{ "cells": [ { "cell_type": "markdown", "id": "f5eabe66", "metadata": {}, "source": [ "Title: The k-means Algorithm\n", "Author: Thomas Breuel\n", "Institution: UniKL" ] }, { "cell_type": "code", "execution_count": 2, "id": "d16a6715", "metadata": { "collapsed": true }, "outputs": [], "source": [ "\n", "from pylab import *\n", "import random as pyrandom\n", "from scipy.spatial.distance import cdist" ] }, { "cell_type": "markdown", "id": "0a36a5b6", "metadata": {}, "source": [ "# Mixture Densities" ] }, { "cell_type": "markdown", "id": "14705633", "metadata": {}, "source": [ "Consider a collection of points that are sampled from three different densities,\n", "in this case normal densities with the same covariances but different means.\n", "\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "b87b2dd0", "metadata": { "collapsed": true }, "outputs": [], "source": [ "data = r_[10*randn(1000,2)+array([70,30]),\n", " 10*randn(1000,2)+array([10,10]),\n", " 10*randn(1000,2)+array([50,80])]\n", "data = data[pyrandom.sample(xrange(len(data)),len(data))]" ] }, { "cell_type": "markdown", "id": "b6aadf0e", "metadata": {}, "source": [ "Here is a scatterplot of this data.\n", "\n", "We clearly see three _clusters_, corresponding to the three _mixture components_.\n", "How can we recover these clusters?\n", "\n", "This is the job of _clustering algorithms_.\n", "One of the most useful clustering algorithms is the _k-means_ algorithm" ] }, { "cell_type": "code", "execution_count": 4, "id": "e946ddd1", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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S9tej1XSCzsND1xnrbPHaAhULINflhwSfFkoQC3bEXKvlA8iR1HR52bXn/Hlf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+fbtzdbezQhi5O1zMTl/6rVXB1Wr3aCaHo6el9vhj03F4kqLfisO+0Xv3ArDA8fdiJuxQqRo0dF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\nPSi4CCGEVBUKLrKko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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(10,10)\n", "plot(data[:,0],data[:,1],'b+')" ] }, { "cell_type": "markdown", "id": "e4478ef3", "metadata": {}, "source": [ "Mixture densities arise in both unsupervised learning and in supervised learning.\n", "In both cases, they commonly represent a problem structure in which data is\n", "generated from a number of ideal prototypes (the cluster centers) but then\n", "corrupted by noise.\n", "\n", "- When each cluster has a distinct class label, we have a regular classification\n", "problem with normal densities.\n", "\n", "- When no cluster has any labels, we can hope to recover the underlying\n", "clusters with a clustering algorithm and then assign labels to these clusters.\n", "This is a form of _semi-supervised learning_.\n", "\n", "- When there is training data with labels available, often each class is\n", "a mixture of multiple clusters. That is, each class is generated by multiple\n", "prototypes (think characters in different fonts).\n", "You can perform clustering either at th\n", "class level or across all samples and then label each cluster with its\n", "corresponding class label." ] }, { "cell_type": "markdown", "id": "db8ffc86", "metadata": {}, "source": [ "k-Means Algorithm\n", "=================" ] }, { "cell_type": "markdown", "id": "cc7e8cfd", "metadata": {}, "source": [ "(: EM Algorithms )\n", "\n", "Expectation Maximization (EM) algorithm:\n", "\n", "- solution depends on hidden information (cluster asignment)\n", "- guess an initial solution (guess can be random)\n", "- update the guess based on the data\n", "- repeat until convergence" ] }, { "cell_type": "markdown", "id": "5db24dea", "metadata": {}, "source": [ " The _k-means algorithm_ is an example of an expectation maximization algorithm.\n", "Such algorithms generally have a form in which we need to find some parameters,\n", "but in order to find those parameters, we need to know some other values that\n", "we can't observe directly.\n", "\n", "In this case, we want to find the cluster centers (`protos` array), but\n", "in order to compute the cluster center for each cluste, we would have to\n", "know what cluster each data point belongs do, which we don't." ] }, { "cell_type": "code", "execution_count": 5, "id": "4f50f23a", "metadata": { "collapsed": true }, "outputs": [], "source": [ "# starting guess\n", "protos = array([[30,30],[40,20],[0,90],[50,50]])\n", "start = protos.copy()" ] }, { "cell_type": "code", "execution_count": 6, "id": "5a3d5754", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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mjVq3JfZFZqQVf/p90tYxa4nUrlXtZtaxdwsLyWLcWksptAgZDhRchNSQONcc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KAAAg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\n/e7dkYvTVzefYEOwv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mHbZSOpvdiWYYrQLIWsUrSE8neB8fFxefzxx+Wb3/zmiffS5u/q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\nMhRchBBCCCEl8/8BfNT4bz5P1hQAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plotting the starting guess\n", "figsize(10,10)\n", "plot(data[:,0],data[:,1],'b+')\n", "plot(protos[:,0],protos[:,1],'ro',markersize=10)" ] }, { "cell_type": "markdown", "id": "6dab175f", "metadata": {}, "source": [ "(update)\n", "\n", "Obviously, those centers are wildly wrong, but let's keep going.\n", "\n", "Now, we compute the assignment of the data points to the prototypes\n", "(array `closest`).