BNW using Octave instead of Matlab.

This version of BNW should perform the same as the original version. The only difference is that it uses Octave instead of Matlab when running BayesNet Toolbox during parameter learning.

I am calling this BNW_1.02. It can be accessed at:
compbio.uthsc.edu/BNW_1.02

1 files changed, 337 insertions, 0 deletions

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+%DEMMLP2 Demonstrate simple classification using a multi-layer perceptron
+%
+%	Description
+%	The problem consists of input data in two dimensions drawn from a
+%	mixture of three Gaussians: two of which are assigned to a single
+%	class.  An MLP with logistic outputs trained with a quasi-Newton
+%	optimisation algorithm is compared with the optimal Bayesian decision
+%	rule.
+%
+%	See also
+%	MLP, MLPFWD, NETERR, QUASINEW
+%
+
+%	Copyright (c) Ian T Nabney (1996-2001)
+
+
+% Set up some figure parameters
+AxisShift = 0.05;
+ClassSymbol1 = 'r.';
+ClassSymbol2 = 'y.';
+PointSize = 12;
+titleSize = 10;
+
+% Fix the seeds
+rand('state', 423);
+randn('state', 423);
+
+clc
+disp('This demonstration shows how an MLP with logistic outputs and')
+disp('and cross entropy error function can be trained to model the')
+disp('posterior class probabilities in a classification problem.')
+disp('The results are compared with the optimal Bayes rule classifier,')
+disp('which can be computed exactly as we know the form of the generating')
+disp('distribution.')
+disp(' ')
+disp('Press any key to continue.')
+pause
+
+fh1 = figure;
+set(fh1, 'Name', 'True Data Distribution');
+whitebg(fh1, 'k');
+
+% 
+% Generate the data
+% 
+n=200;
+
+% Set up mixture model: 2d data with three centres
+% Class 1 is first centre, class 2 from the other two
+mix = gmm(2, 3, 'full');
+mix.priors = [0.5 0.25 0.25];
+mix.centres = [0 -0.1; 1 1; 1 -1];
+mix.covars(:,:,1) = [0.625 -0.2165; -0.2165 0.875];
+mix.covars(:,:,2) = [0.2241 -0.1368; -0.1368 0.9759];
+mix.covars(:,:,3) = [0.2375 0.1516; 0.1516 0.4125];
+
+[data, label] = gmmsamp(mix, n);
+
+% 
+% Calculate some useful axis limits
+% 
+x0 = min(data(:,1));
+x1 = max(data(:,1));
+y0 = min(data(:,2));
+y1 = max(data(:,2));
+dx = x1-x0;
+dy = y1-y0;
+expand = 5/100;			% Add on 5 percent each way
+x0 = x0 - dx*expand;
+x1 = x1 + dx*expand;
+y0 = y0 - dy*expand;
+y1 = y1 + dy*expand;
+resolution = 100;
+step = dx/resolution;
+xrange = [x0:step:x1];
+yrange = [y0:step:y1];
+% 					
+% Generate the grid
+% 
+[X Y]=meshgrid([x0:step:x1],[y0:step:y1]);
+% 
+% Calculate the class conditional densities, the unconditional densities and
+% the posterior probabilities
+% 
+px_j = gmmactiv(mix, [X(:) Y(:)]);
+px = reshape(px_j*(mix.priors)',size(X));
+post = gmmpost(mix, [X(:) Y(:)]);
+p1_x = reshape(post(:, 1), size(X));
+p2_x = reshape(post(:, 2) + post(:, 3), size(X));
+
+% 
+% Generate some pretty pictures !!
+% 
+colormap(hot)
+colorbar
+subplot(1,2,1)
+hold on
+plot(data((label==1),1),data(label==1,2),ClassSymbol1, 'MarkerSize', PointSize)
+plot(data((label>1),1),data(label>1,2),ClassSymbol2, 'MarkerSize', PointSize)
+contour(xrange,yrange,p1_x,[0.5 0.5],'w-');
+axis([x0 x1 y0 y1])
+set(gca,'Box','On')
+title('The Sampled Data');
+rect=get(gca,'Position');
+rect(1)=rect(1)-AxisShift;
+rect(3)=rect(3)+AxisShift;
+set(gca,'Position',rect)
+hold off
+
+subplot(1,2,2)
+imagesc(X(:),Y(:),px);
+hold on
+[cB, hB] = contour(xrange,yrange,p1_x,[0.5 0.5],'w:');
+set(hB,'LineWidth', 2);
+axis([x0 x1 y0 y1])
+set(gca,'YDir','normal')
+title('Probability Density p(x)')
+hold off
+
+drawnow;
+clc;
+disp('The first figure shows the data sampled from a mixture of three')
+disp('Gaussians, the first of which (whose centre is near the origin) is')
+disp('labelled red and the other two are labelled yellow.  The second plot')
+disp('shows the unconditional density of the data with the optimal Bayesian')
+disp('decision boundary superimposed.')
