GMM算法的matlab程序
在https://www.cnblogs.com/kailugaji/p/9648508.html文章中已经介绍了GMM算法，现在用matlab程序实现它。
作者：凯鲁嘎吉 - 博客园 http://www.cnblogs.com/kailugaji/
1.采用iris数据库
iris_data.txt
5.1 3.5 1.4 0.2 4.9 3 1.4 0.2 4.7 3.2 1.3 0.2 4.6 3.1 1.5 0.2 5 3.6 1.4 0.2 5.4 3.9 1.7 0.4 4.6 3.4 1.4 0.3 5 3.4 1.5 0.2 4.4 2.9 1.4 0.2 4.9 3.1 1.5 0.1 5.4 3.7 1.5 0.2 4.8 3.4 1.6 0.2 4.8 3 1.4 0.1 4.3 3 1.1 0.1 5.8 4 1.2 0.2 5.7 4.4 1.5 0.4 5.4 3.9 1.3 0.4 5.1 3.5 1.4 0.3 5.7 3.8 1.7 0.3 5.1 3.8 1.5 0.3 5.4 3.4 1.7 0.2 5.1 3.7 1.5 0.4 4.6 3.6 1 0.2 5.1 3.3 1.7 0.5 4.8 3.4 1.9 0.2 5 3 1.6 0.2 5 3.4 1.6 0.4 5.2 3.5 1.5 0.2 5.2 3.4 1.4 0.2 4.7 3.2 1.6 0.2 4.8 3.1 1.6 0.2 5.4 3.4 1.5 0.4 5.2 4.1 1.5 0.1 5.5 4.2 1.4 0.2 4.9 3.1 1.5 0.2 5 3.2 1.2 0.2 5.5 3.5 1.3 0.2 4.9 3.6 1.4 0.1 4.4 3 1.3 0.2 5.1 3.4 1.5 0.2 5 3.5 1.3 0.3 4.5 2.3 1.3 0.3 4.4 3.2 1.3 0.2 5 3.5 1.6 0.6 5.1 3.8 1.9 0.4 4.8 3 1.4 0.3 5.1 3.8 1.6 0.2 4.6 3.2 1.4 0.2 5.3 3.7 1.5 0.2 5 3.3 1.4 0.2 7 3.2 4.7 1.4 6.4 3.2 4.5 1.5 6.9 3.1 4.9 1.5 5.5 2.3 4 1.3 6.5 2.8 4.6 1.5 5.7 2.8 4.5 1.3 6.3 3.3 4.7 1.6 4.9 2.4 3.3 1 6.6 2.9 4.6 1.3 5.2 2.7 3.9 1.4 5 2 3.5 1 5.9 3 4.2 1.5 6 2.2 4 1 6.1 2.9 4.7 1.4 5.6 2.9 3.6 1.3 6.7 3.1 4.4 1.4 5.6 3 4.5 1.5 5.8 2.7 4.1 1 6.2 2.2 4.5 1.5 5.6 2.5 3.9 1.1 5.9 3.2 4.8 1.8 6.1 2.8 4 1.3 6.3 2.5 4.9 1.5 6.1 2.8 4.7 1.2 6.4 2.9 4.3 1.3 6.6 3 4.4 1.4 6.8 2.8 4.8 1.4 6.7 3 5 1.7 6 2.9 4.5 1.5 5.7 2.6 3.5 1 5.5 2.4 3.8 1.1 5.5 2.4 3.7 1 5.8 2.7 3.9 1.2 6 2.7 5.1 1.6 5.4 3 4.5 1.5 6 3.4 4.5 1.6 6.7 3.1 4.7 1.5 6.3 2.3 4.4 1.3 5.6 3 4.1 1.3 5.5 2.5 4 1.3 5.5 2.6 4.4 1.2 6.1 3 4.6 1.4 5.8 2.6 4 1.2 5 2.3 3.3 1 5.6 2.7 4.2 1.3 5.7 3 4.2 1.2 5.7 2.9 4.2 1.3 6.2 2.9 4.3 1.3 5.1 2.5 3 1.1 5.7 2.8 4.1 1.3 6.3 3.3 6 2.5 5.8 2.7 5.1 1.9 7.1 3 5.9 2.1 6.3 2.9 5.6 1.8 6.5 3 5.8 2.2 7.6 3 6.6 2.1 4.9 2.5 4.5 1.7 7.3 2.9 6.3 1.8 6.7 2.5 5.8 1.8 7.2 3.6 6.1 2.5 6.5 3.2 5.1 2 6.4 2.7 5.3 1.9 6.8 3 5.5 2.1 5.7 2.5 5 2 5.8 2.8 5.1 2.4 6.4 3.2 5.3 2.3 6.5 3 5.5 1.8 7.7 3.8 6.7 2.2 7.7 2.6 6.9 2.3 6 2.2 5 1.5 6.9 3.2 5.7 2.3 5.6 2.8 4.9 2 7.7 2.8 6.7 2 6.3 2.7 4.9 1.8 6.7 3.3 5.7 2.1 7.2 3.2 6 1.8 6.2 2.8 4.8 1.8 6.1 3 4.9 1.8 6.4 2.8 5.6 2.1 7.2 3 5.8 1.6 7.4 2.8 6.1 1.9 7.9 3.8 6.4 2 6.4 2.8 5.6 2.2 6.3 2.8 5.1 1.5 6.1 2.6 5.6 1.4 7.7 3 6.1 2.3 6.3 3.4 5.6 2.4 6.4 3.1 5.5 1.8 6 3 4.8 1.8 6.9 3.1 5.4 2.1 6.7 3.1 5.6 2.4 6.9 3.1 5.1 2.3 5.8 2.7 5.1 1.9 6.8 3.2 5.9 2.3 6.7 3.3 5.7 2.5 6.7 3 5.2 2.3 6.3 2.5 5 1.9 6.5 3 5.2 2 6.2 3.4 5.4 2.3 5.9 3 5.1 1.8
