wolffd@0: %DEMGLM2 Demonstrate simple classification using a generalized linear model.
wolffd@0: %
wolffd@0: %	Description
wolffd@0: %	 The problem consists of a two dimensional input matrix DATA and a
wolffd@0: %	vector of classifications T.  The data is  generated from three
wolffd@0: %	Gaussian clusters, and a generalized linear model with softmax output
wolffd@0: %	is trained using iterative reweighted least squares. A plot of the
wolffd@0: %	data together with regions shaded by the classification given by the
wolffd@0: %	network is generated.
wolffd@0: %
wolffd@0: %	See also
wolffd@0: %	DEMGLM1, GLM, GLMTRAIN
wolffd@0: %
wolffd@0: 
wolffd@0: %	Copyright (c) Ian T Nabney (1996-2001)
wolffd@0: 
wolffd@0: 
wolffd@0: % Generate data from three classes in 2d
wolffd@0: input_dim = 2;
wolffd@0: 
wolffd@0: % Fix seeds for reproducible results
wolffd@0: randn('state', 42);
wolffd@0: rand('state', 42);
wolffd@0: 
wolffd@0: ndata = 100;
wolffd@0: % Generate mixture of three Gaussians in two dimensional space
wolffd@0: mix = gmm(2, 3, 'spherical');
wolffd@0: mix.priors = [0.4 0.3 0.3];            % Cluster priors
wolffd@0: mix.centres = [2, 2; 0.0, 0.0; 1, -1];  % Cluster centres
wolffd@0: mix.covars = [0.5 1.0 0.6];
wolffd@0: 
wolffd@0: [data, label] = gmmsamp(mix, ndata);
wolffd@0: id = eye(3);
wolffd@0: targets = id(label,:);
wolffd@0: 
wolffd@0: % Plot the result
wolffd@0: 
wolffd@0: clc
wolffd@0: disp('This demonstration illustrates the use of a generalized linear model')
wolffd@0: disp('to classify data from three classes in a two-dimensional space. We')
wolffd@0: disp('begin by generating and plotting the data.')
wolffd@0: disp(' ')
wolffd@0: disp('Press any key to continue.')
wolffd@0: pause
wolffd@0: 
wolffd@0: fh1 = figure;
wolffd@0: plot(data(label==1,1), data(label==1,2), 'bo');
wolffd@0: hold on
wolffd@0: axis([-4 5 -4 5]);
wolffd@0: set(gca, 'Box', 'on')
wolffd@0: plot(data(label==2,1), data(label==2,2), 'rx')
wolffd@0: plot(data(label==3, 1), data(label==3, 2), 'go')
wolffd@0: title('Data')
wolffd@0: 
wolffd@0: clc
wolffd@0: disp('Now we fit a model consisting of a softmax function of')
wolffd@0: disp('a linear combination of the input variables.')
wolffd@0: disp(' ')
wolffd@0: disp('The model is trained using the IRLS algorithm for up to 10 iterations')
wolffd@0: disp(' ')
wolffd@0: disp('Press any key to continue.')
wolffd@0: pause
wolffd@0: 
wolffd@0: net = glm(input_dim, size(targets, 2), 'softmax');
wolffd@0: options = foptions;
wolffd@0: options(1) = 1;
wolffd@0: options(14) = 10;
wolffd@0: net = glmtrain(net, options, data, targets);
wolffd@0: 
wolffd@0: disp(' ')
wolffd@0: disp('We now plot the decision regions given by this model.')
wolffd@0: disp(' ')
wolffd@0: disp('Press any key to continue.')
wolffd@0: pause
wolffd@0: 
wolffd@0: x = -4.0:0.2:5.0;
wolffd@0: y = -4.0:0.2:5.0;
wolffd@0: [X, Y] = meshgrid(x,y);
wolffd@0: X = X(:);
wolffd@0: Y = Y(:);
wolffd@0: grid = [X Y];
wolffd@0: Z = glmfwd(net, grid);
wolffd@0: [foo , class] = max(Z');
wolffd@0: class = class';
wolffd@0: colors = ['b.'; 'r.'; 'g.'];
wolffd@0: for i = 1:3
wolffd@0:   thisX = X(class == i);
wolffd@0:   thisY = Y(class == i);
wolffd@0:   h = plot(thisX, thisY, colors(i,:));
wolffd@0:   set(h, 'MarkerSize', 8);
wolffd@0: end
wolffd@0: title('Plot of Decision regions')
wolffd@0: 
wolffd@0: hold off
wolffd@0: 
wolffd@0: clc
wolffd@0: disp('Note that the boundaries of decision regions are straight lines.')
wolffd@0: disp(' ')
wolffd@0: disp('Press any key to end.')
wolffd@0: pause
wolffd@0: close(fh1);
wolffd@0: clear all; 
wolffd@0: