kmeans聚类的简介和代码（python）

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-8import numpy as npimport randomimport matplotlib.pyplot as plt#data:numpy.array dataset#k the number of clusterdef 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_cenif __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()