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1 %DEMSOM1 Demonstrate SOM for visualisation.
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2 %
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3 % Description
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4 % This script demonstrates the use of a SOM with a two-dimensional
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5 % grid to map onto data in two-dimensional space. Both on-line and
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6 % batch training algorithms are shown.
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7 %
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8 % See also
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9 % SOM, SOMPAK, SOMTRAIN
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10 %
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11
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12 % Copyright (c) Ian T Nabney (1996-2001)
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13
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14
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15 randn('state', 42);
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16 rand('state', 42);
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17 nin = 2;
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18 ndata = 300;
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19 % Give data an offset so that network has something to learn.
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20 x = rand(ndata, nin) + ones(ndata, 1)*[1.5 1.5];
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21
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22 clc;
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23 disp('This demonstration of the SOM, or Kohonen network, shows how the')
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24 disp('network units after training lie in regions of high data density.')
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25 disp('First we show the data, which is generated uniformly from a square.')
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26 disp('Red crosses denote the data and black dots are the initial locations')
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27 disp('of the SOM units.')
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28 disp(' ')
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29 disp('Press any key to continue.')
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30 pause
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31 net = som(nin, [8, 7]);
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32 c1 = sompak(net);
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33 h1 = figure;
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34 plot(x(:, 1), x(:, 2), 'r+');
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35 hold on
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36 plot(c1(:,1), c1(:, 2), 'k.');
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37 drawnow; % Force figure to be drawn before training starts
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38 options = foptions;
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39
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40 % Ordering phase
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41 options(1) = 1;
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42 options(14) = 50;
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43 %options(14) = 5; % Just for testing
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44 options(18) = 0.9; % Initial learning rate
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45 options(16) = 0.05; % Final learning rate
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46 options(17) = 8; % Initial neighbourhood size
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47 options(15) = 1; % Final neighbourhood size
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48
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49 disp('The SOM network is trained in two phases using an on-line algorithm.')
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50 disp('Initially the neighbourhood is set to 8 and is then reduced')
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51 disp('linearly to 1 over the first 50 iterations.')
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52 disp('Each iteration consists of a pass through the complete')
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53 disp('dataset, while the weights are adjusted after each pattern.')
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54 disp('The learning rate is reduced linearly from 0.9 to 0.05.')
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55 disp('This ordering phase puts the units in a rough grid shape.')
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56 disp('Blue circles denote the units at the end of this phase.')
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57 disp(' ')
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58 disp('Press any key to continue.')
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59 pause
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60 net2 = somtrain(net, options, x);
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61 c2 = sompak(net2);
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62 plot(c2(:, 1), c2(:, 2), 'bo');
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63 drawnow;
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64
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65 % Convergence phase
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66 options(1) = 1;
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67 options(14) = 400;
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68 options(18) = 0.05;
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69 options(16) = 0.01;
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70 options(17) = 0;
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71 options(15) = 0;
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72
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73 disp('The second, convergence, phase of learning just updates the winning node.')
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74 disp('The learning rate is reduced from 0.05 to 0.01 over 400 iterations.')
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75 disp('Note how the error value does not decrease monotonically; it is')
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76 disp('difficult to decide when training is complete in a principled way.')
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77 disp('The units are plotted as green stars.')
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78 disp(' ')
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79 disp('Press any key to continue.')
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80 pause
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81 net3 = somtrain(net2, options, x);
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82 c3 = sompak(net3);
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83 plot(c3(:, 1), c3(:, 2), 'g*');
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84 drawnow;
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85
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86 % Now try batch training
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87 options(1) = 1;
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88 options(6) = 1;
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89 options(14) = 50;
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90 options(17) = 3;
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91 options(15) = 0;
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92 disp('An alternative approach to the on-line algorithm is a batch update')
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93 disp('rule. Each unit is updated to be the average weights')
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94 disp('in a neighbourhood (which reduces from 3 to 0) over 50 iterations.');
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95 disp('Note how the error is even more unstable at first, though eventually')
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96 disp('it does converge.')
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97 disp('The final units are shown as black triangles.')
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98 disp(' ')
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99 disp('Press any key to continue.')
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100 pause
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101 net4 = somtrain(net, options, x);
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102 c4 = sompak(net4);
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103 plot(c4(:, 1), c4(:, 2), 'k^')
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104 legend('Data', 'Initial weights', 'Weights after ordering', ...
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105 'Weights after convergence', 'Batch weights', 2);
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106 drawnow;
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107
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108 disp(' ')
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109 disp('Press any key to end.')
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110 disp(' ')
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111 pause
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112
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113 close(h1); |