2.matlab源程序
function [label_2,para_pi,para_miu_new,para_sigma]=My_GMM(K)
%输入K：聚类数，K个单高斯模型
%输出label_2:聚的类，para_pi:单高斯权重，para_miu_new:高斯分布参数μ，para_sigma:高斯分布参数sigma
format long
eps=1e-15; %定义迭代终止条件的eps
data=dlmread(‘E:\kailugaji\data\iris\iris_data.txt‘);
%----------------------------------------------------------------------------------------------------
%对data做最大-最小归一化处理
[data_num,data_dim]=size(data);
X=zeros(size(data));
data_min=min(min(data));
data_max=max(max(data));
for j=1:data_dim
for i=1:data_num
X(i,j)=(data(i,j)-data_min)/(data_max-data_min);
end
end
[X_num,X_dim]=size(X);
para_sigma=zeros(X_dim,X_dim,K);
%----------------------------------------------------------------------------------------------------
%随机初始化K个聚类中心
rand_array=randperm(X_num); %产生1~X_num之间整数的随机排列
center=X(rand_array(1:K),:); %随机排列取前K个数，在X矩阵中取这K行作为初始聚类中心
%根据上述聚类中心初始化参数
para_miu_new=center; %初始化参数miu
para_pi=ones(1,K)./K; %K类单高斯模型的权重
for k=1:K
para_sigma(:,:,k)=eye(X_dim); %K类单高斯模型的协方差矩阵,初始化为单位阵
end
%欧氏距离，计算（X-para_miu）^2=X^2+para_miu^2-2*X*para_miu‘，矩阵大小为X_num*K
distant=repmat(sum(X.*X,2),1,K)+repmat(sum(para_miu_new.*para_miu_new,2)‘,X_num,1)-2*X*para_miu_new‘;
%返回distant每行最小值所在的下标
[~,label_1]=min(distant,[],2);
for k=1:K
X_k=X(label_1==k,:); %X_k是一个（X_num/K, X_dim）的矩阵,把X矩阵分为K类
para_pi(k)=size(X_k,1)/X_num; %将（每一类数据的个数/X_num）作为para_pi的初始值
para_sigma(:,:,k)=cov(X_k); %para_sigma是一个（X_dim, X_dim）的矩阵，cov(矩阵)求的是每一列之间的协方差
end
%----------------------------------------------------------------------------------------------------
%EM算法
N_pdf=zeros(X_num,K);
while true
para_miu=para_miu_new;
%----------------------------------------------------------------------------------------------------
%E步
%单高斯分布的概率密度函数N_pdf
for k=1:K
X_miu=X-repmat(para_miu(k,:),X_num,1); %X-miu,(X_num, X_dim)的矩阵
sigma_inv=inv(para_sigma(:,:,k)); %sigma的逆矩阵,(X_dim, X_dim)的矩阵//很可能出现奇异矩阵
exp_up=sum((X_miu*sigma_inv).*X_miu,2); %指数的幂，(X-miu)‘*sigma^(-1)*(X-miu)
coefficient=(2*pi)^(-X_dim/2)*sqrt(det(sigma_inv)); %高斯分布的概率密度函数e左边的系数
N_pdf(:,k)=coefficient*exp(-0.5*exp_up);
end
% N_pdf=guass_pdf(X,K,para_miu,para_sigma);
responsivity=N_pdf.*repmat(para_pi,X_num,1); %响应度responsivity的分子，（X_num,K）的矩阵
