta656JoVHcw6eU59SFLhDGpJKpxBLUmFM6glqXAGtSQVzqCWpMIZ1JJUOINakgpnUEtS4QxqSSqcQS1JhTOoJalwBrUkFc6glqTCtRzUEdEREd+OiPvaWdCycNttMDx87Lrh4fp6SVqghYyorwMOtKuQZeXSS+Gqq5phPTxcX7700mrrkrQktRTUEXE+8C7gs+0tZ5no74fdu+vhfMst9e+7d9fXS9ICRWbOv1PEPcCtwKuA7Zl5xSz7bAO2AXR1dW3ctWvXIpe6MOPj46xdu7bSGnp27qTnrrsY3byZ0a1bK6ujhF6Uwl402YumEnrR39+/PzM3zboxM+f8Aq4A/rLxcx9w33y32bhxY1ZteHi42gL27Mlcty7z5pvr3/fsqayUyntREHvRZC+aSugFsC9PkKmtTH1cBrw7IkaBXcCvRMTdp/77YxmbnpPevRs+9rHmNMjxJxglqQXzBnVm/k5mnp+ZPcDVwJ7MfF/bK1vK9u49dk56es56795q65K0JHkV8na48caXr+vv92SipJOyoKDOzBpQa0slkqRZ+c5ESSqcQS1JhTOoJalwBrUkFc6glqTCGdSSVDiDWpIKZ1BLUuEMakkqnEEtSYUzqCWpcAa1JBXOoJakwhnUklQ4g1ptNzI2wq3fvJWRsZGqS5GWJC8coLYaGRth4M4BJqcm6ezoZGjLEL3dvVWXJS0pjqjVVrXRGpNTk0zlFJNTk9RGa1WXJC05BrXaqq+nj86OTjqig86OTvp6+qouSVpynPpQW/V29zK0ZYjaaI2+nj6nPaSTYFCr7Xq7ew1o6RQ49SFJhTOoJalwBrUkFc6glqTCGdSSVDiDWpIKZ1BLUuEMakkqnEEtSYUzqCWpcAa1JBXOoJakwhnUklQ4g1qSCjdvUEdEd0QMR8SjEfFIRFx3OgqTJNW18nnUR4AbMvPBiHgVsD8ivpGZj7a5NkkSLYyoM/P7mflg4+cXgAPA+nYXpsUxMjbC4MFBrwAuLWELmqOOiB7gYuCBtlSjRTV9BfCdT+5k4M4Bw1paolq+FFdErAW+AHwoM5+fZfs2YBtAV1cXtVptsWo8KePj45XXULXBg4NMHJngKEeZODLBzuGdTGyYqLqsSvm8aLIXTaX3IjJz/p0izgTuA76WmXfMt/+mTZty3759i1DeyavVavT19VVaQ9WmR9QTRyZYvWo1Q1uGVvy1C31eNNmLphJ6ERH7M3PTbNtaedVHAH8NHGglpFWO6SuAb71gqyEtLWGtTH1cBmwGHo6IhxrrPpqZ97etKi2a3u5eJjZMGNLSEjZvUGfm/wLiNNQiSZqF70yUpMIZ1JJUOINakgpnUEtS4QxqSSqcQS1JhTOoJalwBrUkFc6glqTCGdSSVDiDWpIKZ1BLUuEMakkqnEEtSYUzqCWpcAa1JBXOoJakwhnUklQ4g1qSCmdQS1LhDGpJKpxBLUmFM6glqXAGtSQVzqCWpMIZ1JJUOINakgpnUEtS4QxqSSqcQS1JhTOoJalwBrUkFc6glqTCGdSSVDiDWpIK11JQR8Q7I+KxiHg8Ij7S7qIkSU3zBnVEdAB/AVwOXAj8ekRc2O7CTsXI2AiDBwcZGRupuhRJOmWtjKh/EXg8M5/IzElgF/Ce9pZ18kbGRhi4c4CdT+5k4M4Bw1rSkreqhX3WA2Mzlp8Gfun4nSJiG7ANoKuri1qtthj1LdjgwUEmjkxwlKNMHJlg5/BOJjZMVFJLKcbHxyv79yiNvWiyF02l96KVoG5JZn4G+AzApk2bsq+vb7EOvSCrx1YzOFYP69WrVrO1fyu93b2V1FKKWq1GVf8epbEXTfaiqfRetDL18T2ge8by+Y11Rert7mVoyxBbL9jK0JahFR/Skpa+VkbUe4HXR8QF1AP6auC9ba3qFPV29zKxYcKQlrQszBvUmXkkIj4IfA3oAHZm5iNtr0ySBLQ4R52Z9wP3t7kWSdIsfGeiJBXOoJakwhnUklQ4g1qSCmdQS1LhDGpJKpxBLUmFM6glqXAGtSQVzqCWpMIZ1JJUOINakgpnUEtS4QxqSSqcQS1JhTOoJalwkZmLf9CIZ4CnFv3AC7MO+GHFNZTCXjTZiyZ70VRCL16TmefOtqEtQV2CiNiXmZuqrqME9qLJXjTZi6bSe+HUhyQVzqCWpMIt56D+TNUFFMReNNmLJnvRVHQvlu0ctSQtF8t5RC1Jy4JBLUmFW5ZBHRHvjIjHIuLxiPhI1fVUJSK6I2I4Ih6NiEci4rqqa6pSRHRExLcj4r6qa6lSRJwTEfdExHcj4kBE9FZdU1Ui4sON/xvfiYjPR8Qrqq5pNssuqCOiA/gL4HLgQuDXI+LCaquqzBHghsy8EHgL8F9WcC8ArgMOVF1EAT4JfDUzfwF4Eyu0JxGxHrgW2JSZbwQ6gKurrWp2yy6ogV8EHs/MJzJzEtgFvKfimiqRmd/PzAcbP79A/T/k+mqrqkZEnA+8C/hs1bVUKSLOBn4Z+GuAzJzMzGcrLapaq4BXRsQqYA1wqOJ6ZrUcg3o9MDZj+WlWaDjNFBE9wMXAAxWXUpVPADcCRyuuo2oXAM8Af9OYBvpsRJxVdVFVyMzvAbcDB4HvA89l5terrWp2yzGodZyIWAt8AfhQZj5fdT2nW0RcAfxTZu6vupYCrAIuAT6dmRcDLwIr8jxORPwM9b+2LwDOA86KiPdVW9XslmNQfw/onrF8fmPdihQRZ1IP6cHM/GLV9VTkMuDdETFKfSrsVyLi7mpLqszTwNOZOf2X1T3Ug3slejvwZGY+k5mHgS8Cb624plktx6DeC7w+Ii6IiE7qJwf+tuKaKhERQX0u8kBm3lF1PVXJzN/JzPMzs4f682FPZhY5cmq3zPwBMBYRb2isGgAerbCkKh0E3hIRaxr/VwYo9MTqqqoLWGyZeSQiPgh8jfpZ3J2Z+UjFZVXlMmAz8HBEPNRY99HMvL+6klSA3wYGGwOZJ4APVFxPJTLzgYi4B3iQ+iukvk2hbyX3LeSSVLjlOPUhScuKQS1JhTOoJalwBrUkFc6glqTCGdSSVDiDWpIK9/8Bsi7Q+mRmA4QAAAAASUVORK5CYII=\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": "iVBORw0KGgoAAAANSUhEUgAAAWoAAAEICAYAAAB25L6yAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAUz0lEQVR4nO3dfZBddX3H8feXDQmEKKjBpULCpg+KjI61CeLCaHcbxpFC1Zm2FMWgpk5aWiw6WitSFLXUqe1YdVQciqEFtmYyaFtEWtGwa32IlASYIgRba0ICgsQHHjbobh6+/eOe9S7hZvcu2Zvz2933a2Zn99577jnf8927nz33d+69v8hMJEnlOqzuAiRJEzOoJalwBrUkFc6glqTCGdSSVDiDWpIKZ1Br2kTEmyPiGwe4bWlEDEdE16Gua1wN50XEzXVt/2BFRE9EZETMq7sWHVoG9RwWEQsi4rMRcV9EPB4Rd0bEmZ3YVmZuz8xFmbm32vZQRLy1E9uq1v+UUMvMgcx8Vae2eah1uocqh0E9t80DdgC/CRwN/CWwPiJ66iyqHXUemU/GI15NN4N6DsvMXZl5WWZuy8x9mXkjsBVYDhARfRFxf0S8MyIejogHI+ItY/ePiOdExA0R8VhE/BfwKwfa1vgj3Ii4HHgF8MlqOOST1TInRcRXIuInEfHdiDhn3P3/MSKuiIibImIX0B8RZ0XEHdX2d0TEZeM2+Z/V90eqbfTuPzQTEadFxG0R8Wj1/bRxtw1FxIci4pvVs42bI2LxAfZtrE9/EREPAVdHxGER8Z6I+L+I+HFErI+IZ1fLHxER11XXP1Jtu7u6bVtEnDFu3ZdFxHUttvmUHkbD31e/q8ci4q6IeNGBfieaOQxq/UIVFs8H7h539XE0jraPB/4Q+FREPKu67VPAz4FfAlZXX5PKzEuArwMXVsMhF0bEUcBXgH8GngucC3w6Ik4ed9c3AJcDzwC+AewCzgeOAc4CLoiI11XLvrL6fky1jY377euzgS8BnwCeA3wU+FJEPGe/7b2lqmc+8K4Jdus44NnAicAa4G3A62g8W3ke8FMa/QJ4E42eLqm2/cfAzyZY91O06iHwqmq/n1+t/xzgx1NZr8pkUAuAiDgcGAD+KTPvHXfTbuCDmbk7M28ChoEXVEMPvwu8rzoy/w7wTwdRwtnAtsy8OjP3ZOYdwOeB3x+3zL9l5jero/+fZ+ZQZt5VXf5v4HM0grEdZwH/m5nXVtv7HHAv8Dvjlrk6M/8nM38GrAd+fYL17QPen5kj1fJ/DFySmfdn5ghwGfB71bDIbhoB/auZuTczN2fmY23WPZHdNP6JnQREZm7JzAenYb2qmUEtIuIw4FpgFLhwv5t/nJl7xl1+AlgEHEtzjHvMfQdRxonAqdVQwCMR8QhwHo0j1THjt0VEnBoRgxGxMyIepRGOLYcnWnhei3rvo/HMYcxD434e2+8D2ZmZPx93+UTgX8btyxZgL9BNo9dfBtZFxA8i4iPVP8qDkpm3AJ+kceT+cERcGRHPPNj1qn4G9RwXEQF8lkaA/G5m7m7zrjuBPTSevo9ZOoVN7/+xjTuAr2XmMeO+FmXmBRPc55+BG4AlmXk08BkgDrDs/n5AI0zHWwo80PYePFmr/Tlzv/05IjMfqJ6dfCAzTwZOo/Fs4vzqfruAhePWcxwH9pR9zMxPZOZy4GQaQyB//jT3RwUxqHUF8ELgd6qn7G2pXmb3BeCyiFhYjSW/aQrb/SHwy+Mu3wg8PyJWRcTh1dcpEfHCCdbxDOAnmfnziHgZjTHlMTtpDEf8cst7wk3V9t5QneD8AxrhduMU9mEinwEuj4gTASLi2Ih4bfVzf0S8uBo+eozGkMW+6n53AudW+78C+L0JtvGkHlb9OrU6Ot9F4/zBvgPdWTOHQT2HVSHyRzTGXh+qXj0wHBHntbmKC2kMBzwE/CNw9RQ2/3EaY7Y/jYhPZObjNE6GnUvjaPch4G+ABROs40+AD0bE48D7aIwjA5CZT9A48fjNavjh5ePvmJk/pnEk+04aJ9zeDZydmT+awj5Mtn83ADdX9X0bOLW67TjgehohvQX4Go3hEIBLabx65qfAB2g8a5hoG7/oIfBM4B+q+95X7dffTtP+qEbhxAGSVDaPqCWpcAa1JBXOoJakwhnUklS4jnx4zOLFi7Onp6cTq27brl27OOqoo2qtoRT2osleNNmLphJ6sXnz5h9l5rGtbutIUPf09LBp06ZOrLptQ0ND9PX11VpDKexFk71oshdNJfQiIg74zl6HPiSpcAa1JBXOoJakwhnUklQ4g1qSCmdQS1LhDGpJKpxBLUmFM6glqXAGtSQVzqCWpMIZ1JJUOINakgpnUEtS4QxqSSqcQS1JhTOoJalwbQV1RLwjIu6OiO9ExOci4ohOFyapAz7yERgcfPJ1g4ON61WsSYM6Io4H/gxYkZkvArqAcztdmKQOOOUUOOecZlgPDjYun3JKvXVpQu3OmTgPODIidgMLgR90riRJHdPfD+vXwznn0HPmmfDv/9643N9fd2WaQGTm5AtFXARcDvwMuDkzz2uxzBpgDUB3d/fydevWTXOpUzM8PMyiRYtqraEU9qLJXjT0rF1Lz7XXsm3VKratXl13ObUr4XHR39+/OTNXtLwxMyf8Ap4F3AIcCxwO/Cvwxonus3z58qzb4OBg3SUUw1402YvMvOWWzMWLc+uqVZmLFzcuz3ElPC6ATXmATG3nZOIZwNbM3JmZu4EvAKcd/P8