本文共 8109 字，大约阅读时间需要 27 分钟。

一句话总结，即将数据集分为k个类别。原理：1、首先选取k个初始点作为中心；然后遍历所有的点，对于每一个点，计算k个中心中到这个点距离最小的中心，然后将这个点划分到这个中心；3、当所有的点划分完毕，重新计算类别的计算中心（将均值作为中心），直到中心点不再变化。但是这种方式可能陷入局部最小解，为了克服这个缺陷，提出了二分k-means算法，这种方式类似于二分法。即先划分两类，然后，再将其中一类划分为两类，这样就扩展到三类，一次类推。对于到底选取哪一类进行扩张，衡量刻度是到质心的总距离，选取最小的那一个。

---

一、应用场景

这是一种无监督的学习，一般用来划分，实际生活中常常遇到，比如村落的划分，经常是把村落聚集的一个划分为一个村落。同样比如美国的大选，对于某一些地区的选民，很显然有一部分选民很大程度上是一致的态度，如果能找到他们这一个群里，汇集起来，就可以专门针对，来进行宣传。同样，对于推荐系统等，找到某一类共同特制的人群，也可以进行定点推销。

---

二、聚类算法

由于原理简单，只是动手做了原理部分，没有亲自实现案列部分。 代码：kMeans.py

""" @author: zoutai@file: kMeans.py @time: 2017/11/20 @description: K-均值聚类"""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 = list(map(float,curLine)) #map all elements to float()        dataMat.append(fltLine)    return dataMat# 距离计算函数：欧氏距离def distEclud(vecA,vecB):    return sqrt(sum(power(vecA-vecB,2)))def randCent(dataSet,k):    n = shape(dataSet)[1]    centroids = mat(zeros((k,n)))    for j in range(n):        minJ = min(dataSet[:,j])        rangJ = float(max(dataSet[:,j])-minJ)        centroids[:,j] = minJ + rangJ * random.rand(k,1) # 随机数范围0-1，矩阵为k*1    return centroids#def kMeans(dataSet,k,distMeas=distEclud,createCent=randCent):    m = shape(dataSet)[0]    clusterAssment = mat(zeros((m,2)))    centroids = createCent(dataSet,k)    clusterChanged = True    while clusterChanged:        clusterChanged = False        for i in range(m):            minDist = inf;minIndex = -1            for j in range(k):                distJI = distEclud(centroids[j,:],dataSet[i,:])                if distJI < minDist:                    minDist = distJI                    minIndex = j            # 是否更新质心，重新扫描。（即如果全部的点最后都不改变了，则停止学习）            if clusterAssment[i,0] != minIndex:                clusterChanged = True            clusterAssment[i,:] = minIndex,minDist**2 # 记录点所属的簇        print(centroids)        # 更新质心        for cent in range(k):            ptsInClust = dataSet[nonzero(clusterAssment[:,0]==cent)[0]] # 第cent簇的点集合            centroids[cent,:] = mean(ptsInClust,axis=0) #取均值作为质心    return centroids,clusterAssmentdef biKmeans(dataSet,k,disMeas=distEclud):    m = shape(dataSet)[0]    clusterAssment = mat(zeros((m,2)))    # 1，先求出所有点的质心    centroid0 = mean(dataSet,axis=0).tolist()[0]    centList = [centroid0] # 保存所有的质心    # 遍历，求出每个点到质心的距离^2    for j in range(m):        clusterAssment[j,1] = distEclud(mat(centroid0),dataSet[j,:])**2 # ^2是错误的    while len(centList) < k:        lowestSSE = inf        # 2,接下来，对已经划分完成的，尝试将每一个k类二次划分，找出最好的，就相当于增加了一个类        for i in range(len(centList)):            ptsInCurrCluster = dataSet[nonzero(clusterAssment[:,0].A==i)[0],:] # 生成所有第i类的数据集datasetI            # 不知道哪里逻辑错了，这里需要判断空            if len(ptsInCurrCluster)==0:                continue            centroidIMat,splitClustAss = kMeans(ptsInCurrCluster,2,disMeas) # 求出新的子划分            # 计算新的总误差大小：sum = 1第I个新的子划分+2（原始的划分-第I个划分）            # 1.第I个新的子划分误差            firstSplit = sum(splitClustAss[:,1])            secondSplit = sum(clusterAssment[nonzero(clusterAssment[:,0].A != i)[0],1])            print("firstSplit is :",firstSplit,"secondSplit is ；",secondSplit)            # 如果小于原始误差，则划分保存            if firstSplit + secondSplit < lowestSSE:                bestCentToSplit = i                bestNewCents = centroidIMat                bestClustAss = splitClustAss.copy()                lowestSSE = firstSplit+secondSplit        # 更新分配结果，将上面得到的最好结果保存:        # 将新划分的两类划分给原始集合：第一类划分下标为被分解的簇bestCentToSplit，第二类，为新的簇，即len(centList)        bestClustAss[nonzero(bestClustAss[:,0].A == 0)[0],0] = bestCentToSplit        bestClustAss[nonzero(bestClustAss[:,0].A == 1)[0],0] = len(centList)        print("the bestCentToSplit is",bestCentToSplit)        # 将第bestCentToSplit个修改；增加另外一个        centList[bestCentToSplit] = bestNewCents[0,:]        centList.append(bestNewCents[1,:])        # 赋均值        clusterAssment[nonzero(clusterAssment[:,0].A == bestCentToSplit)[0],:] = bestClustAss    return centList,clusterAssmentimport 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(lineArr[0], lat, lng)            fw.write(line,'\t', lat,'\t', lng,'\n')        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):    numClust = numClust+1 # 不知道哪里逻辑错了，必须+1，最后会有一个空集    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, disMeas=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)    newDataSet = zeros((len(myCentroids),2))    newDataSet = [list(array(myCentroids[i])[0]) for i in range(len(myCentroids))]    ax1.scatter(mat(newDataSet)[:, 0].flatten().A[0], mat(newDataSet)[:, 1].flatten().A[0], marker='+', s=300)    plt.show()

