kmeans聚类的简介和代码（python）

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一、k均值聚类的简单介绍：假设样本分为c类，每个类均存在一个中心点，通过随机生成c个中心点进行迭代，计算每个样本点到类中心的距离（可以自定义、常用的是欧式距离）
将该样本点归入到最短距离所在的类，重新计算聚类中心，进行下次的重新划分样本，最终类中心不改变时，聚类完成
二、伪代码

三、代码如下：

 #!/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()

四、结果

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