+disp(' ')
+disp('Press any key to continue.')
+pause
+fh2 = figure;
+set(fh2, 'Name', 'Class-conditional Densities and Posterior Probabilities');
+whitebg(fh2, 'w');
+
+subplot(2,2,1)
+p1=reshape(px_j(:,1),size(X));
+imagesc(X(:),Y(:),p1);
+colormap hot
+colorbar
+axis(axis)
+set(gca,'YDir','normal')
+hold on
+plot(mix.centres(:,1),mix.centres(:,2),'b+','MarkerSize',8,'LineWidth',2)
+title('Density p(x|red)')
+hold off
+
+subplot(2,2,2)
+p2=reshape((px_j(:,2)+px_j(:,3)),size(X));
+imagesc(X(:),Y(:),p2);
+colorbar
+set(gca,'YDir','normal')
+hold on
+plot(mix.centres(:,1),mix.centres(:,2),'b+','MarkerSize',8,'LineWidth',2)
+title('Density p(x|yellow)')
+hold off
+
+subplot(2,2,3)
+imagesc(X(:),Y(:),p1_x);
+set(gca,'YDir','normal')
+colorbar
+title('Posterior Probability p(red|x)')
+hold on
+plot(mix.centres(:,1),mix.centres(:,2),'b+','MarkerSize',8,'LineWidth',2)
+hold off
+
+subplot(2,2,4)
+imagesc(X(:),Y(:),p2_x);
+set(gca,'YDir','normal')
+colorbar
+title('Posterior Probability p(yellow|x)')
+hold on
+plot(mix.centres(:,1),mix.centres(:,2),'b+','MarkerSize',8,'LineWidth',2)
+hold off
+
+% Now set up and train the MLP
+nhidden=6;
+nout=1;
+alpha = 0.2;	% Weight decay
+ncycles = 60;	% Number of training cycles. 
+% Set up MLP network
+net = mlp(2, nhidden, nout, 'logistic', alpha);
+options = zeros(1,18);
+options(1) = 1;                 % Print out error values
+options(14) = ncycles;
+
+mlpstring = ['We now set up an MLP with ', num2str(nhidden), ...
+    ' hidden units, logistic output and cross'];
+trainstring = ['entropy error function, and train it for ', ...
+    num2str(ncycles), ' cycles using the'];
+wdstring = ['quasi-Newton optimisation algorithm with weight decay of ', ...
+    num2str(alpha), '.'];
+
+% Force out the figure before training the MLP
+drawnow;
+disp(' ')
+disp('The second figure shows the class conditional densities and posterior')
+disp('probabilities for each class. The blue crosses mark the centres of')
+disp('the three Gaussians.')
+disp(' ')
+disp(mlpstring)
+disp(trainstring)
+disp(wdstring)
+disp(' ')
+disp('Press any key to continue.')
+pause
+
+% Convert targets to 0-1 encoding
+target=[label==1];
+
+% Train using quasi-Newton.
+[net] = netopt(net, options, data, target, 'quasinew');
+y = mlpfwd(net, data);
+yg = mlpfwd(net, [X(:) Y(:)]);
+yg = reshape(yg(:,1),size(X));
+
+fh3 = figure;
+set(fh3, 'Name', 'Network Output');
+whitebg(fh3, 'k')
+subplot(1, 2, 1)
+hold on
+plot(data((label==1),1),data(label==1,2),'r.', 'MarkerSize', PointSize)
+plot(data((label>1),1),data(label>1,2),'y.', 'MarkerSize', PointSize)
+% Bayesian decision boundary
+[cB, hB] = contour(xrange,yrange,p1_x,[0.5 0.5],'b-');
+[cN, hN] = contour(xrange,yrange,yg,[0.5 0.5],'r-');
+set(hB, 'LineWidth', 2);
+set(hN, 'LineWidth', 2);
+Chandles = [hB(1) hN(1)];
+legend(Chandles, 'Bayes', ...