画图代码：plotTest.py

""" @author: zoutai@file: plotTest.py @time: 2017/11/22 @description: """# 画这个图费了好长时间，主要的问题还是在于各种数据类型的转换和匹配，真是想说python真是个垃圾语言，对初学者很难适应import matplotlib.pyplot as pltfrom numpy import *def plotGraph(dataSet,centList):    fig = plt.figure()    ax = fig.add_subplot(111)    newDataSet = zeros((len(centList),2))    newDataSet = [list(array(centList[i])[0]) for i in range(len(centList))]    # for i in range(len(centList)):    #     newDataSet.(array(centList[i])[0])    newMat = mat(newDataSet)    print(newMat)    # ax.plot(dataSet[:,0],dataSet[:,1],marker = 'x')    # ax.plot(centList[:,0],centList[:,1],marker = '+',color='r')    ax.scatter(dataSet[:,0].flatten().A[0],dataSet[:,1].flatten().A[0],marker='^',s=90)    ax.scatter(newMat[:,0].flatten().A[0],newMat[:,1].flatten().A[0],marker='o',s=90)    plt.show()

测试代码：test.py

""" @author: zoutai@file: test.py @time: 2017/11/21 @description: """from unit10.kMeans import *from unit10.plotTest import *from numpy import *# test1dataMat = mat(loadDataSet('testSet.txt'))myCentroids,clustAssing = kMeans(dataMat,4)print(myCentroids)# test2# dataMat3 = mat(loadDataSet('testSet2.txt'))# centList,newAssment = biKmeans(dataMat3,3)# print(centList)# plotGraph(dataMat3,centList)# # dataLast = row_stack(dataMat3,mat(centList))# print(centList)# test3clusterClubs(5)