机器学习实战5：k-means聚类：二分k均值聚类+地理位置聚簇实例

原文地址：http://www.cnblogs.com/rongyux/p/5641825.html

k-均值聚类是非监督学习的一种，输入必须指定聚簇中心个数k。k均值是基于相似度的聚类，为没有标签的一簇实例分为一类。

　　一 经典的k-均值聚类　　

　　思路：　　

　　1 随机创建k个质心（k必须指定，二维的很容易确定，可视化数据分布，直观确定即可）；

　　2 遍历数据集的每个实例，计算其到每个质心的相似度，这里也就是欧氏距离；把每个实例都分配到距离最近的质心的那一类，用一个二维数组数据结构保存，第一列是最近质心序号，第二列是距离；

　　3 根据二维数组保存的数据，重新计算每个聚簇新的质心；

　　4 迭代2 和 3，直到收敛，即质心不再变化；

from numpy import *def loadDataSet(fileName):      #general function to parse tab -delimited floats    dataMat = []                #assume last column is target value    fr = open(fileName)    for line in fr.readlines():        curLine = line.strip().split('\t')        fltLine = map(float,curLine) #map all elements to float()        dataMat.append(fltLine)    return dataMatdef distEclud(vecA, vecB):    return sqrt(sum(power(vecA - vecB, 2))) #la.norm(vecA-vecB)def randCent(dataSet, k):    n = shape(dataSet)[1]    centroids = mat(zeros((k,n)))#create centroid mat    for j in range(n):#create random cluster centers, within bounds of each dimension        minJ = min(dataSet[:,j])         rangeJ = float(max(dataSet[:,j]) - minJ)        centroids[:,j] = mat(minJ + rangeJ * random.rand(k,1))    return centroids    def kMeans(dataSet, k, distMeas=distEclud, createCent=randCent):    m = shape(dataSet)[0]    clusterAssment = mat(zeros((m,2)))#create mat to assign data points                                       #to a centroid, also holds SE of each point    centroids = createCent(dataSet, k)    clusterChanged = True    while clusterChanged:        clusterChanged = False        for i in range(m):#for each data point assign it to the closest centroid            minDist = inf; minIndex = -1            for j in range(k):                distJI = distMeas(centroids[j,:],dataSet[i,:])                if distJI < minDist:                    minDist = distJI; minIndex = j            if clusterAssment[i,0] != minIndex: clusterChanged = True            clusterAssment[i,:] = minIndex,minDist**2        print centroids        for cent in range(k):#recalculate centroids            ptsInClust = dataSet[nonzero(clusterAssment[:,0].A==cent)[0]]#get all the point in this cluster            centroids[cent,:] = mean(ptsInClust, axis=0) #assign centroid to mean     return centroids, clusterAssment

　　经典的k均值聚类有很大的缺点就是很容易收敛到局部最优，为了避免这种局部最优，我们引入了二分k-均值算法。

 

　　二 二分k-均值聚类算法

　　二分k-均值聚类算法是基于经典k-均值算法实现的；里面调用经典k-均值（k=2），把一个聚簇分成两个，迭代到分成k个停止；

　　具体思路：

　　1 把整个数据集看成一个聚簇，计算质心；并用同样的数据结构二维数组保存每个实例到质心的距离；

　　2 对每一个聚簇进行2-均值聚类划分；

　　3 计算划分后的误差，选择所有被划分的聚簇中总误差最小的划分保存；

　　4 迭代2 和 3 直到聚簇数目达到k停止；

def biKmeans(dataSet, k, distMeas=distEclud):    m = shape(dataSet)[0]    clusterAssment = mat(zeros((m,2)))    centroid0 = mean(dataSet, axis=0).tolist()[0]    centList =[centroid0] #create a list with one centroid    for j in range(m):#calc initial Error        clusterAssment[j,1] = distMeas(mat(centroid0), dataSet[j,:])**2    while (len(centList) < k):        lowestSSE = inf        for i in range(len(centList)):            ptsInCurrCluster = dataSet[nonzero(clusterAssment[:,0].A==i)[0],:]#get the data points currently in cluster i            centroidMat, splitClustAss = kMeans(ptsInCurrCluster, 2, distMeas)            sseSplit = sum(splitClustAss[:,1])#compare the SSE to the currrent minimum            sseNotSplit = sum(clusterAssment[nonzero(clusterAssment[:,0].A!=i)[0],1])            print "sseSplit, and notSplit: ",sseSplit,'--',sseNotSplit            if (sseSplit + sseNotSplit) < lowestSSE:                bestCentToSplit = i                bestNewCents = centroidMat                bestClustAss = splitClustAss.copy()                lowestSSE = sseSplit + sseNotSplit        bestClustAss[nonzero(bestClustAss[:,0].A == 1)[0],0] = len(centList) #change 1 to 3,4, or whatever        bestClustAss[nonzero(bestClustAss[:,0].A == 0)[0],0] = bestCentToSplit        print 'the bestCentToSplit is: ',bestCentToSplit        print 'the len of bestClustAss is: ', len(bestClustAss)        centList[bestCentToSplit] = bestNewCents[0,:].tolist()[0]#replace a centroid with two best centroids         centList.append(bestNewCents[1,:].tolist()[0])        clusterAssment[nonzero(clusterAssment[:,0].A == bestCentToSplit)[0],:]= bestClustAss#reassign new clusters, and SSE    return mat(centList), clusterAssment

