高斯混合模型GMM实现matlab

1、高斯混合模型 GMM 实现matlab(1)以下matlab代码实现了高斯混合模型：function Alpha, Mu, Sigma = GMM_EM(Data, AlphaO, MuO, SigmaO)% EM迭代停止条件loglik_threshold = 1e-10;%初始化参数dim, N = size(Data);M = size(Mu0,2);loglik_old = -realmax;n bStep = 0;Mu = Mu0;Sigma = Sigma0;Alpha = Alpha0;Epsilo n = 0.0001;while (n bStep 1200)nbStep =

2、nbStep+1;% E 步骤 %for i=1:M% PDF of each poi ntPxi(:,i) = GaussPDF(Data, Mu(:,i),Sigma(:，:,i);end%计算后验概率beta(i|x)Pix_tmp = repmat(Alpha,N 1).*Pxi;Pix = Pix_tmp ./ (repmat(sum(Pix_tmp,2),1 M)+realmi n);Beta = sum(Pix);% M步骤 %for i=1:M%更新权值Alpha(i) = Beta(i) / N;%更新均值Mu(:,i) = Data*Pix(:,i) / Beta(i);%

3、更新方差Data_tmp1 = Data - repmat(Mu(:,i),1,N); Sigma(:，:,i) = (repmat(Pix(:,i),dim, 1) .*Data_tmp1*Data_tmp1) / Beta(i);% Add a tiny varia nee to avoid nu merical in stability Sigma(:，:,i) = Sigma(:，:,i) + 1E-5.*diag(o nes(dim,1);end% Stoppi ng eriterio n 1 % for i=1:M%Compute the new probability p(x|i

4、)%Pxi(:,i) = GaussPDF(Data, Mu(:,i), Sigma(i);% end%Compute the log likelihood% F = Pxi*Alpha;%F(fi nd(Freal min) = real min;% loglik = mean (log(F);%Stop the process depe nding on the in crease of the log likelihood % if abs(loglik/loglik_old)-1) loglik_threshold %break;% end% loglik_old = loglik;%

5、 Stoppi ng eriterio n 2 %v = sum(abs(Mu - Mu0), abs(Alpha - AlphaO);s = abs(Sigma-SigmaO);v2 = 0;for i=1:Mv2 = v2 + det(s(:，:,i);endif (sum(v) + v2) Epsilo n)break;endMuO = Mu;SigmaO = Sigma; AlphaO = Alpha;endn bStep(2)以下代码根据高斯分布函数计算每组数据的概率密度，被GMM_E函数所调用fun cti on prob = GaussPDF(Data, Mu, Sigma)%根

6、据高斯分布函数计算每组数据的概率密度Probability DensityFun ction (PDF)%输入 % o Data:D x N ，N 个 D维数据% o Mu:D x 1，M个Gauss模型的中心初始值% o Sigma: M x M ，每个Gauss模型的方差(假设每个方差矩阵都是对 角阵，%即一个数和单位矩阵的乘积)% Outputs% o prob:1 x N array represe nti ng the probabilities for the%N datapoi nts.dim,N = size(Data);Data = Data - repmat(Mu,N,1)

7、;prob = sum(Data*i nv(Sigma).*Data, 2);prob = exp(-0.5*prob) / sqrt(2*pi)Adim * (abs(det(Sigma)+realmi n);(3) 以下是演示代码 demol.m%高斯混合模型参数估计示例(基于 EM算法)% 2010年 11月 9 日data, mu, var, weight = CreateSample(M, dim, N);/生成测试数据Alpha, Mu, Sigma = GMM_EM(Data, Priors, Mu, Sigma)(4) 以下是测试数据生成函数，为demo1.m所调用：funct

8、ion data, mu, var, weight = CreateSample(M, dim, N)%生成实验样本集，由M组正态分布的数据构成% % GMI模型的原理就是仅根据数据估计参数：每组正态分布的均值、方差，%以及每个正态分布函数在GM啲权重alpha。%在本函数中，这些参数均为随机生成，%输入% M:高斯函数个数% dim :数据维数% N:数据总个数%返回值% data : dim-by-N,每列为一个数据% miu : dim-by-M,每组样本的均值，由本函数随机生成% var : 1-by-M,均方差，由本函数随机生成% weight: 1-by-M,每组的权值，由本函数随

9、机生成%随机生成不同组的方差、均值及权值weight = ran d(1,M);weight = weight / norm(weight, 1);% 归一化，保证总合为 1var = double(mod(int16(rand(1,M)*100),10) + 1);% 均方差，取 110之间，采用对角矩阵mu = double(round(randn(dim,M)*100);% 均值，可以有负数for(i = 1: M)if (i 二 M)n(i) = floor(N*weight(i);elsen (i) = N - sum( n);endend%以标准高斯分布生成样本值，并平移到各组相应均值和方差start = 0;for (i=1:M