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 consistencyerrstring = consist(net, 'gtm', data);if ~isempty(errstring)  error(errstring);end% Check type of samplestypes = {'regular', 'uniform', 'gaussian'};if (strcmp(samp_type, stypes)) == 0  error('Undefined sample type.')endif net.dim_latent > size(data, 2)  error('Latent space dimension must not be greater than data dimension')endnlatent = net.gmmnet.ncentres;nhidden = net.rbfnet.nhidden;% Create latent data sample and set RBF centresswitch samp_typecase '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 eigenvaluesA = 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 datanet.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 realmaxnet.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 eigenvalueif net.dim_latent < size(data, 2)  sigma = min(sigma, PCcoeff(net.dim_latent+1));endnet.gmmnet.covars = sigma*ones(1, net.gmmnet.ncentres);% Sub-function to create the sample data in 2dfunction 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 itmaxXY= max(sample);sample(:,1) = 2*(sample(:,1) - maxXY(1)/2)./maxXY(1);sample(:,2) = 2*(sample(:,2) - maxXY(2)/2)./maxXY(2);return;