用matlab编写的EM聚类算法

close all;clear;clc;
% 参考书籍Pattern.Recognition.and.Machine.Learning.pdf
% 2009/10/15
%%
M=3; % number of Gaussian
N=600; % total number of data samples
th=0.000001; % convergent threshold
K=2; % demention of output signal

% 待生成数据的参数
a_real =[2/3;1/6;1/6];
mu_real=[3 4 6;
5 3 7];
cov_real(:,:,1)=[5 0;
0 0.2];
cov_real(:,:,2)=[0.1 0;
0 0.1];
cov_real(:,:,3)=[0.1 0;
0 0.1];
% 这里生成的数据全部符合标准
x=[ mvnrnd( mu_real(:,1) , cov_real(:,:,1) , round(N*a_real(1)) )' ,...
mvnrnd( mu_real(:,2) , cov_real(:,:,2) , round(N*a_real(2)) )' ,...
mvnrnd( mu_real(:,3) , cov_real(:,:,3) , round(N*a_real(3)) )' ];

figure(1),plot(x(1,:),x(2,:),'.')

%% EM Algorothm
% 参数初始化
a=[1/3,1/3,1/3]; %各类的比例
mu=[1 2 3; %均值初始化
2 1 4];
cov(:,:,1)=[1 0; %协方差初始化
0 1];
cov(:,:,2)=[1 0;
0 1];
cov(:,:,3)=[1 0;
0 1];

t=inf;
count=0;
figure(2),hold on
while t>=th
a_old = a;
mu_old = mu;
cov_old= cov;
rznk_p=zeros(M,N);
for cm=1:M
mu_cm=mu(:,cm);
cov_cm=cov(:,:,cm);
for cn=1:N
p_cm=exp(-0.5*(x(:,cn)-mu_cm)'/cov_cm*(x(:,cn)-mu_cm));
rznk_p(cm,cn)=p_cm;
end
rznk_p(cm,:)=rznk_p(cm,:)/sqrt(det(cov_cm));
end
rznk_p=rznk_p*(2*pi)^(-K/2);
%E step
%开始求rznk
rznk=zeros(M,N);%r(Z
pikn=zeros(1,M);%r(Z
pikn_sum=0;
for cn=1:N
for cm=1:M
pikn(1,cm)=a(cm)*rznk_p(cm,cn);
% pikn_sum=pikn_sum+pikn(1,cm);
end
for cm=1:M
rznk(cm,cn)=pikn(1,cm)/sum(pikn);
end
end
%求rank结束
% M step
nk=zeros(1,M);
for cm=1:M
for cn=1:N
nk(1,cm)=nk(1,cm)+rznk(cm,cn);
end
end
a=nk/N;
rznk_sum_mu=zeros(M,1);

% 求均值MU
for cm=1:M
rznk_sum_mu=0;
for cn=1:N
rznk_sum_mu=rznk_sum_mu+rznk(cm,cn)*x(:,cn);
end
mu(:,cm)=rznk_sum_mu/nk(cm);
end

% 求协方差COV
for cm=1:M
rznk_sum_cov=zeros(K,K);
for cn=1:N
rznk_sum_cov=rznk_sum_cov+rznk(cm,cn)*(x(:,cn)-mu(:,cm))*(x(:,cn)-mu(:,cm))';
end
cov(:,:,cm)=rznk_sum_cov/nk(cm);
end

t=max([norm(a_old(:)-a(:))/norm(a_old(:));norm(mu_old(:)-mu(:))/norm(mu_old(:));norm(cov_old(:)-cov(:))/norm(cov_old(:))]);

temp_f=sum(log(sum(pikn)));
plot(count,temp_f,'r+')
count=count+1;
end %while

hold off
f=sum(log(sum(pikn)));

% 输出结果
a
mu
cov

figure(3),
hold on
plot(x(1,:),x(2,:),'k.');
plot(mu_real(1,:),mu_real(2,:),'*c');
plot(mu(1,:),mu(2,:),'+r');
hold off

figure(4),
hold on
for i=1:N
[max_temp,ind

_temp]=max(rznk(:,i));
if ind_temp==1
plot(x(1,i),x(2,i),'k.');
end
if ind_temp==2
plot(x(1,i),x(2,i),'b.');
end
if ind_temp==3
plot(x(1,i),x(2,i),'r.');
end
end


%fcm聚类
[center, U, OBJ_FCN]=fcm(x',3);
figure(5),
hold on
for i=1:N
[max_temp,ind_temp]=max(U(:,i));
if ind_temp==1
plot(x(1,i),x(2,i),'k.');
end
if ind_temp==2
plot(x(1,i),x(2,i),'b.');
end
if ind_temp==3
plot(x(1,i),x(2,i),'r.');
end
end

plot(center(:,1),center(:,2),'c*')

hold off