　　三 地理位置聚簇实例

　　地理位置的经纬度正好是二维的，可以可视化出来，所以很适合聚类算法确定质心个数k值；值得注意的是，球面计算距离，不能简单的用欧式距离，而需要用球面距离公式，见函数distSLC；

　　代码的含义给定n个俱乐部地址名称，然后使用urllib包，调用yahoo地图的API返回经纬度，调用我们上面实现的k均值聚类算法，找到聚簇的中心，最后利用matplotlib工具可视化出来；

import urllibimport jsondef geoGrab(stAddress, city):    apiStem = 'http://where.yahooapis.com/geocode?'  #create a dict and constants for the goecoder    params = {}    params['flags'] = 'J'#JSON return type    params['appid'] = 'aaa0VN6k'    params['location'] = '%s %s' % (stAddress, city)    url_params = urllib.urlencode(params)    yahooApi = apiStem + url_params      #print url_params    print yahooApi    c=urllib.urlopen(yahooApi)    return json.loads(c.read())from time import sleepdef massPlaceFind(fileName):    fw = open('places.txt', 'w')    for line in open(fileName).readlines():        line = line.strip()        lineArr = line.split('\t')        retDict = geoGrab(lineArr[1], lineArr[2])        if retDict['ResultSet']['Error'] == 0:            lat = float(retDict['ResultSet']['Results'][0]['latitude'])            lng = float(retDict['ResultSet']['Results'][0]['longitude'])            print "%s\t%f\t%f" % (lineArr[0], lat, lng)            fw.write('%s\t%f\t%f\n' % (line, lat, lng))        else: print "error fetching"        sleep(1)    fw.close()    def distSLC(vecA, vecB):#Spherical Law of Cosines    a = sin(vecA[0,1]*pi/180) * sin(vecB[0,1]*pi/180)    b = cos(vecA[0,1]*pi/180) * cos(vecB[0,1]*pi/180) * \                      cos(pi * (vecB[0,0]-vecA[0,0]) /180)    return arccos(a + b)*6371.0 #pi is imported with numpyimport matplotlibimport matplotlib.pyplot as pltdef clusterClubs(numClust=5):    datList = []    for line in open('places.txt').readlines():        lineArr = line.split('\t')        datList.append([float(lineArr[4]), float(lineArr[3])])    datMat = mat(datList)    myCentroids, clustAssing = biKmeans(datMat, numClust, distMeas=distSLC)    fig = plt.figure()    rect=[0.1,0.1,0.8,0.8]    scatterMarkers=['s', 'o', '^', '8', 'p', \                    'd', 'v', 'h', '>', '<']    axprops = dict(xticks=[], yticks=[])    ax0=fig.add_axes(rect, label='ax0', **axprops)    imgP = plt.imread('Portland.png')    ax0.imshow(imgP)    ax1=fig.add_axes(rect, label='ax1', frameon=False)    for i in range(numClust):        ptsInCurrCluster = datMat[nonzero(clustAssing[:,0].A==i)[0],:]        markerStyle = scatterMarkers[i % len(scatterMarkers)]        ax1.scatter(ptsInCurrCluster[:,0].flatten().A[0], ptsInCurrCluster[:,1].flatten().A[0], marker=markerStyle, s=90)    ax1.scatter(myCentroids[:,0].flatten().A[0], myCentroids[:,1].flatten().A[0], marker='+', s=300)    plt.show()

 

　　四 总结

　　优点：易实现；

　　缺点：可能收敛到局部最小值，在大数据集上收敛较慢；

　　适用数据类型：数值型；