机器学习-python实现kMeans算法

代码及数据集下载：K-means
聚类是一种无监督的学习，将相似的对象放到同一簇中，有点像是全自动分类，簇内的对象越相似，簇间的对象差别越大，则聚类效果越好。
1.k均值聚类算法
k均值聚类将数据分为k个簇，每个簇通过其质心，即簇中所有点的中心来描述。首先随机确定k个初始点作为质心，然后将数据集分配到距离最近的簇中。然后将每个簇的质心更新为所有数据集的平均值。然后再进行第二次划分数据集，直到聚类结果不再变化为止。
伪代码为

随机创建k个簇质心当任意一个点的簇分配发生改变时：    对数据集中的每个数据点：        对每个质心：            计算数据集到质心的距离        将数据集分配到最近距离质心对应的簇    对每一个簇，计算簇中所有点的均值并将均值作为质心

python实现

import numpy as npimport matplotlib.pyplot as pltdef loadDataSet(fileName):      dataMat = []     with open(fileName) as f:        for line in f.readlines():            line = line.strip().split('\t')            dataMat.append(line)    dataMat = np.array(dataMat).astype(np.float32)    return dataMatdef distEclud(vecA,vecB):    return np.sqrt(np.sum(np.power((vecA-vecB),2)))def randCent(dataSet,k):    m = np.shape(dataSet)[1]    center = np.mat(np.ones((k,m)))    for i in range(m):        centmin = min(dataSet[:,i])        centmax = max(dataSet[:,i])        center[:,i] = centmin + (centmax - centmin) * np.random.rand(k,1)    return centerdef kMeans(dataSet,k,distMeans = distEclud,createCent = randCent):    m = np.shape(dataSet)[0]    clusterAssment = np.mat(np.zeros((m,2)))    centroids = createCent(dataSet,k)    clusterChanged = True    while clusterChanged:        clusterChanged = False        for i in range(m):            minDist = np.inf            minIndex = -1            for j in range(k):                distJI = distMeans(dataSet[i,:],centroids[j,:])                if distJI < minDist:                    minDist = distJI                    minIndex = j            if clusterAssment[i,0] != minIndex:                clusterChanged = True            clusterAssment[i,:] = minIndex,minDist**2        for cent in range(k):            ptsInClust = dataSet[np.nonzero(clusterAssment[:,0].A == cent)[0]]            centroids[cent,:] = np.mean(ptsInClust,axis = 0)    return centroids,clusterAssmentdata = loadDataSet('testSet.txt')muCentroids, clusterAssing = kMeans(data,4)fig = plt.figure(0)ax = fig.add_subplot(111)ax.scatter(data[:,0],data[:,1],c = clusterAssing[:,0].A)plt.show()print(clusterAssing)

2.二分k均值算法
K均值算法可能会收敛到局部最小值，而非全局最小。一种用于度量聚类效果的指标为误差平方和（SSE）。因为取了平方，更加重视原理中心的点。为了克服k均值算法可能会收敛到局部最小值的问题，有人提出来二分k均值算法。
首先将所有点作为一个簇，然后将该簇一分为二，然后选择所有簇中对其划分能够最大程度减低SSE的值的簇，直到满足指定簇数为止。
伪代码

将所有点看成一个簇计算SSEwhile 当簇数目小于k时：    for 每一个簇：        计算总误差        在给定的簇上进行k均值聚类(k=2)        计算将该簇一分为二的总误差    选择使得误差最小的那个簇进行划分操作

import numpy as npimport matplotlib.pyplot as pltdef loadDataSet(fileName):      dataMat = []     with open(fileName) as f:        for line in f.readlines():            line = line.strip().split('\t')            dataMat.append(line)    dataMat = np.array(dataMat).astype(np.float32)    return dataMatdef distEclud(vecA,vecB):    return np.sqrt(np.sum(np.power((vecA-vecB),2)))def randCent(dataSet,k):    m = np.shape(dataSet)[1]    center = np.mat(np.ones((k,m)))    for i in range(m):        centmin = min(dataSet[:,i])        centmax = max(dataSet[:,i])        center[:,i] = centmin + (centmax - centmin) * np.random.rand(k,1)    return centerdef kMeans(dataSet,k,distMeans = distEclud,createCent = randCent):    m = np.shape(dataSet)[0]    clusterAssment = np.mat(np.zeros((m,2)))    centroids = createCent(dataSet,k)    clusterChanged = True    while clusterChanged:        clusterChanged = False        for i in range(m):            minDist = np.inf            minIndex = -1            for j in range(k):                distJI = distMeans(dataSet[i,:],centroids[j,:])                if distJI < minDist:                    minDist = distJI                    minIndex = j            if clusterAssment[i,0] != minIndex:                clusterChanged = True            clusterAssment[i,:] = minIndex,minDist**2        for cent in range(k):            ptsInClust = dataSet[np.nonzero(clusterAssment[:,0].A == cent)[0]]            centroids[cent,:] = np.mean(ptsInClust,axis = 0)    return centroids,clusterAssmentdef biKmeans(dataSet,k,distMeans = distEclud):    m = np.shape(dataSet)[0]    clusterAssment = np.mat(np.zeros((m,2)))    centroid0 = np.mean(dataSet,axis=0).tolist()    centList = [centroid0]    for j in range(m):        clusterAssment[j,1] = distMeans(dataSet[j,:],np.mat(centroid0))**2    while (len(centList)<k):        lowestSSE = np.inf        for i in range(len(centList)):            ptsInCurrCluster = dataSet[np.nonzero(clusterAssment[:,0].A == i)[0],:]            centroidMat,splitClustAss = kMeans(ptsInCurrCluster,2,distMeans)            sseSplit = np.sum(splitClustAss[:,1])            sseNotSplit = np.sum(clusterAssment[np.nonzero(clusterAssment[:,0].A != i)[0],1])            if (sseSplit + sseNotSplit) < lowestSSE:                bestCentToSplit = i                bestNewCents = centroidMat.copy()                bestClustAss = splitClustAss.copy()                lowestSSE = sseSplit + sseNotSplit        print('the best cent to split is ',bestCentToSplit)#        print('the len of the bestClust')        bestClustAss[np.nonzero(bestClustAss[:,0].A == 1)[0],0] = len(centList)        bestClustAss[np.nonzero(bestClustAss[:,0].A == 0)[0],0] = bestCentToSplit        clusterAssment[np.nonzero(clusterAssment[:,0].A == bestCentToSplit)[0],:] = bestClustAss.copy()        centList[bestCentToSplit] = bestNewCents[0,:].tolist()[0]        centList.append(bestNewCents[1,:].tolist()[0])    return np.mat(centList),clusterAssmentdata = loadDataSet('testSet2.txt')muCentroids, clusterAssing = biKmeans(data,3)fig = plt.figure(0)ax = fig.add_subplot(111)ax.scatter(data[:,0],data[:,1],c = clusterAssing[:,0].A,cmap=plt.cm.Paired)ax.scatter(muCentroids[:,0],muCentroids[:,1])plt.show()print(clusterAssing)print(muCentroids)