Question

有matlab实现的EM算法 最基本的就行

Answer 1

这个是我刚开始学习EM算法时候写的，希望对你有帮助。

%%clear the way
% author : liuweimin
% ictcas
close all;
clear;
clc;

%% settings

M=3; % number of Gaussian
N=1000; % total number of data samples

th=1e-3; % convergent threshold
Nit=2000; % maximal iteration
Nrep=10; % number of repetation to find global maximal

K=2; % demention of output signal

pi=3.141592653589793; % in case it is overwriten by smae name variable

cond_num =1000; % prevent the singular covariance matrix in simulation data

plot_flag=1;
print_flag=1;

%% paramethers for random signal genrator

% random parameters for M Gaussian signals
mu_real = randn(K,M); % mean

cov_real =zeros(K,K,M); % covariance matrix
covd_real=zeros(K,K,M); % covariance matrix decomposition
for cm=1:M
while 1
covd_real(:,:,cm)=randn(K,K);
cov_real(:,:,cm)=covd_real(:,:,cm)*covd_real(:,:,cm)';
if cond(cov_real(:,:,cm))>cond_num
continue;
else
break;
end
end
end

% probablilty of a channel being selected
a_real = abs(randn(M,1));
a_real = a_real/sum(a_real); % normlize

if print_flag==1
a_real%类别概率的真值
mu_real%均值的真值
cov_real%协方差的真值
end

%% generate random sample of Gaussian vectors

%m=randdist(1,N,[1:M],a_real); % selector

rand_num_a=rand();%产生随机数
rand_num_b=rand();%产生随机数
while rand_num_a>=rand_num_b
rand_num_a=rand();%产生随机数
rand_num_b=rand();%产生随机数
end

x=randn(K,N);
for c=1:round(rand_num_a*N)
%sel=m(c);
x(:,c)=covd_real(:,:,1)*x(:,c)+mu_real(1);
end
for c=round(rand_num_a*N)+1:round(rand_num_b*N)
%sel=m(c);
x(:,c)=covd_real(:,:,2)*x(:,c)+mu_real(2);
end
for c=round(rand_num_b*N)+1:(N)
%sel=m(c);
x(:,c)=covd_real(:,:,3)*x(:,c)+mu_real(3);
end

%% EM Algorothm

% loop
f_best=-inf;
for crep=1:Nrep
c=1;

% initial values of parameters for EM
a=abs(randn(M,1)); % randomly generated
a=a/sum(a); % normlize, such that sum(a_EM)=1
mu=randn(K,M);
cov =zeros(K,K,M); % covariance matrix
covd=zeros(K,K,M); % covariance matrix decomposition
for cm=1:M
while 1
covd(:,:,cm)=randn(K,K);
cov(:,:,cm)=covd(:,:,cm)*covd(:,:,cm)';
if cond(cov(:,:,cm))>cond_num
continue;
else
break;
end
end
end

% iteration to find local maxima
break_flag=0;
while 1
a_old= a;
mu_old= mu;
cov_old=cov;

fprintf(1,'calculating probability pmx...\n');
pause(0);
% pmx(m,x|param)
pmx=zeros(M,N);
for cm=1:M
cov_cm=cov(:,:,cm);
if cond(cov_cm) > cond_num
break_flag=1;
end
inv_cov_cm=inv(cov_cm);
mu_cm=mu(:,cm);
for cn=1:N
%p_cm=exp(-0.5*(x(:,cn)-mu_cm)'*inv_cov_cm*(x(:,cn)-mu_cm));
p_cm=a(cm,:)*exp(-0.5*(x(:,cn)-mu_cm)'*inv_cov_cm*(x(:,cn)-mu_cm));%这里加上a
pmx(cm,cn)=p_cm;
end
pmx(cm,:)=pmx(cm,:)/sqrt(det(cov_cm));
end
pmx=pmx*(2*pi)^(-K/2);

fprintf(1,'calculating conditional probability, p...\n');
pause(0);
% conditional probability p(m|x,param) for estimated parameters
p=pmx./kron(ones(M,1),sum(pmx));

fprintf(1,'updating parametres\n');
pause(0);
a = 1/N*sum(p')';
mu = 1/N*x*p'*diag(1./a);
for cm=1:M
a_cm=a(cm);
mu_cm=mu(:,cm);
tmp=x-kron(ones(1,N),mu_cm);
cov(:,:,cm)=1/N*(kron(ones(K,1),p(cm,:)).*tmp)*tmp'*diag(1./a_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(:))]);
if print_flag==1
fprintf('c=%04d: t=%f\n',c,t);
c=c+1;
end

if t<th
break;
end

if c>Nit
disp('reach maximal iteration')
break;
end

if break_flag==1
disp('***** break on singular covariance matrix *****');
break;
end
end

f=sum(log(sum(pmx.*kron(ones(1,N),a))));
if f>f_best
a_best=a;
mu_best=mu;
cov_best=cov;
f_best=f;
end
end
!echo 真实的rand_num_a
rand_num_a
!echo 真实的rand_num_b
rand_num_b-rand_num_a
!echo 真实的rand_num_c
1-rand_num_b
!echo 迭代出来的a_best
a_best
!echo 真实的均值矩阵
mu_real
!echo 迭代出来的均值矩阵
mu_best
for cs=1:M
!echo 真实的协方差矩阵
cov_real(:,:,cs)
!echo 迭代出来的协方差矩阵
cov_best(:,:,cs)
end

%% plot all
% for 2D (K=2) only
x1_vect=-1:0.02:1;
x2_vect=-1:0.02:1;
px=zeros(length(x1_vect), length(x2_vect));
for c1=1:length(x1_vect)
for c2=1:length(x2_vect)
for cm=1:3
cov_real_cm=cov_real(:,:,cm);
mu_real_cm=mu_real(:,cm);
a_real_cm=a_real(cm);
x_cm=[x1_vect(c1);
x2_vect(c2)];
pm=a_real_cm*(2*pi)^(-0.5*K)*det(cov_real_cm)^(-0.5)*exp(-0.5*x_cm'*inv(cov_real_cm)*x_cm);
px(c1,c2)=px(c1,c2)+pm;
end
end
end

px_hat=zeros(length(x1_vect), length(x2_vect));
for c1=1:length(x1_vect)
for c2=1:length(x2_vect)
for cm=1:3
cov_cm=cov(:,:,cm);
mu_cm=mu(:,cm);
a_cm=a(cm);
x_cm=[x1_vect(c1);
x2_vect(c2)];
pm=a_cm*(2*pi)^(-0.5*K)*det(cov_cm)^(-0.5)*exp(-0.5*x_cm'*inv(cov_cm)*x_cm);
px_hat(c1,c2)=px_hat(c1,c2)+pm;
end
end
end

figure(1); clf; hold on;

hold on
title('理论图');
xlabel('x');
ylabel('y');
mesh(x1_vect, x2_vect, px);
figure(2); clf; hold on;
mesh(x1_vect, x2_vect, px_hat);
title('统计图');
xlabel('x');
ylabel('y');

追问

能整个简单点的不
比如说 求f（x）=xy+x+y 0<x<2 -1<y<1 的极值

追答

你这个需要EM吗？ 根本永不倒EM 啊。

追问

MATLAB本身有计算最小值算法但是要求用EM算法来实现 出给我的题目就是这样的 我想找个样板我毕竟只是初学所以出给我的题目 就是这样 要不你弄个 计算 距离a b c d （二维）距离 最近点O坐标 更好