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1 %DEMNS1 Demonstrate Neuroscale for visualisation.
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2 %
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3 % Description
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4 % This script demonstrates the use of the Neuroscale algorithm for
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5 % topographic projection and visualisation. A data sample is generated
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6 % from a mixture of two Gaussians in 4d space, and an RBF is trained
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7 % with the stress error function to project the data into 2d. The
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8 % training data and a test sample are both plotted in this projection.
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9 %
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10 % See also
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11 % RBF, RBFTRAIN, RBFPRIOR
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12 %
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13
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14 % Copyright (c) Ian T Nabney (1996-2001)
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15
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16 % Generate the data
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17 % Fix seeds for reproducible results
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18 rand('state', 420);
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19 randn('state', 420);
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20
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21 input_dim = 4;
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22 output_dim = 2;
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23 mix = gmm(input_dim, 2, 'spherical');
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24 mix.centres = [1 1 1 1; 0 0 0 0];
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25 mix.priors = [0.5 0.5];
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26 mix.covars = [0.1 0.1];
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27
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28 ndata = 60;
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29 [data, labels] = gmmsamp(mix, ndata);
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30
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31 clc
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32 disp('This demonstration illustrates the use of the Neuroscale model')
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33 disp('to perform a topographic projection of data. We begin by generating')
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34 disp('60 data points from a mixture of two Gaussians in 4 dimensional space.')
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35 disp(' ')
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36 disp('Press any key to continue')
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37 pause
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38
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39 ncentres = 10;
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40 net = rbf(input_dim, ncentres, output_dim, 'tps', 'neuroscale');
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41 dstring = ['the Sammon mapping. The model has ', num2str(ncentres), ...
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42 ' centres, two outputs, and uses'];
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43 clc
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44 disp('The Neuroscale model is an RBF with a Stress error measure as used in')
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45 disp(dstring)
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46 disp('thin plate spline basis functions.')
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47 disp(' ')
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48 disp('It is trained using the shadow targets algorithm for at most 60 iterations.')
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49 disp(' ')
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50 disp('Press any key to continue')
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51 pause
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52
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53 % First row controls shadow targets, second row controls rbfsetbf
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54 options(1, :) = foptions;
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55 options(2, :) = foptions;
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56 options(1, 1) = 1;
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57 options(1, 2) = 1e-2;
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58 options(1, 3) = 1e-2;
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59 options(1, 6) = 1; % Switch on PCA initialisation
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60 options(1, 14) = 60;
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61 options(2, 1) = -1; % Switch off all warnings
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62 options(2, 5) = 1;
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63 options(2, 14) = 10;
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64 net2 = rbftrain(net, options, data);
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65
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66 disp(' ')
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67 disp('After training the model, we project the training data by a normal')
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68 disp('forward propagation through the RBF network. Because there are two')
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69 disp('outputs, the results can be plotted and visualised.')
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70 disp(' ')
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71 disp('Press any key to continue')
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72 pause
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73
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74 % Plot the result
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75 y = rbffwd(net2, data);
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76 ClassSymbol1 = 'r.';
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77 ClassSymbol2 = 'b.';
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78 PointSize = 12;
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79 fh1 = figure;
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80 hold on;
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81 plot(y((labels==1),1),y(labels==1,2),ClassSymbol1, 'MarkerSize', PointSize)
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82 plot(y((labels>1),1),y(labels>1,2),ClassSymbol2, 'MarkerSize', PointSize)
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83
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84 disp(' ')
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85 disp('In this plot, the red dots denote the first class and the blue')
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86 disp('dots the second class.')
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87 disp(' ')
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88 disp('Press any key to continue.')
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89 disp(' ')
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90 pause
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91
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92 disp('We now generate a further 100 data points from the original distribution')
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93 disp('and plot their projection using star symbols. Note that a Sammon')
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94 disp('mapping cannot be used to generalise to new data in this fashion.')
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95
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96 [test_data, test_labels] = gmmsamp(mix, 100);
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97 ytest = rbffwd(net2, test_data);
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98 ClassSymbol1 = 'ro';
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99 ClassSymbol2 = 'bo';
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100 % Circles are rather large symbols
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101 PointSize = 6;
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102 hold on
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103 plot(ytest((test_labels==1),1),ytest(test_labels==1,2), ...
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104 ClassSymbol1, 'MarkerSize', PointSize)
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105 plot(ytest((test_labels>1),1),ytest(test_labels>1,2),...
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106 ClassSymbol2, 'MarkerSize', PointSize)
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107 hold on
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108 legend('Class 1', 'Class 2', 'Test Class 1', 'Test Class 2')
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109 disp('Press any key to exit.')
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110 pause
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111
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112 close(fh1);
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113 clear all;
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114
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