Daniel@0: function [mix, options, errlog] = gmmem(mix, x, options)
Daniel@0: %GMMEM	EM algorithm for Gaussian mixture model.
Daniel@0: %
Daniel@0: %	Description
Daniel@0: %	[MIX, OPTIONS, ERRLOG] = GMMEM(MIX, X, OPTIONS) uses the Expectation
Daniel@0: %	Maximization algorithm of Dempster et al. to estimate the parameters
Daniel@0: %	of a Gaussian mixture model defined by a data structure MIX. The
Daniel@0: %	matrix X represents the data whose expectation is maximized, with
Daniel@0: %	each row corresponding to a vector.    The optional parameters have
Daniel@0: %	the following interpretations.
Daniel@0: %
Daniel@0: %	OPTIONS(1) is set to 1 to display error values; also logs error
Daniel@0: %	values in the return argument ERRLOG. If OPTIONS(1) is set to 0, then
Daniel@0: %	only warning messages are displayed.  If OPTIONS(1) is -1, then
Daniel@0: %	nothing is displayed.
Daniel@0: %
Daniel@0: %	OPTIONS(3) is a measure of the absolute precision required of the
Daniel@0: %	error function at the solution. If the change in log likelihood
Daniel@0: %	between two steps of the EM algorithm is less than this value, then
Daniel@0: %	the function terminates.
Daniel@0: %
Daniel@0: %	OPTIONS(5) is set to 1 if a covariance matrix is reset to its
Daniel@0: %	original value when any of its singular values are too small (less
Daniel@0: %	than MIN_COVAR which has the value eps).   With the default value of
Daniel@0: %	0 no action is taken.
Daniel@0: %
Daniel@0: %	OPTIONS(14) is the maximum number of iterations; default 100.
Daniel@0: %
Daniel@0: %	The optional return value OPTIONS contains the final error value
Daniel@0: %	(i.e. data log likelihood) in OPTIONS(8).
Daniel@0: %
Daniel@0: %	See also
Daniel@0: %	GMM, GMMINIT
Daniel@0: %
Daniel@0: 
Daniel@0: %	Copyright (c) Ian T Nabney (1996-2001)
Daniel@0: 
Daniel@0: % Check that inputs are consistent
Daniel@0: errstring = consist(mix, 'gmm', x);
Daniel@0: if ~isempty(errstring)
Daniel@0:   error(errstring);
Daniel@0: end
Daniel@0: 
Daniel@0: [ndata, xdim] = size(x);
Daniel@0: 
Daniel@0: % Sort out the options
Daniel@0: if (options(14))
Daniel@0:   niters = options(14);
Daniel@0: else
Daniel@0:   niters = 100;
Daniel@0: end
Daniel@0: 
Daniel@0: display = options(1);
Daniel@0: store = 0;
Daniel@0: if (nargout > 2)
Daniel@0:   store = 1;	% Store the error values to return them
Daniel@0:   errlog = zeros(1, niters);
Daniel@0: end
Daniel@0: test = 0;
Daniel@0: if options(3) > 0.0
Daniel@0:   test = 1;	% Test log likelihood for termination
Daniel@0: end
Daniel@0: 
Daniel@0: check_covars = 0;
Daniel@0: if options(5) >= 1
Daniel@0:   if display >= 0
Daniel@0:     disp('check_covars is on');
Daniel@0:   end
Daniel@0:   check_covars = 1;	% Ensure that covariances don't collapse
Daniel@0:   MIN_COVAR = eps;	% Minimum singular value of covariance matrix
Daniel@0:   init_covars = mix.covars;
Daniel@0: end
Daniel@0: 
Daniel@0: % Main loop of algorithm
Daniel@0: for n = 1:niters
Daniel@0:   
Daniel@0:   % Calculate posteriors based on old parameters
Daniel@0:   [post, act] = gmmpost(mix, x);
Daniel@0:   
Daniel@0:   % Calculate error value if needed
Daniel@0:   if (display | store | test)
Daniel@0:     prob = act*(mix.priors)';
Daniel@0:     % Error value is negative log likelihood of data
Daniel@0:     e = - sum(log(prob));
Daniel@0:     if store
Daniel@0:       errlog(n) = e;
Daniel@0:     end
Daniel@0:     if display > 0
