[实战] K-means算法 & 二分K-means算法

K-means算法： K-means算法是一个被广泛使用且简单的无监督算法。 K-means算法将数据分为k个簇类，使得每个簇类内部数据尽可能的相似，而簇之间的数据尽可能的不同。 K-means算法中的簇类数目为k,是用户认为给定的。

算法流程： K-means代码：

from numpy import * #加载数据 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 dataMat #计算欧式距离 def distEclud(vecA, vecB): return sqrt(sum(power(vecA - vecB, 2))) #la.norm(vecA-vecB) #随机生成k个质点 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 #K-means算法 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

实验结果：

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由于簇类数目k是用户给定的，并且K-means算法对初始的质点非常的敏感，很容易进入局部最小值。 因此，一开始就随机生成k个质点是存在问题的。 二分K-means算法很好的解决了上述的问题。 二分K-means算法并不一开始就生成k个质点，而是慢慢的增加质点的数目。

二分K-means算法流程： 二分K-means算法代码：

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