comparison toolboxes/FullBNT-1.0.7/netlab3.3/demgtm1.m @ 0:e9a9cd732c1e tip

first hg version after svn

+%DEMGTM1 Demonstrate EM for GTM.
+%
+%	Description
+%	 This script demonstrates the use of the EM algorithm to fit a one-
+%	dimensional GTM to a two-dimensional set of data using maximum
+%	likelihood. The location and spread of the Gaussian kernels in the
+%	data space is shown during training.
+%
+%	See also
+%	DEMGTM2, GTM, GTMEM, GTMPOST
+%
+
+%	Copyright (c) Ian T Nabney (1996-2001)
+
+% Demonstrates the GTM with a 2D target space and a 1D latent space.
+%
+%		This script generates a simple data set in 2 dimensions, 
+%		with an intrinsic dimensionality of 1, and trains a GTM 
+%		with a 1-dimensional latent variable to model this data 
+%		set, visually illustrating the training process
+%
+% Synopsis:	gtm_demo
+
+% Generate and plot a 2D data set
+
+data_min = 0.15;
+data_max = 3.05;
+T = [data_min:0.05:data_max]';
+T = [T (T + 1.25*sin(2*T))];
+fh1 = figure;
+plot(T(:,1), T(:,2), 'ro');
+axis([data_min-0.05 data_max+0.05 data_min-0.05 data_max+0.05]);
+clc;
+disp('This demonstration shows in detail how the EM algorithm works')
+disp('for training a GTM with a one dimensional latent space.')
+disp(' ')
+fprintf([...
+'The figure shows data generated by feeding a 1D uniform distribution\n', ...
+'(on the X-axis) through a non-linear function (y = x + 1.25*sin(2*x))\n', ...
+'\nPress any key to continue ...\n\n']);
+pause;
+
+% Generate a unit circle figure, to be used for plotting
+src = [0:(2*pi)/(20-1):2*pi]';
+unitC = [sin(src) cos(src)];
+
+% Generate and plot (along with the data) an initial GTM model
+
+clc;
+num_latent_points = 20;
+num_rbf_centres = 5;
+
+net = gtm(1, num_latent_points, 2, num_rbf_centres, 'gaussian');
+
+options = zeros(1, 18);
+options(7) = 1;
+net = gtminit(net, options, T, 'regular', num_latent_points, ...
+   num_rbf_centres);
+
+mix = gtmfwd(net);
+% Replot the figure
+hold off;
+plot(mix.centres(:,1),  mix.centres(:,2), 'g');
+hold on;
+for i=1:num_latent_points
+  c = 2*unitC*sqrt(mix.covars(1)) + [ones(20,1)*mix.centres(i,1) ...
+      ones(num_latent_points,1)*mix.centres(i,2)];
+  fill(c(:,1), c(:,2), [0.8 1 0.8]);
+end
+plot(T(:,1), T(:,2), 'ro');
+plot(mix.centres(:,1),  mix.centres(:,2), 'g+');
+plot(mix.centres(:,1),  mix.centres(:,2), 'g');
+axis([data_min-0.05 data_max+0.05 data_min-0.05 data_max+0.05]);
+drawnow;
+title('Initial configuration');
+disp(' ')
+fprintf([...
+'The figure shows the starting point for the GTM, before the training.\n', ...
+'A discrete latent variable distribution of %d points in 1 dimension \n', ...
+'is mapped to the 1st principal component of the target data by an RBF.\n', ...
+'with %d basis functions.  Each of the %d points defines the centre of\n', ...
+'a Gaussian in a Gaussian mixture, marked by the green ''+''-signs.  The\n', ...
+'mixture components all have equal variance, illustrated by the filled\n', ...
+'circle around each ''+''-sign, the radii corresponding to 2 standard\n', ...
+'deviations.  The ''+''-signs are connected with a line according to their\n', ...
+'corresponding ordering in latent space.\n\n', ...
+'Press any key to begin training ...\n\n'], num_latent_points, ...
+num_rbf_centres, num_latent_points);
+pause;
+
+figure(fh1);
+%%%% Train the GTM and plot it (along with the data) as training proceeds %%%%
+options = foptions;
+options(1) = -1;  % Turn off all warning messages
+options(14) = 1;
+for j = 1:15
+  [net, options] = gtmem(net, T, options);
+  hold off;
+  mix = gtmfwd(net);
+  plot(mix.centres(:,1),  mix.centres(:,2), 'g');
+  hold on;
+  for i=1:20
+    c = 2*unitC*sqrt(mix.covars(1)) + [ones(20,1)*mix.centres(i,1) ...
+	ones(20,1)*mix.centres(i,2)];
+    fill(c(:,1), c(:,2), [0.8 1.0 0.8]);
+  end
+  plot(T(:,1), T(:,2), 'ro');
+  plot(mix.centres(:,1),  mix.centres(:,2), 'g+');
+  plot(mix.centres(:,1),  mix.centres(:,2), 'g');
+  axis([0 3.5 0 3.5]);
+  title(['After ', int2str(j),' iterations of training.']);
+  drawnow;
+  if (j == 4)
+    fprintf([...
+'The GTM initially adapts relatively quickly - already after \n', ...
+'4 iterations of training, a rough fit is attained.\n\n', ...
+'Press any key to continue training ...\n\n']);
+pause;
+figure(fh1);
+  elseif (j == 8)
+    fprintf([...
+'After another 4 iterations of training:  from now on further \n', ...
+'training only makes small changes to the mapping, which combined with \n', ...
+'decrements of the Gaussian mixture variance, optimize the fit in \n', ...
+'terms of likelihood.\n\n', ...
+'Press any key to continue training ...\n\n']);
+pause;
+figure(fh1);
+  else
+    pause(1);
+  end
+end
+
+clc;
+fprintf([...
+'After 15 iterations of training the GTM can be regarded as converged. \n', ...
+'Is has been adapted to fit the target data distribution as well \n', ...
+'as possible, given prior smoothness constraints on the mapping. It \n', ...
+'captures the fact that the probabilty density is higher at the two \n', ...
+'bends of the curve, and lower towards its end points.\n\n']);
+disp(' ');
+disp('Press any key to exit.');
+pause;
+
+close(fh1);
+clear all;
+