wolffd@0: %DEMSOM1 Demonstrate SOM for visualisation.
wolffd@0: %
wolffd@0: %	Description
wolffd@0: %	 This script demonstrates the use of a SOM with  a two-dimensional
wolffd@0: %	grid to map onto data in  two-dimensional space.  Both on-line and
wolffd@0: %	batch training algorithms are shown.
wolffd@0: %
wolffd@0: %	See also
wolffd@0: %	SOM, SOMPAK, SOMTRAIN
wolffd@0: %
wolffd@0: 
wolffd@0: %	Copyright (c) Ian T Nabney (1996-2001)
wolffd@0: 
wolffd@0: 
wolffd@0: randn('state', 42);
wolffd@0: rand('state', 42);
wolffd@0: nin = 2; 
wolffd@0: ndata = 300;
wolffd@0: % Give data an offset so that network has something to learn.
wolffd@0: x = rand(ndata, nin) + ones(ndata, 1)*[1.5 1.5];
wolffd@0: 
wolffd@0: clc;
wolffd@0: disp('This demonstration of the SOM, or Kohonen network, shows how the')
wolffd@0: disp('network units after training lie in regions of high data density.')
wolffd@0: disp('First we show the data, which is generated uniformly from a square.')
wolffd@0: disp('Red crosses denote the data and black dots are the initial locations')
wolffd@0: disp('of the SOM units.')
wolffd@0: disp(' ')
wolffd@0: disp('Press any key to continue.')
wolffd@0: pause
wolffd@0: net = som(nin, [8, 7]);
wolffd@0: c1 = sompak(net);
wolffd@0: h1 = figure;
wolffd@0: plot(x(:, 1), x(:, 2), 'r+');
wolffd@0: hold on
wolffd@0: plot(c1(:,1), c1(:, 2), 'k.');
wolffd@0: drawnow;  % Force figure to be drawn before training starts
wolffd@0: options = foptions;
wolffd@0: 
wolffd@0: % Ordering phase
wolffd@0: options(1) = 1;
wolffd@0: options(14) = 50;
wolffd@0: %options(14) = 5; % Just for testing
wolffd@0: options(18) = 0.9;  % Initial learning rate
wolffd@0: options(16) = 0.05; % Final learning rate
wolffd@0: options(17) = 8;    % Initial neighbourhood size
wolffd@0: options(15) = 1;    % Final neighbourhood size
wolffd@0: 
wolffd@0: disp('The SOM network is trained in two phases using an on-line algorithm.')
wolffd@0: disp('Initially the neighbourhood is set to 8 and is then reduced')
wolffd@0: disp('linearly to 1 over the first 50 iterations.')
wolffd@0: disp('Each iteration consists of a pass through the complete')
wolffd@0: disp('dataset, while the weights are adjusted after each pattern.')
wolffd@0: disp('The learning rate is reduced linearly from 0.9 to 0.05.')
wolffd@0: disp('This ordering phase puts the units in a rough grid shape.')
wolffd@0: disp('Blue circles denote the units at the end of this phase.')
wolffd@0: disp(' ')
wolffd@0: disp('Press any key to continue.')
wolffd@0: pause
wolffd@0: net2 = somtrain(net, options, x);
wolffd@0: c2 = sompak(net2);
wolffd@0: plot(c2(:, 1), c2(:, 2), 'bo');
wolffd@0: drawnow;
wolffd@0: 
wolffd@0: % Convergence phase
wolffd@0: options(1) = 1;
wolffd@0: options(14) = 400;
wolffd@0: options(18) = 0.05;
wolffd@0: options(16) = 0.01;
wolffd@0: options(17) = 0;
wolffd@0: options(15) = 0;
wolffd@0: 
wolffd@0: disp('The second, convergence, phase of learning just updates the winning node.')
wolffd@0: disp('The learning rate is reduced from 0.05 to 0.01 over 400 iterations.')
wolffd@0: disp('Note how the error value does not decrease monotonically; it is')
wolffd@0: disp('difficult to decide when training is complete in a principled way.')
wolffd@0: disp('The units are plotted as green stars.')
wolffd@0: disp(' ')
wolffd@0: disp('Press any key to continue.')
wolffd@0: pause
wolffd@0: net3 = somtrain(net2, options, x);
wolffd@0: c3 = sompak(net3);
wolffd@0: plot(c3(:, 1), c3(:, 2), 'g*');
wolffd@0: drawnow;
wolffd@0: 
wolffd@0: % Now try batch training
wolffd@0: options(1) = 1;
wolffd@0: options(6) = 1;
wolffd@0: options(14) = 50;
wolffd@0: options(17) = 3;
wolffd@0: options(15) = 0;
wolffd@0: disp('An alternative approach to the on-line algorithm is a batch update')
wolffd@0: disp('rule.  Each unit is updated to be the average weights')
wolffd@0: disp('in a neighbourhood (which reduces from 3 to 0) over 50 iterations.');
wolffd@0: disp('Note how the error is even more unstable at first, though eventually')
wolffd@0: disp('it does converge.')
wolffd@0: disp('The final units are shown as black triangles.')
wolffd@0: disp(' ')
wolffd@0: disp('Press any key to continue.')
wolffd@0: pause
wolffd@0: net4 = somtrain(net, options, x);
wolffd@0: c4 = sompak(net4);
wolffd@0: plot(c4(:, 1), c4(:, 2), 'k^')
wolffd@0: legend('Data', 'Initial weights', 'Weights after ordering', ...
wolffd@0:     'Weights after convergence', 'Batch weights', 2);
wolffd@0: drawnow;
wolffd@0: 
wolffd@0: disp(' ')
wolffd@0: disp('Press any key to end.')
wolffd@0: disp(' ')
wolffd@0: pause
wolffd@0: 
wolffd@0: close(h1);