PSYfc2Jj0+vWNI+lqGOQpJxhVlHaCejvw8ohYGBEBrAS2dLYsSR1x221PHpMeG7O+7bZ669KEJj2ZmJm3RsT1wO3AHuAO4MpOFyapA9797qde19/vycTCtfWqj8x8P/D+DtciSWrBdyZKUuEMakkqnEEtSYUzqCWpcAa1JBXOoJakwhnUklQ4g1qSCmdQS1LhDGpJKpxBLUmFM6glqXAGtSQVzqBW5zjjdZO9aCqlF6XU0QaDWp3jjNdN9qKplF6UUkcb2p2FXJq6cTNec8EFcMUVc3fGa3vRVEovZtCM7B5Rq7P6+xt/jB/6UON7gX8Eh4y9aCqlF1UdPddeW/TvxKBWZw0ONo6YLr208X0uT6JqL5pK6UVVx7ZVq4r+nRjU6pxxM17zwQ/O7Rmv7UVTKb2YQTOyG9TqHGe8brIXTaX0opQ62uDJRHWOM1432YumUnpRSh1t8IhakgpnUEtS4QxqzVyt3ll2IIW+40xqh0GtmWv/d5YdSMHvOJPaYVBr5hr/DrcDhfX4l4IVeJJIaodBrZltorA2pDVLGNSa+VqFtSGtWcTXUWt2KOWDfqQO8Ihas0cpH/QjTTODWrNHKR/0I00zg1qzQykf9CN1gEGtma/VicN2XronzRAGtWa2iV7dYVhrlmgrqCPimIi4PiLujYgtEdHb6cKkSbXzEjzDWrNAu0fUHwf+IzNPAl4CbOlcSVKb9v884YmWu/jiJ3/OsJ/9oRlk0tdRR8TRwCuBNwNk5igw2tmypDa0+jzhVsY+E2T9+sbl8Ufi0gzQzhtelgE7gasj4iXAZuCizNzV0cqk6TKDZpuWWonMnHiBiBXAt4HTM/PWiPg48FhmXrrfcmuANQDd3d3L161b16GS2zM8PMyiRYtqraEU9qKhZ+1aeq69lm2rVjXmyJvjfFw0ldCL/v7+zZm5ouWNmTnhF3AcsG3c5VcAX5roPsuXL8+6DQ4O1l1CMexFZt5yS+bixbl11arMxYsbl+c4HxdNJfQC2JQHyNRJTyZm5kPAjoh4QXXVSuCeafgHIh0aM2i2aamVdl/18TZgICL+G/h14K87VpE03WbQbNNSK219el5m3gm0HjuRSjeDZpuWWvGdiZJUOINakgpnUEtS4QxqSSqcQS1JhTOoJalwBrUkFc6glqTCGdSSVDiDWpIKZ1BLUuEMakkqnEEtSYUzqCWpcAa1dAht3LGRD3/9w2zcsbHuUmpnL9rX1udRSzp4G3dsZOU1KxndO8r8rvlsOH8DvUt66y6rFvZiajyilg6RoW1DjO4dZW/uZXTvKEPbhuouqTb2YmoMaukQ6evpY37XfLqii/ld8+nr6au7pNrYi6lx6EM6RHqX9LLh/A0MbRuir6dvTj/VtxdTY1BLh1Dvkl5DqWIv2ufQhyQVzqCWpMIZ1JJUOINakgpnUEtS4QxqSSqcQS1JhTOoJalwBrUkFc6glqTCGdSSVDiDWpIKZ1BLUzRw1wA9H+vhsA8cRs/Hehi4a6DukjTL+el50hQM3DXAmi+u4YndTwBw36P3seaLawA478Xn1VmaZjGPqKUpuGTDJb8I6TFP7H6CSzZcUlNFmgvaDuqI6IqIOyLixk4WJJVs+6Pbp3S9NB2mckR9EbClU4XMRs6yPPssPXrplK6XpkNbQR0RJwBnAVd1tpzZY2yW5UsHL2XlNSsN61ni8pWXs/DwhU+6buHhC7l85eU1VaS5IDJz8oUirgc+DDwDeFdmnt1imTXAGoDu7u7l69atm+ZSp2Z4eJhFixbVtv2B7QOs3bqWfezjMA5j9bLVnLe0npNNdfeiJNPRi6/+8KtctfUqHh55mOcueC5vXfZWzug+Y5oqPHR8XDSV0Iv+/v7Nmbmi5Y2ZOeEXcDbw6ernPuDGye6zfPnyrNvg4GCt2//W9m/lkX91ZHZ9oCuP/Ksj81vbv1VbLXX3