Daniel@0:       fprintf(1, 'Cycle %4d  Error %11.6f\n', n, e);
Daniel@0:     end
Daniel@0:     if test
Daniel@0:       if (n > 1 & abs(e - eold) < options(3))
Daniel@0:         options(8) = e;
Daniel@0:         return;
Daniel@0:       else
Daniel@0:         eold = e;
Daniel@0:       end
Daniel@0:     end
Daniel@0:   end
Daniel@0:   
Daniel@0:   % Adjust the new estimates for the parameters
Daniel@0:   new_pr = sum(post, 1);
Daniel@0:   new_c = post' * x;
Daniel@0:   
Daniel@0:   % Now move new estimates to old parameter vectors
Daniel@0:   mix.priors = new_pr ./ ndata;
Daniel@0:   
Daniel@0:   mix.centres = new_c ./ (new_pr' * ones(1, mix.nin));
Daniel@0:   
Daniel@0:   switch mix.covar_type
Daniel@0:   case 'spherical'
Daniel@0:     n2 = dist2(x, mix.centres);
Daniel@0:     for j = 1:mix.ncentres
Daniel@0:       v(j) = (post(:,j)'*n2(:,j));
Daniel@0:     end
Daniel@0:     mix.covars = ((v./new_pr))./mix.nin;
Daniel@0:     if check_covars
Daniel@0:       % Ensure that no covariance is too small
Daniel@0:       for j = 1:mix.ncentres
Daniel@0:         if mix.covars(j) < MIN_COVAR
Daniel@0:           mix.covars(j) = init_covars(j);
Daniel@0:         end
Daniel@0:       end
Daniel@0:     end
Daniel@0:   case 'diag'
Daniel@0:     for j = 1:mix.ncentres
Daniel@0:       diffs = x - (ones(ndata, 1) * mix.centres(j,:));
Daniel@0:       mix.covars(j,:) = sum((diffs.*diffs).*(post(:,j)*ones(1, ...
Daniel@0:         mix.nin)), 1)./new_pr(j);
Daniel@0:     end
Daniel@0:     if check_covars
Daniel@0:       % Ensure that no covariance is too small
Daniel@0:       for j = 1:mix.ncentres
Daniel@0:         if min(mix.covars(j,:)) < MIN_COVAR
Daniel@0:           mix.covars(j,:) = init_covars(j,:);
Daniel@0:         end
Daniel@0:       end
Daniel@0:     end
Daniel@0:   case 'full'
Daniel@0:     for j = 1:mix.ncentres
Daniel@0:       diffs = x - (ones(ndata, 1) * mix.centres(j,:));
Daniel@0:       diffs = diffs.*(sqrt(post(:,j))*ones(1, mix.nin));
Daniel@0:       mix.covars(:,:,j) = (diffs'*diffs)/new_pr(j);
Daniel@0:     end
Daniel@0:     if check_covars
Daniel@0:       % Ensure that no covariance is too small
Daniel@0:       for j = 1:mix.ncentres
Daniel@0:         if min(svd(mix.covars(:,:,j))) < MIN_COVAR
Daniel@0:           mix.covars(:,:,j) = init_covars(:,:,j);
Daniel@0:         end
Daniel@0:       end
Daniel@0:     end
Daniel@0:   case 'ppca'
Daniel@0:     for j = 1:mix.ncentres
Daniel@0:       diffs = x - (ones(ndata, 1) * mix.centres(j,:));
Daniel@0:       diffs = diffs.*(sqrt(post(:,j))*ones(1, mix.nin));
Daniel@0:       [tempcovars, tempU, templambda] = ...
Daniel@0: 	ppca((diffs'*diffs)/new_pr(j), mix.ppca_dim);
Daniel@0:       if length(templambda) ~= mix.ppca_dim
Daniel@0: 	error('Unable to extract enough components');
Daniel@0:       else 
Daniel@0:         mix.covars(j) = tempcovars;
Daniel@0:         mix.U(:, :, j) = tempU;
Daniel@0:         mix.lambda(j, :) = templambda;
Daniel@0:       end
Daniel@0:     end
Daniel@0:     if check_covars
Daniel@0:       if mix.covars(j) < MIN_COVAR
Daniel@0:         mix.covars(j) = init_covars(j);
Daniel@0:       end
Daniel@0:     end
Daniel@0:     otherwise
Daniel@0:       error(['Unknown covariance type ', mix.covar_type]);               
Daniel@0:   end
Daniel@0: end
Daniel@0: 
Daniel@0: options(8) = -sum(log(gmmprob(mix, x)));
Daniel@0: if (display >= 0)
Daniel@0:   disp(maxitmess);
Daniel@0: end
Daniel@0: