{ "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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" ] }, "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": [ "
" ] }, "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", 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" ] }, "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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" ] }, "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": "
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sepal-lengthsepal-widthpetal-lengthpetal-widthclass
05.13.51.40.2Iris-setosa
14.93.01.40.2Iris-setosa
24.73.21.30.2Iris-setosa
34.63.11.50.2Iris-setosa
45.03.61.40.2Iris-setosa
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" }, "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": "
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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": [ { 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RijKOQFQfgCTGXYgl6kRvYsCM0f5+Fixdms4XTpoymWTQtv0LkhiLIGobWd3jv7sbSqVNdHcvSH9nbaAo4whE9QFIYtyFWKJO9JgDZmwqlVgwlS9dEl9aAeJfM3ieu78tjUBERCQ/DUsGZnYjlYF0a3D3MxKPSEREMhdVTfT5TKJoIyMjU6/CjNrGpZfC6tVw5pmwYsXkY5XiGdmxI/1rG0mcYDpJCyfqFtZrswqkHWTRV+HSS+Gznw2eV6b6rk0PmfSHSOIE00laSHFvYX2Emd1gZg+Z2a8rj7SDK5os+iqsXt14XtpXJv0hkjjBdJIWUtwLyNcCXwV2AicC3wKuSyuoosqir8KZZzael/aVSX+IJE4wnaSFFLdp6Qx3/7GZmbs/BvxvM7sbuCLF2Aoni74KldK2qmOnn0z6QyRxgukkLaS4yaBkZh3Af5nZR4AngP3TC6u4suirsGKFvl/TVSb9IZI4wXSSFk7caqILgRcDFwBdwLuA96QVlIiIZCtWycDdfwEQlg4ucPc/Rb3HzF5EMAbCvuF+bnD3T05YZ1+C6w9dwB+Bc9x9tJkPICIiUxe3NdFxZnY/sAG438zuM7OuiLeVgLe4+9HAMcDbzOyECeu8D9jm7q8C/hVQuVJEJAdxq4n6gQ+5+zx3nwd8mKCFUV0eGAtn9w4fE3szvx34Zvj8BmCxmVnMmJoSc6yNlhgnI2oAnLifZWBgbq6fJYnjGWcwoCQGpmk0aMyWUoljf/ELrqHxoDFRA89k4tJLOf6884K2/vUkMQJTFl+WonxpixJnFHePfADra7x2T4z3dQL3AmPAihrLHwAOr5r/FXBIo212dXV5s4aH3WfMcO/sDKbDw5Nbx919cHCw6f03Y+XK3UccWLmy+Tgr63R0lBt+ljTFPZ7u9Y9p1LFwdx/evt1nrF3rnYODPmPtWh/evr3pWFc+8YQzOPj8Y+UTT+y2/B0bNjy/rN4+oraRiUsucQcvVw7YJZfsuU7UHybWQW/ijxuh7vcpyS9tAgofp7sD67zBb2vc1kRrzWwl8G2C/+7PAYbM7HVhQrmnTqLZBRxjZjOB75vZa939gWYTlpn1AD0As2fPZqjJ3lwDA3MpleZTLhulUpn+/lFKpU1NrwMwNjbW9P6b0dd3FHAgYIDT17eNhQs3pPJZ0tRMDPWOadSxABggqI8sA6Vymf716yk1GWvfxPmNG1kYjij2R2BN1bJ6+2i0jawcPzDADCpHC/48MMDPTzllt3XmDgwwv1TCymXKpRKj/f1sKr3waY7q66s64rCtr48NCxc2tY1m1Pvbx9lHknG0e5yxNMoUlQcw2OBxR8xtXAF8fMJrtwLd4fO9gD8A1mg7Khk0UzLYpZJBDI3+q//gI4/4XlXL9hocVMlAJYPixenRJYNYyWAyD2AWMDN8PoNg7OTTJ6zzYeBr4fNzge9GbXcyycA9OP5XXdX47xBnnbSTgXvw/TvppNrfQ/f4n+X97/9VLomgOoaoON0bH9OoY+EeJISrRkcnlQie388TT/hJ996724/45uee8xetXbvbj/w+Q0O+5bnnYm8jc5dc4s8cdljtRFAR9YeJddBj/nEjNPw+JfWlTUA7xJlIMgBmA18Hbg7njwTeF/Geo4D1BC2QHgCuCF//NHBG+PxFwPeAR4GfAwuiYplsMkhKFskgKUWJtVXj/OAjj/g+Q0N7JIMP/fKXeYfW0JSP5+bN7m9+s/uWLYnE00ir/u0naoc4o5JB3NZE3wirdCpDLG0EPtroDe6+wd2Pdfej3P217v7p8PUr3H1N+Pw5d/87d3+Vux/v7rr5nbSELaUS1/7ud4z77g3gxt259skneTKlOt+WsHw53HlnMJVpI24yOMTdv0twnQ533wnsSi0qkZwtHx2lPCERVOxyZ/ljj2UcUUa2bIFrr4VyOZg++WTeEUlG4iaDZ8zsYMJ+AmHnsck36m5RRWgKPN3E6UOQRD+DavVKBRX1SgdRccSKM+okTOIkbbSN5cuDRADBfdSLXjrQlzq2uE1LLyJoYfdKM/spwcXhs1KLKgdJDEwjyYozmEsaA740KhVUVEoHXwmbXUbFESvOqJMw7dGTKqWC8fFgfnw8mL/8cjj00Ob20wr0pW5K3JLBK4FTgDcQXDv4L+InkkJIYmAaSVacwVySHvAlqlRQMbF0EBVHrDijTsK0R0+qLhVUFLl0oC91U+Img8vd/WmCHkAnAv+HYLCbtpHEwDSSrDiDuSQ94EucUkFF9bWDqDhixRl1EqY5etLEUkFFpXRQxGsH+lI3Je5/95WLxacBfe7+QzO7MqWYcpHEwDSSrDiDuSQ54EvcUkFFpXRw+SteERlHrDijTsI0R0+qVSqoqJQOvvKV5veXJ32pmxI3GTwR3o7ircCK8NbTcUsVhZHEwDSSrDiDuSQ14EszpYKK6msHUXHEijPqJExj9KR6pYKKIl870Jc6trg/6GcTXCs42d23AwcBF6cVlEgeRp5+OnapoGLcneGEWjHlplGpoKLI1w4klriD2zwLrK6a3wJsSSsokTys/6u/arh8aGiIRe1W7xxVKqgoculAYmm7qh5pL3Ha5keNI5B0P4TJxpHIfe9jDHYxd2Agfrv6OKWCiurSQTu132+VsRly1lbNQ6W9xGmb37t5M8vCW0Xftm0bAD1z5jS1jSRExRGrzXvUOr29sGxZ8Py224JpT88e759fKsHAQHS7+rilgopK6eCUU+Dss9uj/X4WfREK0t9BJQNpWXHa5q/aurXhfNL9EOqJiiNWm/eodVatajwfvt/K5Xjt6pspFVTs2gVXXtk+7fez6ItQkP4OSgbSsuK0zV8ya1bD+aT7IdQTFUesNu9R6yxZ0ng+fH+5oyNeu/qRkfilgorxcXjqqfZpv59FX4SC9HdQNZG0rDht8ytVMau2bmXJrFm7V83E3EYSouKI1eY9ap1KldCqVUEiqK4iqnr/aH8/C5Yuja6KWL8+5qerYWSkPdrvZ9EXoSD9HZQMpKXFaZvfM2fOnj++TW4jCVFxxGrzHrVOT8+eSWDC+zeVSixI+wenndrvZ/FZCnC8VE0kIiJKBiIiomQgDbRC0+gk+gic99BDHHznnZz30ENTCKTJ9vtT2E/q4xmI1KBrBlJTKzSNTqKPwHkPPcTA738P8Pz0uiOPbDKQJtvvT1YW4xmI1KGSgdTUCk2jk+gjcPNTTzWcjxfIUHPt9ycri/EMROpQMpCaWqFpdBJ9BE456KCG8/ECWdRc+/3JymI8A5E6VE0kNbVC0+gk+ghUqoRufuopTjnooOariKD59vuTlcV4BiJ1KBlIXa3QNDqJPgKTSgB7BNIi7fdb4Y8ibUnVRCIiomQgIiJKBpKzkR07GAinU9lGo74IWY1noD4AUlcBzg1dM5DcVPoRlICB++6bVD+CqL4IWY1noD4AUldBzg2VDCQ3lX4EZSbfjyCqL0JW4xmoD4DUVZBzQ8lAclPpR9DB5PsRRPVFyGo8A/UBkLoKcm6omkhyU+lH0L9+PUsnWX0T1Rchq/EM1AdA6irIuaFkILnqPuAASuF0Ktto9P6sxjNQHwCpqwDnhqqJREQkvWRgZi83s0Eze8jMHjSzC2uss8jMdpjZveHjirTiERGR+tKsJtoJ/IO732NmLwHuNrPb3X3iTeV/4u6npxiHiIhESK1k4O5b3P2e8PmfgIeBw9La33SSRP+VVukDE9XpLFaHsVb5MEno7YWTTw6meWmn4ymxZXIB2czmAccCd9VY3G1m9wGbgY+7+4NZxFRUSfRfaZU+MFGdzmJ1GGuVD5OE3l5Ytix4ftttwbSnJ9sY2ul4SlNSTwZmtj+wCviouz89YfE9wCvcfczMTgV+ABxRYxs9QA/A7NmzGcqx08bY2Fiu+x8YmEupNJ9y2SiVyvT3j1Iqbaq5br1Ym9lGmgaAElAGSuUy/evXU2piOcDcgQHml0pYuUy5VGK0v59NpYlrJSPtv/1RfX0cCBjgwLa+PjYsXNj0dqYSZ5bHE/L/PsU1LeJ099QewN7ArcBFMdcfBQ5ptE5XV5fnaXBwMNf9Dw+7z5jh3tkZTIeH669bL9ZmtpGm4e3bfcbatd4xOOgz1q714e3bay7vrLM8WCm7D5P6337lSnd44bFy5aQ2M6U4Mz458v4+xdUOcQLrvMFva2olAzMz4OvAw+7+L3XWORT4nbu7mR1PcA3jj2nF1A6S6L/SKn1gojqdxeow1iofJgmVKqFVq2DJkuyriKC9jqc0Jc1qojcC7wLuN7N7w9f+CZgL4O5fA84CPmhmO4E/A+eGGUwaSKL/Sqv0gYnqdBarw1irfJgk9PTkkwSqtdPxlNhSSwbufidB9Wejdf4d+Pe0YhARkXjUA1lERJQMiqidmoH3bt7MxeFURPKjG9UVTDs1A+/dvJllGzcCsC6c9syZk2dIItOWSgYFU5BxMmJZtXVrw3kRyY6SQcEUZJyMWJbMmtVwXkSyo2qigmmnZuCVKqG+jRv5wMKFqiISyZGSQQG1UzPwnjlzWLhxI4uUCERypWoiERFRMhARESWDpoyMBHf8LEL7/sLEOjLC3IGB9ug0kYR26kQihaJrBjFV2veXSvMZGGjt9v2FiTUMdH6pRGsHmpF26kQihaOSQUyV9v3lsrV8+/7CxBoGauVy8TtNJKGdOpFI4SgZxFRp39/RUW759v2FiTUMtNzRUfxOE0lop04kUjhKBjFV2vcvXTra8qX3wsQaBjq6dKmqROCFP9zy5ToekjldM2hCdzeUSpvo7l6QdyiRChNrdzebSiUW6Icv0E6dSKRQVDIQERElAxERUTIQiae3l6Muvhh6eye/DfUhkBamawYiUXp7YdkyDgRYty54rdlxitWHQFqcSgYiUVatAqoG9A7nm6I+BNLilAxEoixZAoBPmG+K+hBIi1M1kUiUsEpoW18fB33gA81XEUF7DUQhbUnJQCSOnh42LFzIoqn8R68+BNLCVE0kIiJKBiIiomQgIiIoGYi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Xv2NoiKUrV6Y3gKTVib5nD3zkI3DTTfDgg5ETZswqVs3/kKiZJIOOHV+QxK3ko9aRVRfugQGoVHYyMLA0/Y11gFhzDRRB1Ak0MMDOSoWlaX8xNjvRV62Cu++GV77yV7MptVjHrGPV/A+JiXvN4Bnu/sY0AhGRkquNfqxWdb/0EmpZMzCzr1KbSLcBdz878YhEpJzqRz/WRjVG1Q6kMKKaif4qkyg6yPj47Jswo9ZxxRWwYQOccw6sXj3zWKWEkjjBoszkBJt+T5SpKbjmGjCDz30unTglUS2TgbtvzCqQTjA+DitWzG6egKh1XHEFfPrTwevasxJCl0jiBIsy0xOs0T1R3IOawbx5OklLIO4trE8ws5vNbJuZfb/2SDu4sslirMKGDa3fSwfLol/9TE6wqDslfuUrs49LUhf3AvJ1wDXAAeBU4J+B69MKqqyyGKtwzjmt30sHy6Jf/UxOsKg7JZahl5bE7lo6193vNDNz98eA/21mm4GrUoytdLIYq1CrbeuaQRfKol99uydYnPunf/e7Qc8i3S+90OImg4qZ9QD/aWYfAHYBR6cXVnllMVZh9Wolga6VRb/6dk6wuHOtqmdR4cVtJroUeDZwCdAPvAN4Z1pBiUgJtDPXqsYdFF7cexP9P3efJJjk5hJ3P8fdv9PqZ8zsWWZ2r5ltNbOHzezjDcocZWY3mtmjZnaPmS2e0V6ISPbamVVJsykVXtzeRKeY2YPAA8CD4Rd8f8SPVYA3uPtJwMnAG83sddPKvBvY5+4vA/4WUOOHSBnMZK5V1Q4KLW4z0RDwPndf7O6LgfcT9DBqKryF9mT49sjwMX0085uBL4WvbwZWmJnFjKktMefaKMQ8GTHmL4m1L8PDi3LdlySO59rduzl961bW7t7dfDsJTEwTtZ3x/fsZDp9nE2vqrriC115wQTBeoJkkZmB6//vhl79sL7Z2awdl+aMtS5xRWk12UHsAWxp8dl+Mn+sF7gcmgdUNlj8EHF/3/nvAMa3WOZPJbdqYa2NWk9skIeb8JbH2Jc/JbdqZd6TZMV2za5czMvLMY82uXYdvJ+bENK1Ebae2jZ4W24gTa+ouv9wdvFo7eS6//PAySczANDbmbtZsAr3Wj5NPPmRVTf+ekvyjTUDp4/ToyW3i9ibaaGZrgC8T/Hf/VmDUzF4TJpT7miSag8DJZtYH/KuZvdLdH2o3YZnZIDAIsHDhQkbbHGwzPLyISmUJ1apRqVQZGtpBpbKz7TIAk5OTbW+/HevWvQp4HmCAs27dPpYteyCVfUlTOzE0O6brpr/fvp1l27cfuh2C9sgqUKlWGdqyhUqbsUZtJ8424sSattcODzOX2pkDPx8e5t4zzjikzKLhYZZUKli1SrVSYcfQEDsrv9qbV61bV3f2wb5163hg2bLD12GGuVPt6WHHypXsfPvb4wda97tu9ruPijNumaSUPc5YWmWK2gMYafG4K+Y6rgIum/bZ7cBA+PoI4MeAtVqPagbt1AwOqmYQg2oGdeLWDBL6T7f0/3GXJU6PrhnESgYzeQALgL7w9VzgW8BZ08q8H/hC+Pp84Kao9c50DuSxMfdPfar17yFOmSzmQl2zxv2005rPkRx3Xy666Hu5zn8cJ0731sd0za5dftr997f8ch2bmPBP7dgxo0QQdztjExN+0chIy23EiTV1l1/uPzvuuMaJoCbqFxN1AsZZR0wt/56S+qNNQCfEmUgyABYCXwRuC9+fCLw74mdeBWwh6IH0EHBV+PkngLPD188CvgI8CtwLLI2KZabJICllmRjbvTyxKs5klSVO9/LE2glxRiWDuNcM/omg99D/Ct9vB24ME0Sz5qcHgFc3+Pyqute/AP4wZgwiIpKSuF1Lj3H3mwiuoeHuB4CDqUUlIiKZipsMfmZmLyAcJxAOHpt5p+6CKkNX4G4TZwxBEuMM4sQRNc4gKo5E9iWJk7SbTvRu2tdZittM9CHgFuClZvZtgovD56UWVQ6ymDdE2jO+fz8rtm5lqlplTk8Pd5500mGT1scpk1QcFWB469YZxZHIvmQxe1In6aZ9TUDcmsFLgTOA3yToDvqfxE8kpZDFvCHSntGJCaaqVQ4CU9UqoxMTMyqTVBzVWcSRyL5kMXtSJ+mmfU1A3GTwMXd/imA01KnAPxJMdtMxspg3RNqzvK+POT099AJzenpY3tc3ozJJxdEzizgS2ZcsZk/qJN20rwmI+9997WLxm4B17v41M/tkSjHlIot5Q6Q9A/Pnc+dJJzE6McHyvr6GzT9xyiQVx9CWLaxs0gwVFUci+5LF7EmdpJv2NQFxk8Gu8HYUvwesNrOjiF+rKI0s5g2R9gzMnx/5BR+nTBJxVMLnmcaRyL5kMXtSJ+mmfZ2luF/obyG4VnC6u08Azwc+nFZQIiKSrVg1A3d/GthQ934PsCetoEREJFsd19QjnSVO3/w4cxGkPQ4hqTiiykTOmTA+zqLh4fT71XdS//0s9qUEx6ujuodKZ4nTN3/t7t1cHN4q+o59+wAYPPbYttYBsKdS4fxt27jxxBN54VFHtR1rEnFElYnaRq1f/ZJKBYaH0+tX30n997PYl5IcL9UMpLDi9M1fv3dvy/dxxyGs2rGDu/fvZ9Vjj80o1iTiiCoTtY1av3qrVtPtV99J/fez2JeSHC8lAymsOH3zz12woOX7OOvYU6lw3Q9/SBW47okneGIGE48kEUdUmaht1PrVV3t60u1X30n997PYl5IcLzUTSWHF6ZtfayZZv3cv5y5YcGizScx1rNqxg2pwS3UOurPqscf4/LTZvaIkEUdUmaht1PrV7xgaYunKlek1RXRS//0s9qUkx0vJQAotTt/8wWOPPfyLMeY6arWCqTAZTLlz3RNP8LGXvKTtaweziSNumahtMDDAzkqFpWl/4XRS//0s9qUEx0vNRNLV6msFNbXagUg3UTKQrjW9VlBTqx3M5NqBSFkpGUhTRegancQYgQu2beMFd9/NBdu2HfJ5o1pBzfTaQZz5DJKQxJwIIjOhawbSUBG6RicxV8EF27Yx/KMfATzzfP2JJzatFdTUXzv4r1/8InI+gyQkMSeCyEypZiANFaFrdBJzFdz25JMN37eqFdTUagdx5jNIQhJzIojMlJKBNFSErtFJzFVwxvOff9j7qFpBTa128Gvz5kXOZ5CEJOZEEJkpNRNJQ0XoGp3EXAXXn3giENQIznj+87n+xBN533e/G1krqDnozm1PPhk5n0ESkpgTQWSmlAykqSJ0jU5iroJaQoDmPYiaqb928HZaz2eQhCTmRBCZCTUTSVeJc61gOo07kG6gZCBdZfypp2LXCmqm3BlTV07pcGomklzV+u8ftX//jJs/xvfvb9mOXr98y6//+oxjHY3oUhUVh3Sx8XHdm0ikmVq/+dn03y9K33yNAZCmijBoJwY1E0lukui/X5S++RoDIE0VYdBODEoGkptav/nZ9N8vSt98jQGQpoowaCcGNRNJbmr95mfTf78offM1BkCaKsKgnRiUDCRXA/PnU2F2/feL0jdfYwCkqSIM2omgZiIREUkvGZjZi81sxMy2mdnDZnZpgzLLzWy/md0fPq5KKx4REWkuzWaiA8Cfuvt9ZvYcYLOZfdPdt00r9y13PyvFOEREJEJqNQN33+Pu94Wvfwo8AhyX1va6SRKTzhRh4hqInjQmzmQunTThy9rduzl961bW7t6dXxBFOTkkU5lcQDazxcCrgXsaLB4ws63AbuAyd384i5jKKonxK0UZAxM16CzOQK5OGuy1