高斯模型MATLAB的实现,高斯混合模型GMM实现matlab.doc

高斯混合模型GMM实现matlab

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, Alpha0, Mu0, Sigma0)

%% EM?

loglik_threshold = 1e-10;

%%?初始化参数

[dim, N] = size(Data);

M = size(Mu0,2);

loglik_old = -realmax;

nbStep = 0;

?

Mu = Mu0;

Sigma = Sigma0;

Alpha = Alpha0;

Epsilon = 0.0001;

while (nbStep < 1200)

??nbStep = nbStep+1;

??%% E-步骤?%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

??for i=1:M

????% PDF of each point

????Pxi(:,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])+realmin);

??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);

????%?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 variance to avoid numerical instability

????Sigma(:,:,i) = Sigma(:,:,i) + 1E-5.*diag(ones(dim,1));

??end

?

%??%% Stopping criterion 1 %%%%%%%%%%%%%%%%%%%%

%??for i=1:M

????%Compute the new probability p(x|i)

%????Pxi(:,i) = GaussPDF(Data, Mu(:,i), Sigma(i));

%??end

??%Compute the log likelihood

%??F = Pxi*Alpha';

%??F(find(F

%??loglik = mean(log(F));

??%Stop the process depending on the increase of the log likelihood

%??if abs((loglik/loglik_old)-1) < loglik_threshold

%????break;

%??end

%??loglik_old = loglik;

?

??%% Stopping criterion 2 %%%%%%%%%%%%%%%%%%%%

??v = [sum(abs(Mu - Mu0)), abs(Alpha - Alpha0)];

??s = abs(Sigma-Sigma0);

??v2 = 0;

??for i=1:M

????v2 = v2 + det(s(:,:,i));

??end

?

??if ((sum(v) + v2) < Epsilon)

????break;

??end

??Mu0 = Mu;

??Sigma0 = Sigma;

??Alpha0 = Alpha;

end

nbStep

(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_EM函数所调用

function prob = GaussPDF(Data, Mu, Sigma)

%

%??Probability Density Function (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

%???