最近看到了朴素贝叶斯定理，看着看着就看到了em聚类的算法中（K-means聚类的原型）。

动手自己编个程序：

%EM algorithm
clc;
clear;

sigma = 1.5;
miu1 = 3;
miu2 = 7;
N = 1000;
x = zeros(1,N);
for i = 1:N
    if rand>0.5
        x(1,i) = randn*sigma + miu1;
        y(1,i) = randn*sigma + miu1;
    else 
        %sigma = 0.5;
        x(1,i) = randn*sigma + miu2;
        y(1,i) = randn*sigma + miu2;
    end
end

plot(x,y,'o');

k = 2;
%miu = rand(1,k)*40;
miu(1) = 4;
miu(2) = 6;
cov(1) = 2;
cov(2) = 2;
%cov = rand(1,k)*6;
a(1) = 1.5;
a(2) = 1.5;
% expectations = zeros(N,k);
num = [0,0];
n = 1;
for step = 1:10000
    n = 1;
    m = 1;
    x1 = [];
    y1 = [];
    x2 = [];
    y2 = [];
    num = [1 1];
    for i = 1:N
        p1 = exp(-(x(i)-miu(1))*(x(i)-miu(1))/(2*cov(1)*cov(1)))/sqrt((2*pi))*cov(1);
        p2 = exp(-(x(i)-miu(2))*(x(i)-miu(2))/(2*cov(2)*cov(2)))/sqrt((2*pi))*cov(2);
        
        p(i) = a(1)*p1+a(2)*p2;
        if p1>p2
            x1(n) = x(i);
            y1(n) = y(i);
            n = n+1;
            num(1) = num(1) + 1;
        else
            x2(m) = x(i);
            y2(m) = y(i);
            m = m+1;
            num(2) = num(2) + 1;
        end
    end
        
        oldmiu = miu;
        oldcov = cov;
        miu(1) = sum(x1)/num(1);
        miu(2) = sum(x2)/num(2);
        cov(1) = sqrt(sum((x1-miu(1))*(x1-miu(1))')/num(1));
        cov(2) = sqrt(sum((x2-miu(2))*(x2-miu(2))')/num(2));
        a(1) = num(1)/N;
        a(2) = num(2)/N;
        
    plot(x1,y1,'ro',x2,y2,'go');
    epsilon = 0.0001;
    if sum(abs(oldmiu-miu))<epsilon
        break;
    end
    step
%     miu
end
plot(x1,y1,'ro',x2,y2,'go');

运行后的结果图如下：

不知道是我自己编的不对，还是别的原因（应该是我编的不对），在初始化参数的时候，不能跟实际的偏离太大，如果偏离太大了

最终的结果就完全不对。不知道是算法本身的缺陷还是自己没有把算法理解对。

希望有高手来指导下。