dvduLt6+HYA79u0DYPDYY7MNoignh2Qu9WRgZkcD64EPuvtT0xbfB7zE3SfN7Ezg34ATGqxjEBgEWLhwYeRtAdI0OTmZ6/aHhxdRqSyhWjUqlSpDQzuoVHY2LNss1nbWkaZhoAJUgUq1ytCWLVTaWB63TFLS/t2vm/5++3aWhcmhHbOJc9HwMEsqFaxapVqpsGNoiJ0pzgWd999TXF0Rp7un9gCOBG4HPhSz/A7gmFZl+vv7PU8jIyO5bn9szH3uXPfe3uB5bKx52WaxtrOONI1NTPjcjRu9Z2TE527c6GMTEw2X9zZZHrdMUtL+3a/ZtcsZGXnmsWbXrhmtZ1ZxZnxy5P33FFcnxAls8hbfranVDMzMgC8Cj7j73zQp80Lgh+7uZvZagmsYP0krpk6QxPiVooyBiRp0FmcgVycN9qo1Ca3fu5dzFyzIvokIinNySObSbCZ6PfAO4EEzuz/87M+ARQDu/gXgPOC9ZnYA+DlwfpjBpIUkxq8UZQxM1KCzOAO5Ommw1+Cxx+aTBOoV5eSQTKWWDNz9bsAiynwO+FxaMYiISDwagSwiIkoGZdRJ3cDX7t7Nh8NnEcmPblRXMp3UDby+X/2m8Dn39nKRLqWaQcmUZJ6MWNbv3dvyvYhkR8mgZEoyT0Ys5y5Y0PK9iGRHzUQl00ndwGtNQuu2b+c9y5apiUgkR0oGJdRJ3cAHjz2WZdu3s1yJQCRXaiYSERElAxERUTJoy/h4cMfPMvTvL0usUfMZdJtOmptBykXXDGKq9e+vVJYwPFzs/v1liTVqPoNu00lzM0j5qGYQU61/f7Vqhe/fX5ZYRycmmKpWqQJT1SqjExN5h5Sr2vE4iI6HZE/JIKZa//6enmrh+/eXJdblfX3M6emhB5jT08Pyvr68Q8pV7Xj0ouMh2VMyiKnWv3/lyh2FbXapKUustbkIVoKaRPjV8Vi1ZImOh2RO1wzaMDAAlcpOBgaW5h1KpLLEGjWfQbfppLkZpFxUMxARESUDERFRMhCJJYl5FzSGQIpM1wxEIiQx74LGEEjRqWYgEiGJeRc0hkCKTslAJEIS8y5oDIEUnZqJRCIkMe9CbQzB6MQEy/v61EQkhaNkIBJDEvMuaAyBFJmaiURERMlARESUDEREBCUDERFByUBERFAyEBERlAxERAQlAxERQclARERIMRmY2YvNbMTMtpnZw2Z2aYMyZmZ/b2aPmtkDZvaatOIREZHm0rwdxQH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\n" 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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": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "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": [ "
" ] }, "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", 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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]) #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", 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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": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "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 }