matlab---k-means算法、fuzzy-c-means算法详解和比较

    clear all;close all;clc;
    % µÚÒ»×éÊý¾Ý
    mu1=[0 0 ];  %¾ùÖµ
    S1=[.1 0 ;0 .1];  %Э·½²î
    data1=mvnrnd(mu1,S1,100);   %²úÉú¸ß˹·Ö²¼Êý¾Ý
    %µÚ¶þ×éÊý¾Ý
    mu2=[1.25 1.25 ];
    S2=[.1 0 ;0 .1];
    data2=mvnrnd(mu2,S2,100);
    % µÚÈý×éÊý¾Ý
    mu3=[-1.25 1.25 ];
    S3=[.1 0 ;0 .1];
    data3=mvnrnd(mu3,S3,100);
    % ÏÔʾÊý¾Ý
    plot(data1(:,1),data1(:,2),'b+');
    hold on;
    plot(data2(:,1),data2(:,2),'r+');
    plot(data3(:,1),data3(:,2),'g+');
    grid on;
    %  ÈýÀàÊý¾ÝºÏ³ÉÒ»¸ö²»´ø±êºÅµÄÊý¾ÝÀà
    data=[data1;data2;data3]; 
    N=3;%ÉèÖþÛÀàÊýÄ¿
    [m,n]=size(data);
    pattern=zeros(m,n+1);
    center=zeros(N,n);%³õʼ»¯¾ÛÀàÖÐÐÄ
    pattern(:,1:n)=data(:,:);
    for x=1:N
    center(x,:)=data( randi(300,1),:);%µÚÒ»´ÎËæ»ú²úÉú¾ÛÀàÖÐÐÄ
    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,:));%¼ÆË㵽ÿ¸öÀàµÄ¾àÀë
    end
    [~, temp]=min(distence);%Çó×îСµÄ¾àÀë
    pattern(x,n+1)=temp;         
    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);
           num(y)=num(y)+1;
        end
    end
    new_center(y,:)=new_center(y,:)/num(y);
    if norm(new_center(y,:)-center(y,:))<0.1
        k=k+1;
    end
    end
    if k==N
     break;
    else
     center=new_center;
    end
    end
    [m, n]=size(pattern);
     
    %×îºóÏÔʾ¾ÛÀàºóµÄÊý¾Ý
    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;

    function [U,P,Dist,Cluster_Res,Obj_Fcn,iter]=fuzzycm(Data,C,plotflag,M,epsm)
    % 模糊 C 均值聚类 FCM: 从随机初始化划分矩阵开始迭代
    % [U,P,Dist,Cluster_Res,Obj_Fcn,iter] = fuzzycm(Data,C,plotflag,M,epsm)
    % 输入:
    % Data: N×S 型矩阵,聚类的原始数据,即一组有限的观测样本集,
    % Data 的每一行为一个观测样本的特征矢量,S 为特征矢量
    % 的维数,N 为样本点的个数
    % C: 聚类数,1
    % plotflag: 聚类结果 2D/3D 绘图标记,0 表示不绘图,为缺省值
    % M: 加权指数,缺省值为 2
    % epsm: FCM 算法的迭代停止阈值,缺省值为 1.0e-6
    % 输出:
    % U: C×N 型矩阵,FCM 的划分矩阵
    % P: C×S 型矩阵,FCM 的聚类中心,每一行对应一个聚类原型
    % Dist: C×N 型矩阵,FCM 各聚类中心到各样本点的距离,聚类中
    % 心 i 到样本点 j 的距离为 Dist(i,j)
    % Cluster_Res: 聚类结果,共 C 行,每一行对应一类
    % Obj_Fcn: 目标函数值
    % iter: FCM 算法迭代次数
    % See also: fuzzydist maxrowf fcmplot
    if nargin<5
    epsm=1.0e-6;
    end
    if nargin<4
    M=2;
    end
    if nargin<3
    plotflag=0;
    end
    [N,S]=size(Data);m=2/(M-1);iter=10000;
    Dist(C,N)=0; U(C,N)=0; P(C,S)=0;
    % 随机初始化划分矩阵
    U0 = rand(C,N);
    U0=U0./(ones(C,1)*sum(U0));
    % FCM 的迭代算法
    while true
    % 迭代计数器
    iter=iter+1;
    % 计算或更新聚类中心 P
    Um=U0.^M;
    P=Um*Data./(ones(S,1)*sum(Um'))';
    % 更新划分矩阵 U
    for i=1:C
    for j=1:N
    Dist(i,j)=fuzzydist(P(i,:),Data(j,:));
    end
    end
    U=1./(Dist.^m.*(ones(C,1)*sum(Dist.^(-m))));
    % 目标函数值: 类内加权平方误差和
    if nargout>4 | plotflag
    Obj_Fcn(iter)=sum(sum(Um.*Dist.^2));
    end
    % FCM 算法迭代停止条件
    if norm(U-U0,Inf) break
    end
    U0=U;
    end
    % 聚类结果
    if nargout > 3
    res = maxrowf(U);
    for c = 1:
    v = find(res==c);
    Cluster_Res(c,1:length(v))=v;
    end
    end
    % 绘图
    if plotflag
    fcmplot(Data,U,P,Obj_Fcn);
    end