+  'Network', 3);
+
+axis([x0 x1 y0 y1])
+set(gca,'Box','on','XTick',[],'YTick',[])
+
+title('Training Data','FontSize',titleSize);
+hold off
+
+subplot(1, 2, 2)
+imagesc(X(:),Y(:),yg);
+colormap hot
+colorbar
+axis(axis)
+set(gca,'YDir','normal','XTick',[],'YTick',[])
+title('Network Output','FontSize',titleSize)
+
+clc
+disp('This figure shows the training data with the decision boundary')
+disp('produced by the trained network and the network''s prediction of')
+disp('the posterior probability of the red class.')
+disp(' ')
+disp('Press any key to continue.')
+pause
+
+% 
+% Now generate and classify a test data set
+% 
+[testdata testlabel] = gmmsamp(mix, n);
+testlab=[testlabel==1 testlabel>1];
+
+% This is the Bayesian classification
+tpx_j = gmmpost(mix, testdata);
+Bpost = [tpx_j(:,1), tpx_j(:,2)+tpx_j(:,3)];
+[Bcon Brate]=confmat(Bpost, [testlabel==1 testlabel>1]);
+
+% Compute network classification
+yt = mlpfwd(net, testdata);
+% Convert single output to posteriors for both classes
+testpost = [yt 1-yt];
+[C trate]=confmat(testpost,[testlabel==1 testlabel>1]);
+
+fh4 = figure;
+set(fh4, 'Name', 'Decision Boundaries');
+whitebg(fh4, 'k');
+hold on
+plot(testdata((testlabel==1),1),testdata((testlabel==1),2),...
+  ClassSymbol1, 'MarkerSize', PointSize)
+plot(testdata((testlabel>1),1),testdata((testlabel>1),2),...
+  ClassSymbol2, 'MarkerSize', PointSize)
+% Bayesian decision boundary
+[cB, hB] = contour(xrange,yrange,p1_x,[0.5 0.5],'b-');
+set(hB, 'LineWidth', 2);
+% Network decision boundary
+[cN, hN] = contour(xrange,yrange,yg,[0.5 0.5],'r-');
+set(hN, 'LineWidth', 2);
+Chandles = [hB(1) hN(1)];
+legend(Chandles, 'Bayes decision boundary', ...
+  'Network decision boundary', -1);
+axis([x0 x1 y0 y1])
+title('Test Data')
+set(gca,'Box','On','Xtick',[],'YTick',[])
+
+clc
+disp('This figure shows the test data with the decision boundary')
+disp('produced by the trained network and the optimal Bayes rule.')
+disp(' ')
+disp('Press any key to continue.')
+pause
+
+fh5 = figure;
+set(fh5, 'Name', 'Test Set Performance');
+whitebg(fh5, 'w');
+% Bayes rule performance
+subplot(1,2,1)
+plotmat(Bcon,'b','k',12)
+set(gca,'XTick',[0.5 1.5])
+set(gca,'YTick',[0.5 1.5])
+grid('off')
+set(gca,'XTickLabel',['Red   ' ; 'Yellow'])
+set(gca,'YTickLabel',['Yellow' ; 'Red   '])
+ylabel('True')
+xlabel('Predicted')
+title(['Bayes Confusion Matrix (' num2str(Brate(1)) '%)'])
+
+% Network performance
+subplot(1,2, 2)
+plotmat(C,'b','k',12)
+set(gca,'XTick',[0.5 1.5])
+set(gca,'YTick',[0.5 1.5])
+grid('off')
+set(gca,'XTickLabel',['Red   ' ; 'Yellow'])
+set(gca,'YTickLabel',['Yellow' ; 'Red   '])
+ylabel('True')
+xlabel('Predicted')
+title(['Network Confusion Matrix (' num2str(trate(1)) '%)'])
+
+disp('The final figure shows the confusion matrices for the')
+disp('two rules on the test set.')
+disp(' ')
+disp('Press any key to exit.')
+pause
+whitebg(fh1, 'w');
+whitebg(fh2, 'w');
+whitebg(fh3, 'w');
+whitebg(fh4, 'w');
+whitebg(fh5, 'w');
+close(fh1); close(fh2); close(fh3);
+close(fh4); close(fh5);
+clear all;
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