15 ML k-means

k-means 为聚类的一种方法，可以根据给定的k个聚点来分类。即计算距离根据最近点的距离来分类。
二分 k-means 用来克服 k-means算法收敛于局部最小值的问题。

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 dataMat

def 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

datMat = mat(loadDataSet('testSet.txt'))
randC = randCent(datMat, 2)
print('randC', randC)
print('max dist', distEclud(datMat[0], datMat[1]))

def kMeans(dataSet, k, distMeas=distEclud, createCent=randCent):
    m = shape(dataSet)[0] # m -> row
    clusterAssment = mat(zeros((m,2)))
    #create mat to assign data points 
    #to a centroid, also holds SE of each point

    # 1.get rand centro
    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
            
            # 2.calc k dist and get min dist
            for j in range(k):
                distJI = distMeas(centroids[j,:],dataSet[i,:])
                if distJI < minDist:
                    minDist = distJI; 
                    minIndex = j

            # 3.no min dist
            if clusterAssment[i,0] != minIndex: 
                clusterChanged = True

            clusterAssment[i,:] = minIndex, minDist**2

        print centroids

        # update centro position
        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

# bisecting k-means
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