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

first hg version after svn

+function net = gtminit(net, options, data, samp_type, varargin)
+%GTMINIT Initialise the weights and latent sample in a GTM.
+%
+%	Description
+%	NET = GTMINIT(NET, OPTIONS, DATA, SAMPTYPE) takes a GTM NET and
+%	generates a sample of latent data points and sets the centres (and
+%	widths if appropriate) of NET.RBFNET.
+%
+%	If the SAMPTYPE is 'REGULAR', then regular grids of latent data
+%	points and RBF centres are created.  The dimension of the latent data
+%	space must be 1 or 2.  For one-dimensional latent space, the
+%	LSAMPSIZE parameter gives the number of latent points and the
+%	RBFSAMPSIZE parameter gives the number of RBF centres.  For a two-
+%	dimensional latent space, these parameters must be vectors of length
+%	2 with the number of points in each of the x and y directions to
+%	create a rectangular grid.  The widths of the RBF basis functions are
+%	set by a call to RBFSETFW passing OPTIONS(7) as the scaling
+%	parameter.
+%
+%	If the SAMPTYPE is 'UNIFORM' or 'GAUSSIAN' then the latent data is
+%	found by sampling from a uniform or Gaussian distribution
+%	correspondingly.  The RBF basis function parameters are set by a call
+%	to RBFSETBF with the DATA parameter as dataset and the OPTIONS
+%	vector.
+%
+%	Finally, the output layer weights of the RBF are initialised by
+%	mapping the mean of the latent variable to the mean of the target
+%	variable, and the L-dimensional latent variale variance to the
+%	variance of the targets along the first L principal components.
+%
+%	See also
+%	GTM, GTMEM, PCA, RBFSETBF, RBFSETFW
+%
+
+%	Copyright (c) Ian T Nabney (1996-2001)
+
+% Check for consistency
+errstring = consist(net, 'gtm', data);
+if ~isempty(errstring)
+  error(errstring);
+end
+
+% Check type of sample
+stypes = {'regular', 'uniform', 'gaussian'};
+if (strcmp(samp_type, stypes)) == 0
+  error('Undefined sample type.')
+end
+
+if net.dim_latent > size(data, 2)
+  error('Latent space dimension must not be greater than data dimension')
+end
+nlatent = net.gmmnet.ncentres;
+nhidden = net.rbfnet.nhidden;
+
+% Create latent data sample and set RBF centres
+
+switch samp_type
+case 'regular'
+   if nargin ~= 6
+      error('Regular type must specify latent and RBF shapes');
+   end
+   l_samp_size = varargin{1};
+   rbf_samp_size = varargin{2};
+   if round(l_samp_size) ~= l_samp_size
+      error('Latent sample specification must contain integers')
+   end
+   % Check existence and size of rbf specification
+   if any(size(rbf_samp_size) ~= [1 net.dim_latent]) | ...
+         prod(rbf_samp_size) ~= nhidden
+      error('Incorrect specification of RBF centres')
+   end
+   % Check dimension and type of latent data specification
+   if any(size(l_samp_size) ~= [1 net.dim_latent]) | ...
+         prod(l_samp_size) ~= nlatent
+      error('Incorrect dimension of latent sample spec.')
+   end
+   if net.dim_latent == 1
+      net.X = [-1:2/(l_samp_size-1):1]';
+      net.rbfnet.c = [-1:2/(rbf_samp_size-1):1]';
+      net.rbfnet = rbfsetfw(net.rbfnet, options(7));
+   elseif net.dim_latent == 2
+      net.X = gtm_rctg(l_samp_size);
+      net.rbfnet.c = gtm_rctg(rbf_samp_size);
+      net.rbfnet = rbfsetfw(net.rbfnet, options(7));
+   else
+      error('For regular sample, input dimension must be 1 or 2.')
+   end
+   
+   
+case {'uniform', 'gaussian'}
+   if strcmp(samp_type, 'uniform')
+      net.X = 2 * (rand(nlatent, net.dim_latent) - 0.5);
+   else
+      % Sample from N(0, 0.25) distribution to ensure most latent 
+      % data is inside square
+      net.X = randn(nlatent, net.dim_latent)/2;
+   end   
+   net.rbfnet = rbfsetbf(net.rbfnet, options, net.X);
+otherwise
+   % Shouldn't get here
+   error('Invalid sample type');
+   
+end
+
+% Latent data sample and basis function parameters chosen.
+% Now set output weights
+[PCcoeff, PCvec] = pca(data);
+
+% Scale PCs by eigenvalues
+A = PCvec(:, 1:net.dim_latent)*diag(sqrt(PCcoeff(1:net.dim_latent)));
+
+[temp, Phi] = rbffwd(net.rbfnet, net.X);
+% Normalise X to ensure 1:1 mapping of variances and calculate weights
+% as solution of Phi*W = normX*A'
+normX = (net.X - ones(size(net.X))*diag(mean(net.X)))*diag(1./std(net.X));
+net.rbfnet.w2 = Phi \ (normX*A');
+% Bias is mean of target data
+net.rbfnet.b2 = mean(data);
+
+% Must also set initial value of variance
+% Find average distance between nearest centres
+% Ensure that distance of centre to itself is excluded by setting diagonal
+% entries to realmax
+net.gmmnet.centres = rbffwd(net.rbfnet, net.X);
+d = dist2(net.gmmnet.centres, net.gmmnet.centres) + ...
+  diag(ones(net.gmmnet.ncentres, 1)*realmax);
+sigma = mean(min(d))/2;
+
+% Now set covariance to minimum of this and next largest eigenvalue
+if net.dim_latent < size(data, 2)
+  sigma = min(sigma, PCcoeff(net.dim_latent+1));
+end
+net.gmmnet.covars = sigma*ones(1, net.gmmnet.ncentres);
+
+% Sub-function to create the sample data in 2d
+function sample = gtm_rctg(samp_size)
+
+xDim = samp_size(1);
+yDim = samp_size(2);
+% Produce a grid with the right number of rows and columns
+[X, Y] = meshgrid([0:1:(xDim-1)], [(yDim-1):-1:0]);
+
+% Change grid representation 
+sample = [X(:), Y(:)];
+
+% Shift grid to correct position and scale it
+maxXY= max(sample);
+sample(:,1) = 2*(sample(:,1) - maxXY(1)/2)./maxXY(1);
+sample(:,2) = 2*(sample(:,2) - maxXY(2)/2)./maxXY(2);
+return;
+
+   
+