一、k均值聚類的簡單介紹

假設樣本分為c類，每個類均存在一個中心點，通過隨機生成c個中心點進行迭代，計算每個樣本點到類中心的距離（可以自定義、常用的是歐式距離）  

將該樣本點歸入到最短距離所在的類，重新計算聚類中心，進行下次的重新劃分樣本，最終類中心不改變時，聚類完成   

二、偽代碼  

三、python代碼實現  

#!/usr/bin/env python # coding=utf-8  import numpy as np import random import matplotlib.pyplot as plt  #data:numpy.array dataset #k the number of cluster def k_means(data,k):      #random generate cluster_center   sample_num=data.shape[0]   center_index=random.sample(range(sample_num),k)   cluster_cen=data[center_index,:]    is_change=1   cat=np.zeros(sample_num)       while is_change:     is_change=0      for i in range(sample_num):       min_distance=100000       min_index=0        for j in range(k):         sub_data=data[i,:]-cluster_cen[j,:]         distance=np.inner(sub_data,sub_data)         if distance<min_distance:           min_distance=distance           min_index=j+1        if cat[i]!=min_index:         is_change=1         cat[i]=min_index     for j in range(k):       cluster_cen[j]=np.mean(data[cat==(j+1)],axis=0)    return cat,cluster_cen   if __name__=='__main__':    #generate data   cov=[[1,0],[0,1]]   mean1=[1,-1]   x1=np.random.multivariate_normal(mean1,cov,200)    mean2=[5.5,-4.5]   x2=np.random.multivariate_normal(mean2,cov,200)    mean3=[1,4]   x3=np.random.multivariate_normal(mean3,cov,200)    mean4=[6,4.5]   x4=np.random.multivariate_normal(mean4,cov,200)    mean5=[9,0.0]   x5=np.random.multivariate_normal(mean5,cov,200)      X=np.vstack((x1,x2,x3,x4,x5))      #data distribution   fig1=plt.figure(1)   p1=plt.scatter(x1[:,0],x1[:,1],marker='o',color='r',label='x1')   p2=plt.scatter(x2[:,0],x2[:,1],marker='+',color='m',label='x2')   p3=plt.scatter(x3[:,0],x3[:,1],marker='x',color='b',label='x3')   p4=plt.scatter(x4[:,0],x4[:,1],marker='*',color='g',label='x4')   p5=plt.scatter(x5[:,0],x4[:,1],marker='+',color='y',label='x5')   plt.title('original data')   plt.legend(loc='upper right')      cat,cluster_cen=k_means(X,5)       print 'the number of cluster 1:',sum(cat==1)   print 'the number of cluster 2:',sum(cat==2)   print 'the number of cluster 3:',sum(cat==3)   print 'the number of cluster 4:',sum(cat==4)   print 'the number of cluster 5:',sum(cat==5)       fig2=plt.figure(2)   for i,m,lo,label in zip(range(5),['o','+','x','*','+'],['r','m','b','g','y'],['x1','x2','x3','x4','x5']):      p=plt.scatter(X[cat==(i+1),0],X[cat==(i+1),1],marker=m,color=lo,label=label)   plt.legend(loc='upper right')   plt.title('the clustering result')   plt.show() 

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