comparison toolboxes/FullBNT-1.0.7/netlab3.3/ppca.m @ 0:e9a9cd732c1e tip

first hg version after svn

+function [var, U, lambda] = ppca(x, ppca_dim)
+%PPCA	Probabilistic Principal Components Analysis
+%
+%	Description
+%	 [VAR, U, LAMBDA] = PPCA(X, PPCA_DIM) computes the principal
+%	component subspace U of dimension PPCA_DIM using a centred covariance
+%	matrix X. The variable VAR contains the off-subspace variance (which
+%	is assumed to be spherical), while the vector LAMBDA contains the
+%	variances of each of the principal components.  This is computed
+%	using the eigenvalue and eigenvector  decomposition of X.
+%
+%	See also
+%	EIGDEC, PCA
+%
+
+%	Copyright (c) Ian T Nabney (1996-2001)
+
+
+if ppca_dim ~= round(ppca_dim) | ppca_dim < 1 | ppca_dim > size(x, 2)
+   error('Number of PCs must be integer, >0, < dim');
+end
+
+[ndata, data_dim] = size(x);
+% Assumes that x is centred and responsibility weighted
+% covariance matrix
+[l Utemp] = eigdec(x, data_dim);
+% Zero any negative eigenvalues (caused by rounding)
+l(l<0) = 0;
+% Now compute the sigma squared values for all possible values
+% of q
+s2_temp = cumsum(l(end:-1:1))./[1:data_dim]';
+% If necessary, reduce the value of q so that var is at least
+% eps * largest eigenvalue
+q_temp = min([ppca_dim; data_dim-min(find(s2_temp/l(1) > eps))]);
+if q_temp ~= ppca_dim
+  wstringpart = 'Covariance matrix ill-conditioned: extracted';
+  wstring = sprintf('%s %d/%d PCs', ...
+      wstringpart, q_temp, ppca_dim);
+  warning(wstring);
+end
+if q_temp == 0
+  % All the latent dimensions have disappeared, so we are
+  % just left with the noise model
+  var = l(1)/data_dim;
+  lambda = var*ones(1, ppca_dim);
+else
+  var = mean(l(q_temp+1:end));
+end  
+U = Utemp(:, 1:q_temp);
+lambda(1:q_temp) = l(1:q_temp);
+
+