K-means of prototype clustering algorithm

table of Contents

1 Introduction

"Prototype" refers to a representative point in the sample space. Prototype clustering can be described as classifying representative points in the sample space, that is, removing some abnormal points or noise points in the sample space.

k-means is an unsupervised learning algorithm with good clustering effect and wide application.

2. Principle

3. Algorithm steps

4. MATLAB code

% k均值算法的MATLAB实现
clear all;
close all;
clc;
tic;
% 第一组数据
mu1=[0 0 ];  %均值
S1=[.1 0 ;0 .1];  %协方差
data1=mvnrnd(mu1,S1,100);   %产生高斯分布数据
%第二组数据
mu2=[1.25 1.25 ];
S2=[.1 0 ;0 .1];
data2=mvnrnd(mu2,S2,100);
% 第三组数据
mu3=[-1.25 1.25 ];
S3=[.1 0 ;0 .1];
data3=mvnrnd(mu3,S3,100);
% 显示数据
plot(data1(:,1),data1(:,2),'b+');
hold on;
plot(data2(:,1),data2(:,2),'r+');
plot(data3(:,1),data3(:,2),'g+');
grid on;
%  三类数据合成一个不带标号的数据类
data=[data1;data2;data3]; 
N=3;%设置聚类数目
[m,n]=size(data);
pattern=zeros(m,n+1);
center=zeros(N,n);%初始化聚类中心
pattern(:,1:n)=data(:,:);
for x=1:N
    center(x,:)=data( randi(300,1),:);%第一次随机产生聚类中心
end
while 1
distence=zeros(1,N);
num=zeros(1,N);
new_center=zeros(N,n);
 
for x=1:m
    for y=1:N
    distence(y)=norm(data(x,:)-center(y,:));%计算到每个类的距离
    end
    [~, temp]=min(distence);%求最小的距离
    pattern(x,n+1)=temp;   % 变量pattern的第三列存放数据的类别标签     
end
k=0;
for y=1:N
    for x=1:m
        if pattern(x,n+1)==y
           new_center(y,:)=new_center(y,:)+pattern(x,1:n);    % 将对应类别的样本数据累加 
           num(y)=num(y)+1;
        end
    end
    new_center(y,:)=new_center(y,:)/num(y);           % 将对应类别的样本数据累加后，除以类别中样本的数量，得到新的聚类中心，即样本数据的均值
    if norm(new_center(y,:)-center(y,:))<0.1    % 当聚类中心变化的范围小于阈值0.1时，k值加1
        k=k+1;
    end
end
if k==N
     break;         % 直到k值等于聚类数N时，跳出while循环
else
     center=new_center;  % 更新聚类中心  
end
end
[m, n]=size(pattern);   
 
%最后显示聚类后的数据
figure;
hold on;
for i=1:m
    if pattern(i,n)==1 
         plot(pattern(i,1),pattern(i,2),'r*');
         plot(center(1,1),center(1,2),'ko');
    elseif pattern(i,n)==2
         plot(pattern(i,1),pattern(i,2),'g*');
         plot(center(2,1),center(2,2),'ko');
    elseif pattern(i,n)==3
         plot(pattern(i,1),pattern(i,2),'b*');
         plot(center(3,1),center(3,2),'ko');
    elseif pattern(i,n)==4
         plot(pattern(i,1),pattern(i,2),'y*');
         plot(center(4,1),center(4,2),'ko');
    else
         plot(pattern(i,1),pattern(i,2),'m*');
         plot(center(4,1),center(4,2),'ko');
    end
end
grid on;
toc;

references

[1] Zhou Zhihua. Machine learning [M]. Beijing: Tsinghua University Press, 2017: 202-203.

[2] K-Means algorithm for machine learning

[3] K-means clustering algorithm and its MATLAB implementation