k-means算法思想较简单，说的通俗易懂点就是物以类聚，花了一点时间在python中实现k-means算法，k-means算法有本身的缺点，比如说k初始位置的选择，针对这个有不少人提出k-means++算法进行改进；另外一种是要对k大小的选择也没有很完善的理论，针对这个比较经典的理论是轮廓系数，二分聚类的算法确定k的大小，在最后还写了二分聚类算法的实现，代码主要参考机器学习实战那本书：

#encoding:utf-8 
''''' 
Created on 2015年9月21日 
@author: ZHOUMEIXU204 
''' 
 
 
path=u"D:\\Users\\zhoumeixu204\\Desktop\\python语言机器学习\\机器学习实战代码  python\\机器学习实战代码\\machinelearninginaction\\Ch20\\" 
import numpy as np 
def loadDataSet(fileName): #读取数据 
  dataMat=[] 
  fr=open(fileName) 
  for line in fr.readlines(): 
    curLine=line.strip().split('\t') 
    fltLine=map(float,curLine) 
    dataMat.append(fltLine) 
  return dataMat 
def distEclud(vecA,vecB):  #计算距离 
  return np.sqrt(np.sum(np.power(vecA-vecB,2))) 
def randCent(dataSet,k):   #构建镞质心 
  n=np.shape(dataSet)[1] 
  centroids=np.mat(np.zeros((k,n))) 
  for j in range(n): 
    minJ=np.min(dataSet[:,j]) 
    rangeJ=float(np.max(dataSet[:,j])-minJ) 
    centroids[:,j]=minJ+rangeJ*np.random.rand(k,1) 
  return centroids 
dataMat=np.mat(loadDataSet(path+'testSet.txt')) 
print(dataMat[:,0]) 
 
 
# 所有数都比-inf大 
# 所有数都比+inf小 
def kMeans(dataSet,k,distMeas=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 #np.inf表示无穷大 
      for j in range(k): 
        distJI=distMeas(centroids[j,:],dataSet[i,:]) 
        if distJI 
          minDist=distJI;minIndex=j 
      if clusterAssment[i,0]!=minIndex:clusterChanged=True 
      clusterAssment[i,:]=minIndex,minDist**2 
    print centroids 
    for cent in range(k): 
      ptsInClust=dataSet[np.nonzero(clusterAssment[:,0].A==cent)[0]] #[0]这里取0是指去除坐标索引值，结果会有两个 
      #np.nonzero函数，寻找非0元素的下标 nz=np.nonzero([1,2,3,0,0,4,0])结果为0,1,2 
      centroids[cent,:]=np.mean(ptsInClust,axis=0) 
     
  return centroids,clusterAssment 
myCentroids,clustAssing=kMeans(dataMat,4)  
print(myCentroids,clustAssing)  
   
#二分均值聚类(bisecting k-means) 
def  biKmeans(dataSet,k,distMeas=distEclud): 
  m=np.shape(dataSet)[0] 
  clusterAssment=np.mat(np.zeros((m,2))) 
  centroid0=np.mean(dataSet,axis=0).tolist()[0] 
  centList=[centroid0] 
  for j in range(m): 
    clusterAssment[j,1]=distMeas(np.mat(centroid0),dataSet[j,:])**2 
  while (len(centList) 
    lowestSSE=np.Inf 
    for i in range(len(centList)): 
      ptsInCurrCluster=dataSet[np.nonzero(clusterAssment[:,0].A==i)[0],:] 
      centroidMat,splitClusAss=kMeans(ptsInCurrCluster,2,distMeas) 
      sseSplit=np.sum(splitClusAss[:,1]) 
      sseNotSplit=np.sum(clusterAssment[np.nonzero(clusterAssment[:,0].A!=i)[0],1]) 
      print "sseSplit, and notSplit:",sseSplit,sseNotSplit 
      if (sseSplit+sseNotSplit) 
        bestCenToSplit=i 
        bestNewCents=centroidMat 
        bestClustAss=splitClusAss.copy() 
        lowestSSE=sseSplit+sseNotSplit 
    bestClustAss[np.nonzero(bestClustAss[:,0].A==1)[0],0]=len(centList) 
    bestClustAss[np.nonzero(bestClustAss[:,0].A==0)[0],0]=bestCenToSplit 
    print "the bestCentToSplit is:",bestCenToSplit 
    print 'the len of bestClustAss is:',len(bestClustAss) 
    centList[bestCenToSplit]=bestNewCents[0,:] 
    centList.append(bestNewCents[1,:]) 
    clusterAssment[np.nonzero(clusterAssment[:,0].A==bestCenToSplit)[0],:]=bestClustAss 
  return centList,clusterAssment 
print(u"二分聚类分析结果开始") 
dataMat3=np.mat(loadDataSet(path+'testSet2.txt')) 
centList,myNewAssments=biKmeans(dataMat3, 3) 
print(centList)