wolffd@0: function [mu, Sigma] = mixgaussTrainObserved(obsData, hiddenData, nstates, varargin);
wolffd@0: % mixgaussTrainObserved Max likelihood estimates of conditional Gaussian from raw data
wolffd@0: % function [mu, Sigma] = mixgaussTrainObserved(obsData, hiddenData, nstates, ...);
wolffd@0: %
wolffd@0: % Input:
wolffd@0: % obsData(:,i)
wolffd@0: % hiddenData(i)  - this is the mixture component label for example i
wolffd@0: % Optional arguments - same as mixgauss_Mstep
wolffd@0: %
wolffd@0: % Output:
wolffd@0: % mu(:,q)
wolffd@0: % Sigma(:,:,q) - same as mixgauss_Mstep
wolffd@0: 
wolffd@0: [D numex] = size(obsData);
wolffd@0: Y = zeros(D, nstates);
wolffd@0: YY = zeros(D,D,nstates);
wolffd@0: YTY = zeros(nstates,1);
wolffd@0: w = zeros(nstates, 1);
wolffd@0: for q=1:nstates
wolffd@0:   ndx = find(hiddenData==q);
wolffd@0:   w(q) = length(ndx); % each data point has probability 1 of being in this cluster
wolffd@0:   data = obsData(:,ndx);
wolffd@0:   Y(:,q) = sum(data,2);
wolffd@0:   YY(:,:,q) = data*data';
wolffd@0:   YTY(q) = sum(diag(data'*data));
wolffd@0: end
wolffd@0: [mu, Sigma] = mixgauss_Mstep(w, Y, YY, YTY, varargin{:});