function model=melgmm(X,Alpha,cov_type)% MELGMM Maximizes Expectation of Log-Likelihood for Gaussian mixture.% % Synopsis:%  model = melgmm(X,Alpha)%  model = melgmm(X,Alpha,cov_type)% % Description:%  model = melgmm(X,Alpha) maximizes expectation of log-likelihood %  function for Gaussian mixture model%                        %   (Mean,Cov,Prior) =  argmax  F(Mean,Cov,Prior)%                    Mean,Cov,Prior %%  where%   F = sum sum Alpha(j,i)*log(pdfgauss(X(:,i),Mean(:,y),Cov(:,:,y)))%        y   i %%  The solution is returned in the structure model with fields%  Mean [dim x ncomp], Cov [dim x dim x ncomp] and Prior [1 x ncomp].%%  model = melgmm(X,Alpha,cov_type) specifies covariance matrix:%   cov_type = 'full'      full covariance matrix (default)%   cov_type = 'diag'      diagonal covarinace matrix%   cov_type = 'spherical' spherical covariance matrix%% Input:%  X [dim x num_data] Data sample.%  Alpha [ncomp x num_data] Distribution of hidden state given sample.%  cov_type [string] Type of covariacne matrix (see above).%% Output:%  model [struct] Gaussian mixture model:%   .Mean [dim x ncomp] Mean vectors.%   .Cov [dim x dim x ncomp] Covariance matrices.%   .Prior [1 x ncomp] Distribution of hidden state.%% See also %  EMGMM, MLCGMM.%% About: Statistical Pattern Recognition Toolbox% (C) 1999-2003, Written by Vojtech Franc and Vaclav Hlavac% <a href="http://www.cvut.cz">Czech Technical University Prague</a>% <a href="http://www.feld.cvut.cz">Faculty of Electrical Engineering</a>% <a href="http://cmp.felk.cvut.cz">Center for Machine Perception</a>% Modifications:% 30-apr-2004, VF% 19-sep-2003, VF% 27-feb-2003, VF% Processing of input arguments %----------------------------------------if nargin < 3, cov_type = 'full'; end[dim, num_data] = size( X );  % ------------------------------------ncomp = size(Alpha,1);model.Mean = zeros(dim,ncomp);model.Cov = zeros(dim,dim,ncomp);for i=1:ncomp,  nconst = sum( Alpha(i,:) );  if ~nconst,    model.Mean(:,i) = NaN*ones(dim,1);    model.Cov(:,:,i) = NaN*ones(dim,dim);    model.Prior(i) = 0;  else    model.Mean(:,i) = X*Alpha(i,:)'/nconst;    XC = X - model.Mean(:,i)*ones(1,num_data);        switch cov_type,      case 'full'        model.Cov(:,:,i) = (XC.*(repmat(Alpha(i,:),dim,1)))*XC'/nconst;      case 'diag'        model.Cov(:,:,i)=diag(sum(XC.*(ones(dim,1)*Alpha(i,:)).*XC,2))/nconst;      case 'spherical'                model.Cov(:,:,i) = eye(dim)*...          sum(sum(XC.^2.*(ones(dim,1)*Alpha(i,:)) ))/(nconst*dim);      otherwise        error('Wrong cov_type.');    end      model.Prior(i) = nconst/num_data;  endend    return;