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