responsivity=responsivity./repmat(sum(responsivity,2),1,K); %responsivity:在当前模型下第n个观测数据来自第k个分模型的概率，即分模型k对观测数据Xn的响应度
%----------------------------------------------------------------------------------------------------
%M步
R_k=sum(responsivity,1); %(1,K)的矩阵，把responsivity每一列求和
%更新参数miu
para_miu_new=diag(1./R_k)*responsivity‘*X;
%更新k个参数sigma
for i=1:K
X_miu=X-repmat(para_miu_new(i,:),X_num,1);
para_sigma(:,:,i)=(X_miu‘*(diag(responsivity(:,i))*X_miu))/R_k(i);
end
%更新参数pi
para_pi=R_k/sum(R_k);
%----------------------------------------------------------------------------------------------------
%迭代终止条件
if norm(para_miu_new-para_miu)<=eps
break;
end
end
%----------------------------------------------------------------------------------------------------
%聚类
[~,label_2]=max(responsivity,[],2);
3.结果
>> [label_2,para_pi,para_miu_new,para_sigma]=My_GMM(3)
label_2 =
2
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para_pi =
0.367473478930455 0.333333333333333 0.299193187736212
para_miu_new =
0.826224185813464 0.365212967951040 0.689686337779126 0.241616019595889
0.628974358974359 0.426666666666667 0.174615384615385 0.018717948717949
0.745508921566646 0.343313288035667 0.525840157141014 0.153457288790627
para_sigma(:,:,1) =
0.006361674786115 0.001515580551453 0.004977181640354 0.001013330843816
0.001515580551453 0.001813571701777 0.001385397422113 0.000920636146120
0.004977181640354 0.001385397422113 0.005387859279713 0.001225017162907
0.001013330843816 0.000920636146120 0.001225017162907 0.001410219155888
para_sigma(:,:,2) =
0.002001380670611 0.001598159105851 0.000263445101907 0.000166403681788
0.001598159105851 0.002314529914530 0.000188428665352 0.000149769888231
0.000263445101907 0.000188428665352 0.000485798816568 0.000097764628534
0.000166403681788 0.000149769888231 0.000097764628534 0.000178895463511
para_sigma(:,:,3) =
0.004525292275076 0.001593382338014 0.003035213559581 0.000893996379601
0.001593382338014 0.001522781744993 0.001498079786108 0.000706728261037
0.003035213559581 0.001498079786108 0.003297672805131 0.001002275979414
0.000893996379601 0.000706728261037 0.001002275979414 0.000525919691773
4.注意
由于初始化聚类中心是随机的，所以每次出现的结果并不一样，如果答案与上述不一致，很正常，可以设置迭代次数，求精度。如有不对之处，望指正。
原文地址：https://www.cnblogs.com/kailugaji/p/9920781.html
时间： 2024-08-28 13:43:22