模糊C均值聚类算法（原理+Matlab代码）

FCM代码

function[center,U,obj_fun]=FCMCluster(data,n,options)%采用模糊C均值将数据集data分为n类%用法% 1 [center,U,obj_fcn]=FCMCluster(data,n,options);% 2 [center,U,obj_fcn]=FCMCluster(data,n);%输入 % data    n*m矩阵，n个样本数，每个样本的维度为m% n       类别数% options 4*1 矩阵%   options(1):隶属度矩阵U的加权指数%   options(2):最大迭代次数%   options(3):隶属度最小变化量，迭代终止条件%   options(4):每次迭代是否输出信息标志%输出% center    聚类中心% U         隶属度矩阵% obj_fun   目标函数值if nargin~=2 && nargin~=3    error('Too many or too few input arguments');end data_n=size(data,1);in_n=size(data,2);%默认参数default_options=[2;100;1e-5;1];%参数配置  %如果只输入前两个参数，选用默认的参数;如果参数个数小于4，其他选用默认参数  if nargin==2      options=default_options;  else       if length(options)<4           tmp=default_options;           tmp(1:length(options))=options;           options=tmp;       end        nan_index=find(isnan(options)==1);       options(nan_index)=default_options(nan_index);       if options(1)<=1           error('The exponent should be greater than 1!');       end   end   %将options 中的分量分别赋值给四个变量  expo=options(1);  max_iter=options(2);  min_impro=options(3);  display=options(4);  obj_fun=zeros(max_iter,1);  %初始化模糊分配矩阵  U=initfcm(n,data_n);  %主程序   for i=1:max_iter       [U,center,obj_fun(i)]=stepfcm(data,U,n,expo);       if display           fprintf('FCM:Iteration count=%d,obj_fun=%f\n',i,obj_fun(i));       end       %终止条件判别       if i>1           if abs(obj_fun(i)-obj_fun(i-1))<min_impro               break;           end        end    end   iter_n=i;   obj_fun(iter_n+1:max_iter)=[];%   end%%子函数 模糊矩阵初始化    function U= initfcm(n,data_n)        U=rand(n,data_n);        col_sum=sum(U);        U=U./col_sum(ones(n,1),:);    end%%子函数 逐步聚类        function [U_new,center,obj_fun]=stepfcm(data,U,n,expo)            mf=U.^expo;            center=mf*data./((ones(size(data,2),1)*sum(mf'))');            dist=distfcm(center,data);            obj_fun=sum(sum((dist.^2).*mf));            tmp=dist.^(-2/(expo-1));            U_new=tmp./(ones(n,1)*sum(tmp));        end%%子函数 计算距离            function out=distfcm(center,data)                out=zeros(size(center,1),size(data,1));                for k=1:size(center,1)                    out(k,:)=sqrt(sum(((data-ones(size(data,1),1)*center(k,:)).^2)',1));                end             end算法测试

data=rand(100,2);
[center,U,obj_fcn] = FCMCluster(data,2);
plot(data(:,1),data(:,2),’o’);
hold on;
index1=find(U(1,:)==max(U));%找出划分为第一类的数据索引
index2=find(U(2,:)==max(U));%找出划分为第二类的数据索引
plot(data(index1,1),data(index1,2),’g*’);
hold on;
plot(data(index2,1),data(index2,2),’r*’);
hold on;
plot([center([1 2],1)],[center([1 2],2)],’*’,’color’,’k’);

实验结果展示：
原数据分布

聚类结果