\n", "\n", "This is also wildly wrong, but we're going to be using it anyay." ] }, { "cell_type": "code", "execution_count": 7, "id": "25a7e8e7", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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xP3/KpO1kHYIWa8ePr6JW8xpii09WJuPg5s1Nk6KUovVC4Wyr9dDpDhGoi/n1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\nCOkPCi5CRkg3DZYFFj33T9R9H4WoiDJ47YdpFkn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BPIuHmZkM7t1rtoTXFWQy70K1utqx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\ncSfGCdHEcWaRzIZBMkOiMHG+spkNXZ+0n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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "# k-means update\n", "figsize(10,10)\n", "dists = cdist(protos,data)\n", "closest = argmin(dists,axis=0)\n", "for i in range(len(protos)):\n", " plot(data[closest==i,0],data[closest==i,1],['c+','g+','b+','y+'][i])\n", "plot(protos[:,0],protos[:,1],'ro',markersize=10)" ] }, { "cell_type": "code", "execution_count": 8, "id": "0c334862", "metadata": { "collapsed": true }, "outputs": [], "source": [ "\n", "history = [protos.copy()]\n", "\n", "for i in range(len(protos)):\n", " protos[i,:] = average(data[closest==i],axis=0)\n", " \n", "history.append(protos.copy())" ] }, { "cell_type": "markdown", "id": "2cc8b91a", "metadata": {}, "source": [ "Now we pretend that the cluster assignments are correct and\n", "recompute the location of the centers.\n" ] }, { "cell_type": "code", "execution_count": 106, "id": "a13b0f19", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 106, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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iuVQUXGSjQ8FFSJewb5pR6wnGZcuW+P1PTibv67LLmpPKtfiTWlQHDwI7djTn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\nLeRcJIwqEwBcNblEBGrEOaxUmheMlnOyRVgS2vm50M68M1IcKLj6hCT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Xxw2Xz5tybGEn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\nF7oUQ2D8EiGEEELSgIIrhEYUX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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(10,10)\n", "plot(data[:,0],data[:,1],'b+')\n", "harray = array(history)\n", "for i in range(len(protos)):\n", " plot(harray[:,i,0],harray[:,i,1],'r')\n", "plot(harray[0,:,0],harray[0,:,1],'ko',markersize=10)\n", "plot(protos[:,0],protos[:,1],'ro',markersize=10)" ] }, { "cell_type": "markdown", "id": "ae70d366", "metadata": {}, "source": [ "As you can see, the centers have moved, and it looks like they have generally moved in the right direction. Now let's just repeat this process multiple times.\n", "\n" ] }, { "cell_type": "code", "execution_count": 107, "id": "f4a52927", "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "0 100 200 300 400 500 600 700 800 900 " ] } ], "source": [ "for round in range(1000):\n", " if round%100==0: sys.stderr.write(\"%d \"%round)\n", " dists = cdist(protos,data)\n", " closest = argmin(dists,axis=0)\n", " for i in range(len(protos)):\n", " protos[i,:] = average(data[closest==i],axis=0)\n", " history.append(protos.copy())" ] }, { "cell_type": "markdown", "id": "68409dfa", "metadata": {}, "source": [ "We can now plot the path that the prototype guesses have taken.\n", "\n" ] }, { "cell_type": "code", "execution_count": 108, "id": "7ebaea52", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 108, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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7pYWniLEzzjDjOXIEeOop4OSTzTV45SuBvXvN8ZWKGWehEIg1CUPK2o9DQ6Y/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\nvnvmBVnAXCLBThIa5hLUddl5q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b349re/jaeeegqLFy/G9OnT8fTTT+OMM87A4sWLy93U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\nCCGEEEIShoKLEEIIISRh/n9kCWcVt5l5SwAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(10,10)\n", "plot(data[:,0],data[:,1],'b+')\n", "history = array(history)\n", "for i in range(len(protos)):\n", " plot(history[:,i,0],history[:,i,1],'r')\n", "plot(history[0,:,0],history[0,:,1],'ko',markersize=10)\n", "plot(protos[:,0],protos[:,1],'ro',markersize=10)" ] }, { "cell_type": "markdown", "id": "10c9d8f7", "metadata": {}, "source": [ "As you can see, the final location of the prototype centers (red) are nicely\n", "in the center of the classes.\n", "\n", "The algorithm doesn't give us exactly the cluster centers because there are\n", "three clusters but we postulated four cluster centers." ] }, { "cell_type": "code", "execution_count": 110, "id": "68a4a6f8", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 110, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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F5Po8EVxANH2oI2zmmHmxzTFuIYJeiSljard3s73tvmZNd45D/RkhJBkKLkLGjEFGLPJE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\n0c7MdtVU9brgEo+j1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YUFdQxvFeR3bYlUCYIgCF6I4NLotNobHj3i9gknqiKPXNDp/VzV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\nXEREREQLxsJFREREtGBvhD6T5idQi6IAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(10,10)\n", "dists = cdist(protos,data)\n", "closest = argmin(dists,axis=0)\n", "for i in range(len(protos)):\n", " plot(data[closest==i,0],data[closest==i,1],['c+','g+','b+','y+'][i])\n", "plot(protos[:,0],protos[:,1],'ro',markersize=10)" ] }, { "cell_type": "code", "execution_count": 109, "id": "90ac8dd7", "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": {}, "nbformat": 4, "nbformat_minor": 5 }