%DEMNS1	Demonstrate Neuroscale for visualisation.%%	Description%	This script demonstrates the use of the Neuroscale algorithm for%	topographic projection and visualisation.  A data sample is generated%	from a mixture of two Gaussians in 4d space, and an RBF is trained%	with the stress error function to project the data into 2d.  The%	training data and a test sample are both plotted in this projection.%%	See also%	RBF, RBFTRAIN, RBFPRIOR%%	Copyright (c) Ian T Nabney (1996-2001)% Generate the data% Fix seeds for reproducible resultsrand('state', 420);randn('state', 420);input_dim = 4;output_dim = 2;mix = gmm(input_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];ndata = 60;[data, labels] = gmmsamp(mix, ndata);clcdisp('This demonstration illustrates the use of the Neuroscale model')disp('to perform a topographic projection of data.  We begin by generating')disp('60 data points from a mixture of two Gaussians in 4 dimensional space.')disp(' ')disp('Press any key to continue')pausencentres = 10;net = rbf(input_dim, ncentres, output_dim, 'tps', 'neuroscale');dstring = ['the Sammon mapping.  The model has ', num2str(ncentres), ...    ' centres, two outputs, and uses'];clcdisp('The Neuroscale model is an RBF with a Stress error measure as used in')disp(dstring)disp('thin plate spline basis functions.')disp(' ')disp('It is trained using the shadow targets algorithm for at most 60 iterations.')disp(' ')disp('Press any key to continue')pause% First row controls shadow targets, second row controls rbfsetbfoptions(1, :) = foptions;options(2, :) = foptions;options(1, 1) = 1;options(1, 2) = 1e-2;options(1, 3) = 1e-2;options(1, 6) = 1;    % Switch on PCA initialisationoptions(1, 14) = 60;options(2, 1) = -1;   % Switch off all warningsoptions(2, 5) = 1;options(2, 14) = 10;net2 = rbftrain(net, options, data);disp(' ')disp('After training the model, we project the training data by a normal')disp('forward propagation through the RBF network.  Because there are two')disp('outputs, the results can be plotted and visualised.')disp(' ')disp('Press any key to continue')pause% Plot the resulty = rbffwd(net2, data);ClassSymbol1 = 'r.';ClassSymbol2 = 'b.';PointSize = 12;fh1 = figure;hold on;plot(y((labels==1),1),y(labels==1,2),ClassSymbol1, 'MarkerSize', PointSize)plot(y((labels>1),1),y(labels>1,2),ClassSymbol2, 'MarkerSize', PointSize)disp(' ')disp('In this plot, the red dots denote the first class and the blue')disp('dots the second class.')disp(' ')disp('Press any key to continue.')disp(' ')pausedisp('We now generate a further 100 data points from the original distribution')disp('and plot their projection using star symbols.  Note that a Sammon')disp('mapping cannot be used to generalise to new data in this fashion.')[test_data, test_labels] = gmmsamp(mix, 100);ytest = rbffwd(net2, test_data);ClassSymbol1 = 'ro';ClassSymbol2 = 'bo';% Circles are rather large symbolsPointSize = 6;hold onplot(ytest((test_labels==1),1),ytest(test_labels==1,2), ...  ClassSymbol1, 'MarkerSize', PointSize)plot(ytest((test_labels>1),1),ytest(test_labels>1,2),...  ClassSymbol2, 'MarkerSize', PointSize)hold onlegend('Class 1', 'Class 2', 'Test Class 1', 'Test Class 2')disp('Press any key to exit.')pauseclose(fh1);clear all;