oiT2osleNJXQC2BTHiBT23l53unAayLit4EjgGdGxHWZ+cZp+CcyaznLsqTpMmlQZ+bFwMUAEdFHY+jDkG6DsyxLmg6+jlqSCjeldyZm5hAw1JFKJEkteUQtSYUzqCWpcAa1JBXOoJakwhnUklQ4g1qSCmdQS1LhDGpJKpxBLUmFM6glqXAGtSQVzqCWpMIZ1JJUOINakgpnUKvjnI1dOjhT+jxqaarGZmMf3TvK/K75bDh/g7PeSFPkEbU6amjbEKN7R9mbexndO8rQtqG6S5JmHINaHdXX08f8rvl0RRfzu+bT19NXd0nSjOPQhzrK2dilg2dQq+OcjV06OA59SFLhDGpJKpxBLUmFM6glqXAGtSQVzqCWpMIZ1JJUOINakgpnUEtS4QxqSSqcQS1JhTOoJalwBrUkFc6glqTCTRrUEbEkIgYj4p6IuDsiLjoUhUmSGtr5POo9wDsz8/aIeAawOSK+kpn3dLg2SRJtHFFn5oOZeXv18+PAFuD4Them6bFxx0YGtg84A7g0g01pjDoieoCXArd2pBpNq7EZwNduXcvKa1Ya1tIM1fZUXBGxCPg88PbMfKzF7WuANQDd3d0MDQ1NV41Py/DwcO011G1g+wAje0bYxz5G9oywdnAtI0tH6i6rVj4umuxFU+m9iMycfKGIw4EbgS9n5kcnW37FihW5adOmaSjv6RsaGqKvr6/WGuo2dkQ9smeEBfMWsOH8DXN+7kIfF032oqmEXkTE5sxc0eq2dl71EcBngS3thLTKMTYD+Oplqw1paQZrZ+jjdGAVcFdE3Fld997MvKljVWna9C7pZWTpiCEtzWCTBnVmfgOIQ1CLJKkF35koSYUzqCWpcAa1JBXOoJakwhnUklQ4g1qSCmdQS1LhDGpJKpxBLUmFM6glqXAGtSQVzqCWpMIZ1JJUOINakgpnUEtS4QxqSSqcQS1JhTOoJalwBrUkFc6glqTCGdSSVDiDWpIKZ1BLUuEMakkqnEEtSYUzqCWpcAa1JBXOoJakwhnUklQ4g1qSCmdQS1LhDGpJKpxBLUmFM6glqXAGtSQVrq2gjohXR8R3I+J7EfGeThclSWqaNKgjogv4FHAmcDLw+og4udOFHYyNOzYysH2AjTs21l2KJB20do6oXwZ8LzO/n5mjwDrgtZ0t6+nbuGMjK69Zydqta1l5zUrDWtKMN6+NZY4Hdoy7fD9w6v4LRcQaYA1Ad3c3Q0ND01HflA1sH2Bkzwj72MfInhHWDq5lZOlILbWUYnh4uLbfR2nsRZO9aCq9F+0EdVsy80rgSoAVK1ZkX1/fdK16ShbsWMDAjkZYL5i3gNX9q+ld0ltLLaUYGhqirt9HaexFk71oKr0X7Qx9PAAsGXf5hOq6IvUu6WXD+RtYvWw1G87fMOdDWtLM184R9W3Ar0XEMhoBfS7who5WdZB6l/QysnTEkJY0K0wa1Jm5JyIuBL4MdAFrM/PujlcmSQLaHKPOzJuAmzpciySpBd+ZKEmFM6glqXAGtSQVzqCWpMIZ1JJUOINakgpnUEtS4QxqSSqcQS1JhTOoJalwBrUkFc6glqTCGdSSVDiDWpIKZ1BLUuEMakkqXGTm9K80Yidw37SveGoWAz+quYZS2Isme9FkL5pK6MWJmXlsqxs6EtQliIhNmbmi7jpKYC+a7EWTvWgqvRcOfUhS4QxqSSrcbA7qK+suoCD2osleNNmLpqJ7MWvHqCVptpjNR9SSNCsY1JJUuFkZ1BHx6oj4bkR8LyLeU3c9dYmIJRExGBH3RMTdEXFR3TXVKSK6IuKOiLix7lrqFBHHRMT1EXFvRGyJiN66a6pLRLyj+tv4TkR8LiKOqLumVmZdUEdEF/Ap4EzgZOD1EXFyvVXVZg/wzsw8GXg58KdzuBcAFwFb6i6iAB8H/iMzTwJewhztSUQcD/wZsCIzXwR0AefWW1Vrsy6ogZcB38vM72fmKLAOeG3NNdUiMx/MzNurnx+n8Qd5fL1V1SMiTgDOAq6qu5Y6RcTRwCuBzwJk5mhmPlJrUfWaBxwZEfOAhcAPaq6npdkY1McDO8Zdvp85Gk7jRUQP8FLg1ppLqcvHgHcD+2quo27LgJ3A1dUw0FURcVTdRdUhMx8A/g7YDjwIPJqZN9dbVWuzMai1n4hYBHweeHtmPlZ3PYdaRJwNPJyZm+uupQDzgN8ArsjMlwK7gDl5HicinkXj2fYy4HnAURHxxnqram02BvUDwJJxl0+orpuTIuJwGiE9kJlfqLuempwOvCYittEYCvutiLiu3pJqcz9wf2aOPbO6nkZwz0VnAFszc2dm7ga+AJxWc00tzcagvg34tYhYFhHzaZwcuKHmmmoREUFjLHJLZn607nrqkpkXZ+YJmdlD4/FwS2YWeeTUaZn5ELAjIl5QXbUSuKfGkuq0HXh5RCys/lZWUuiJ1Xl1FzDdMnNPRFwIfJnGWdy1mXl3zWXV5XRgFXBXRNxZXffezLypvpJUgLcBA9WBzPeBt9RcTy0y89aIuB64ncYrpO6g0LeS+xZySSrcbBz6kKRZxaCWpMIZ1JJUOINakgpnUEtS4QxqSSqcQS1Jhft/uEEZ1c5o3CIAAAAASUVORK5CYII=\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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\n", 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" ] }, "metadata": { "needs_background": "light" }, "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.show()\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# k-means\n", "\n", "def calc_distance(v1, v2):\n", " return np.sum(np.square(v1-v2))\n", "\n", "def rand_cluster_cents(X, k):\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", " # 样本数\n", " m=np.shape(X)[0]\n", " \n", " # 生成随机下标列表\n", " dataIndex=list(range(m))\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", " # 样本总数\n", " m = np.shape(X)[0]\n", " # 分配样本到最近的簇:存[簇序号,距离的平方] (m行 x 2 列)\n", " clusterAssment = np.zeros((m, 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", " # 初始化迭代次数计数器\n", " iterN = 0\n", " \n", " # 所有样本分配结果不再改变,迭代终止\n", " while True: \n", " # 标志位,如果迭代前后样本分类发生变化值为True,否则为False\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(m):\n", " # 初始定义距离为无穷大\n", " minDist = np.inf;\n", " # 初始化索引值\n", " minIndex = -1\n", " # 计算每个样本与k个中心点距离\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", " # 判断距离是否为最小\n", " if distJI < minDist:\n", " # 更新获取到最小距离\n", " minDist = distJI\n", " # 获取对应的簇序号\n", " minIndex = j\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", " # 获取该簇所有的样本点,nonzero[0]表示A == cent的元素所在的行,如果没有[0],列也会表示\n", " ptsInClust = X[clusterAssment[:, 0] == cent, :]\n", " # 更新聚类中心:axis=0沿列方向求均值。\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": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "最初的中心= [[ 7.35701549 -0.6929096 ]\n", " [ 0.95042384 -0.57690366]\n", " [ 0.05572491 1.09419152]]\n", "the SSE of 1th iteration is 239885.100070\n", "the SSE of 2th iteration is 37348.235353\n", "the SSE of 3th iteration is 8260.155429\n", "the SSE of 4th iteration is 3635.163186\n", "the SSE of 5th iteration is 3502.239035\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": 12, "metadata": {}, "outputs": [], "source": [ "def datashow(dataSet, k, centroids, clusterAssment): # 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", " plt.show()\n", " \n", " \n", "# 画出实际图像\n", "def trgartshow(dataSet, k, labels):\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": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# 绘图显示\n", "datashow(X, k, mycentroids, clusterAssment)\n", "trgartshow(X, 3, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 利用sklearn进行分类\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "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": 17, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "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", 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\n", 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" ] }, "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", 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" ] }, "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": [ "
" ] }, "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。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\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": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 2 }