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、python代码实现

#!/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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