comparison toolboxes/FullBNT-1.0.7/netlab3.3/demgtm2.m @ 0:e9a9cd732c1e tip

first hg version after svn

+%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 results
+rand('state', 420);
+randn('state', 420);
+
+ndata = 300
+clc;
+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 data
+data_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 dimension
+nlatent = prod(latent_shape);  % Number of latent points
+num_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 model
+net = gtm(latent_dim, nlatent, data_dim, num_rbf_centres, ...
+   'gaussian', 0.1);
+
+options = foptions;
+options(1) = -1;
+options(7) = 1;    % Set width factor of RBF
+net = 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 means
+means = 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 modes
+for n = 1:ndata
+   plot([means(n,1); modes(n,1)], [means(n,2); modes(n,2)], 'g-')
+end
+% Place legend outside data plot
+legend('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);
+colorbar
+disp(' ');
+disp('Press any key to continue.')
+pause
+
+clc
+disp('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 form
+Mags = reshape(mags, fliplr(latent_shape));
+imagesc(net.X(:, 1), net.X(:,2), Mags);
+hold on
+title('Dataset visualisation with magnification factors')
+set(gca,'YDir','normal')
+colormap(hot);
+colorbar
+hold on; % Else the magnification plot disappears
+plot(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.')
+pause
+
+close(fh1);
+close(fh2);
+close(fh3);
+clear all;