python kmeans聚类简单介绍和实现代码

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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