%DEMSOM1 Demonstrate SOM for visualisation.%%	Description%	 This script demonstrates the use of a SOM with  a two-dimensional%	grid to map onto data in  two-dimensional space.  Both on-line and%	batch training algorithms are shown.%%	See also%	SOM, SOMPAK, SOMTRAIN%%	Copyright (c) Ian T Nabney (1996-2001)randn('state', 42);rand('state', 42);nin = 2; ndata = 300;% Give data an offset so that network has something to learn.x = rand(ndata, nin) + ones(ndata, 1)*[1.5 1.5];clc;disp('This demonstration of the SOM, or Kohonen network, shows how the')disp('network units after training lie in regions of high data density.')disp('First we show the data, which is generated uniformly from a square.')disp('Red crosses denote the data and black dots are the initial locations')disp('of the SOM units.')disp(' ')disp('Press any key to continue.')pausenet = som(nin, [8, 7]);c1 = sompak(net);h1 = figure;plot(x(:, 1), x(:, 2), 'r+');hold onplot(c1(:,1), c1(:, 2), 'k.');drawnow;  % Force figure to be drawn before training startsoptions = foptions;% Ordering phaseoptions(1) = 1;options(14) = 50;%options(14) = 5; % Just for testingoptions(18) = 0.9;  % Initial learning rateoptions(16) = 0.05; % Final learning rateoptions(17) = 8;    % Initial neighbourhood sizeoptions(15) = 1;    % Final neighbourhood sizedisp('The SOM network is trained in two phases using an on-line algorithm.')disp('Initially the neighbourhood is set to 8 and is then reduced')disp('linearly to 1 over the first 50 iterations.')disp('Each iteration consists of a pass through the complete')disp('dataset, while the weights are adjusted after each pattern.')disp('The learning rate is reduced linearly from 0.9 to 0.05.')disp('This ordering phase puts the units in a rough grid shape.')disp('Blue circles denote the units at the end of this phase.')disp(' ')disp('Press any key to continue.')pausenet2 = somtrain(net, options, x);c2 = sompak(net2);plot(c2(:, 1), c2(:, 2), 'bo');drawnow;% Convergence phaseoptions(1) = 1;options(14) = 400;options(18) = 0.05;options(16) = 0.01;options(17) = 0;options(15) = 0;disp('The second, convergence, phase of learning just updates the winning node.')disp('The learning rate is reduced from 0.05 to 0.01 over 400 iterations.')disp('Note how the error value does not decrease monotonically; it is')disp('difficult to decide when training is complete in a principled way.')disp('The units are plotted as green stars.')disp(' ')disp('Press any key to continue.')pausenet3 = somtrain(net2, options, x);c3 = sompak(net3);plot(c3(:, 1), c3(:, 2), 'g*');drawnow;% Now try batch trainingoptions(1) = 1;options(6) = 1;options(14) = 50;options(17) = 3;options(15) = 0;disp('An alternative approach to the on-line algorithm is a batch update')disp('rule.  Each unit is updated to be the average weights')disp('in a neighbourhood (which reduces from 3 to 0) over 50 iterations.');disp('Note how the error is even more unstable at first, though eventually')disp('it does converge.')disp('The final units are shown as black triangles.')disp(' ')disp('Press any key to continue.')pausenet4 = somtrain(net, options, x);c4 = sompak(net4);plot(c4(:, 1), c4(:, 2), 'k^')legend('Data', 'Initial weights', 'Weights after ordering', ...    'Weights after convergence', 'Batch weights', 2);drawnow;disp(' ')disp('Press any key to end.')disp(' ')pauseclose(h1);