机器学习之经典算法（十七）二分Kmeans算法

（1）      二分Kmeans算法简介：

二分KMeans(Bisecting KMeans)是基于KMeans算法之上，KMeans聚类结果易受到初始聚类中心点选择的影响。如果不需要选取初始值呢。二分KMeans克服初始中心点影响，各簇中心点的距离较远，这就完全避免了初始聚类中心会选到一个类别上，一定程度上克服了算法陷入局部最优状态。

基本思想：首先将所有点作为一个簇，然后将该簇一分为二，每次选择能最大限度降低聚类代价函数（也就是误差平方和）的簇划分为两个簇（不管是否刚才是否已经分裂过）。以此进行下去，直到簇的数目等于用户给定的数目k为止。那么，如何选择某簇进行分裂呢。那就只能用聚类的性能指标来衡量：误差平方和。搜索当前簇分类，选择分类误差平方和最小的，因为聚类的误差平方和越小表示数据点越接近于他们的质心，聚类效果就越好。

算法流程：

初始化簇表，使之包含由所有的点组成的簇（初始为一簇）。

while（簇数未达到用户指定数目）：

  从簇表中取出一个簇。

  {对选定的簇进行多次二分探试}

  for i in range(探试次数):

      使用基本k均值，二分选定的簇。

  从二分试验中选择具有最小误差的两个簇。

  将这两个簇添加到簇表中。

缺点：

二分k均值建立在k均值算法基础之上，相对于传统k均值，复杂度高，需要不断地搜索分类方式，当样本数量大，该方法不太适用。

（2）   二分k均值代码实现：

from numpy import *

import numpy as np

import matplotlib.pyplot as plt

def loadDataSet(fileName):      #general function to parse tab -delimitedfloats

   dataMat = []               #assume last column is target value

   fr = open(fileName)

   for line in fr.readlines():

        curLine = [float(y) for y inline.strip().split(',')]

       dataMat.append(curLine)

   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 eachdimension

       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

                                     #toa 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 allthe point in this cluster

           centroids[cent,:] = mean(ptsInClust, axis=0) #assign centroid to mean

   return centroids, clusterAssment

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],:]#getthe data points currently in cluster i

           centroidMat, splitClustAss = kMeans(ptsInCurrCluster, 2, distMeas)

           sseSplit = sum(splitClustAss[:,1])#compare the SSE to the currrentminimum

           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 acentroid 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

# show your cluster only available with 2-Ddata

def showCluster(dataSet, k, centroids,clusterAssment):

   numSamples, dim = dataSet.shape

   if dim != 2:

       print("I can not draw !")

       return 1

   mark = ['or', 'ob', 'og', 'ok', '^r', '+r', 'sr', 'dr', '<r', 'pr']

   if k > len(mark):

       print("Sorry!")

       return 1

    #draw all samples

   for i in range(numSamples):

       markIndex = int(clusterAssment[i, 0])

       plt.plot(dataSet[i, 0], dataSet[i, 1], mark[markIndex])

   mark = ['Dr', 'Db', 'Dg', 'Dk', '^b', '+b', 'sb', 'db', '<b', 'pb']

    #draw the centroids

   for i in range(k):

       plt.plot(centroids[i, 0], centroids[i, 1], mark[i], markersize = 12)

   plt.show()

if __name__=='__main__':

   datMat = mat(loadDataSet('d:\\test.txt'))

   myCentList,myNewAssment = biKmeans(datMat,2)

   print ("centers：",myCentList,myNewAssment)  

（3）   二分k均值应用举例：

测试代码：

import biKmeans as bT

from numpy import *

import time

import matplotlib.pyplot as plt

## step 1: load data

dataSet = []

fileIn = open('d:\\testSet.txt')

for line in fileIn.readlines():

   lineArr = line.strip().split('\t')

   dataSet.append([float(lineArr[0]), float(lineArr[1])])

## step 2: train

dataSet = mat(dataSet)

k = 4

centroids, clusterAssment =bT.biKmeans(dataSet, k)

## step 3: the result

bT.showCluster(dataSet,k, centroids, clusterAssment)

效果如下：

 部分代码参考《机器学习实战》源代码。

原文出处