%DEMGTM2 Demonstrate GTM for visualisation.%%	Description%	 This script demonstrates the use of a GTM with  a two-dimensional%	latent space to visualise data in a higher dimensional space. This is%	done through the use of the mean responsibility and magnification%	factors.%%	See also%	DEMGTM1, GTM, GTMEM, GTMPOST%%	Copyright (c) Ian T Nabney (1996-2001)% Fix seeds for reproducible resultsrand('state', 420);randn('state', 420);ndata = 300clc;disp('This demonstration shows how a Generative Topographic Mapping')disp('can be used to model and visualise high dimensional data.  The')disp('data is generated from a mixture of two spherical Gaussians in')dstring = ['four dimensional space. ', num2str(ndata), ...      ' data points are generated.'];disp(dstring);disp(' ');disp('Press any key to continue.')pause% Create datadata_dim = 4;latent_dim = 2;mix = gmm(data_dim, 2, 'spherical');mix.centres = [1 1 1 1; 0 0 0 0];mix.priors = [0.5 0.5];mix.covars = [0.1 0.1];[data, labels] = gmmsamp(mix, ndata);latent_shape = [15 15];  % Number of latent points in each dimensionnlatent = prod(latent_shape);  % Number of latent pointsnum_rbf_centres = 16;clc;dstring = ['Next we generate and initialise the GTM.  There are ',...      num2str(nlatent), ' latent points'];disp(dstring);dstring = ['arranged in a square of ', num2str(latent_shape(1)), ...      ' points on a side.  There are ', num2str(num_rbf_centres), ...      ' centres in the'];disp(dstring);disp('RBF model, which has Gaussian activation functions.')disp(' ')disp('Once the model is created, the latent data sample')disp('and RBF centres are placed uniformly in the square [-1 1 -1 1].')disp('The output weights of the RBF are computed to map the latent');disp('space to the two dimensional PCA subspace of the data.');disp(' ')disp('Press any key to continue.');pause;% Create and initialise GTM modelnet = gtm(latent_dim, nlatent, data_dim, num_rbf_centres, ...   'gaussian', 0.1);options = foptions;options(1) = -1;options(7) = 1;    % Set width factor of RBFnet = gtminit(net, options, data, 'regular', latent_shape, [4 4]);options = foptions;options(14) = 30;options(1) = 1;clc;dstring = ['We now train the model with ', num2str(options(14)), ...      ' iterations of'];disp(dstring)disp('the EM algorithm for the GTM.')disp(' ')disp('Press any key to continue.')pause;[net, options] = gtmem(net, data, options);disp(' ')disp('Press any key to continue.')pause;clc;disp('We now visualise the data by plotting, for each data point,');disp('the posterior mean and mode (in latent space).  These give');disp('a summary of the entire posterior distribution in latent space.')disp('The corresponding values are joined by a line to aid the')disp('interpretation.')disp(' ')disp('Press any key to continue.');pause;% Plot posterior meansmeans = gtmlmean(net, data);modes = gtmlmode(net, data);PointSize = 12;ClassSymbol1 = 'r.';ClassSymbol2 = 'b.';fh1 = figure;hold on;title('Visualisation in latent space')plot(means((labels==1),1), means(labels==1,2), ...  ClassSymbol1, 'MarkerSize', PointSize)plot(means((labels>1),1),means(labels>1,2),...   ClassSymbol2, 'MarkerSize', PointSize)ClassSymbol1 = 'ro';ClassSymbol2 = 'bo';plot(modes(labels==1,1), modes(labels==1,2), ...  ClassSymbol1)plot(modes(labels>1,1),modes(labels>1,2),...   ClassSymbol2)% Join up means and modesfor n = 1:ndata   plot([means(n,1); modes(n,1)], [means(n,2); modes(n,2)], 'g-')end% Place legend outside data plotlegend('Mean (class 1)', 'Mean (class 2)', 'Mode (class 1)',...   'Mode (class 2)', -1);% Display posterior for a data point% Choose an interesting one with a large distance between mean and% mode[distance, point] = max(sum((means-modes).^2, 2));resp = gtmpost(net, data(point, :));disp(' ')disp('For more detailed information, the full posterior distribution')disp('(or responsibility) can be plotted in latent space for a')disp('single data point.  This point has been chosen as the one')disp('with the largest distance between mean and mode.')disp(' ')disp('Press any key to continue.');pause;R = reshape(resp, fliplr(latent_shape));XL = reshape(net.X(:,1), fliplr(latent_shape));YL = reshape(net.X(:,2), fliplr(latent_shape));fh2 = figure;imagesc(net.X(:, 1), net.X(:,2), R);hold on;tstr = ['Responsibility for point ', num2str(point)];title(tstr);set(gca,'YDir','normal')colormap(hot);colorbardisp(' ');disp('Press any key to continue.')pauseclcdisp('Finally, we visualise the data with the posterior means in')disp('latent space as before, but superimpose the magnification')disp('factors to highlight the separation between clusters.')disp(' ')disp('Note the large magnitude factors down the centre of the')disp('graph, showing that the manifold is stretched more in')disp('this region than within each of the two clusters.')ClassSymbol1 = 'g.';ClassSymbol2 = 'b.';fh3 = figure;mags = gtmmag(net, net.X);% Reshape into grid formMags = reshape(mags, fliplr(latent_shape));imagesc(net.X(:, 1), net.X(:,2), Mags);hold ontitle('Dataset visualisation with magnification factors')set(gca,'YDir','normal')colormap(hot);colorbarhold on; % Else the magnification plot disappearsplot(means(labels==1,1), means(labels==1,2), ...  ClassSymbol1, 'MarkerSize', PointSize)plot(means(labels>1,1), means(labels>1,2), ...  ClassSymbol2, 'MarkerSize', PointSize)disp(' ')disp('Press any key to exit.')pauseclose(fh1);close(fh2);close(fh3);clear all;