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=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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本文标题: python kmeans聚类简单介绍和实现代码

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