Algo rbf et pmc sous matlab comment les modifier?

Bonjour,

J'essaye depuis pas mal de temps de modifier un fichier qui contient une comparaison entre l'algo PMC (Perceptron Multi Couche) et une méthode Bayesienne de classification.

En fait j'ai deux problèmes:
1- Je doit modifier ce code pour mettre l'algo RBF (Réseaux à Fonctions de Base Radiales) à la place de la méthode Bayesienne.
2- (Facultatif) Pouvoir lire les données dans un fichier (.data) au lieu de les générer aléatoirement.

Voici le fichier en question:

Code:

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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 ') 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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Et voici une demonstration de RBF:

Code:

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%DEMRBF1 Demonstrate simple regression using a radial basis function network. % % Description % The problem consists of one input variable X and one target variable % T with data generated by sampling X at equal intervals and then % generating target data by computing SIN(2*PI*X) and adding Gaussian % noise. This data is the same as that used in demmlp1. % % Three different RBF networks (with different activation functions) % are trained in two stages. First, a Gaussian mixture model is trained % using the EM algorithm, and the centres of this model are used to set % the centres of the RBF. Second, the output weights (and biases) are % determined using the pseudo-inverse of the design matrix. % % See also % DEMMLP1, RBF, RBFFWD, GMM, GMMEM %   % Copyright (c) Ian T Nabney (1996-2001)     % Generate the matrix of inputs x and targets t. randn('state', 42); rand('state', 42); ndata = 20; % Number of data points. noise = 0.2; % Standard deviation of noise distribution. x = (linspace(0, 1, ndata))'; t = sin(2*pi*x) + noise*randn(ndata, 1); mu = mean(x); sigma = std(x); tr_in = (x - mu)./(sigma);   clc disp('This demonstration illustrates the use of a Radial Basis Function') disp('network for regression problems. The data is generated from a noisy') disp('sine function.') disp(' ') disp('Press any key to continue.') pause % Set up network parameters. nin = 1; % Number of inputs. nhidden = 7; % Number of hidden units. nout = 1; % Number of outputs.   clc disp('We assess the effect of three different activation functions.') disp('First we create a network with Gaussian activations.') disp(' ') disp('Press any key to continue.') pause % Create and initialize network weight and parameter vectors. net = rbf(nin, nhidden, nout, 'gaussian');   disp('A two-stage training algorithm is used: it uses a small number of') disp('iterations of EM to position the centres, and then the pseudo-inverse') disp('of the design matrix to find the second layer weights.') disp(' ') disp('Press any key to continue.') pause disp('Error values from EM training.') % Use fast training method options = foptions; options(1) = 1; % Display EM training options(14) = 10; % number of iterations of EM net = rbftrain(net, options, tr_in, t);   disp(' ') disp('Press any key to continue.') pause clc disp('The second RBF network has thin plate spline activations.') disp('The same centres are used again, so we just need to calculate') disp('the second layer weights.') disp(' ') disp('Press any key to continue.') pause % Create a second RBF with thin plate spline functions net2 = rbf(nin, nhidden, nout, 'tps');   % Re-use previous centres rather than calling rbftrain again net2.c = net.c; [y, act2] = rbffwd(net2, tr_in);   % Solve for new output weights and biases from RBF activations temp = pinv([act2 ones(ndata, 1)]) * t; net2.w2 = temp(1:nhidden, :); net2.b2 = temp(nhidden+1, :);   disp('The third RBF network has r^4 log r activations.') disp(' ') disp('Press any key to continue.') pause % Create a third RBF with r^4 log r functions net3 = rbf(nin, nhidden, nout, 'r4logr');   % Overwrite weight vector with parameters from first RBF net3.c = net.c; [y, act3] = rbffwd(net3, tr_in); temp = pinv([act3 ones(ndata, 1)]) * t; net3.w2 = temp(1:nhidden, :); net3.b2 = temp(nhidden+1, :);   disp('Now we plot the data, underlying function, and network outputs') disp('on a single graph to compare the results.') disp(' ') disp('Press any key to continue.') pause % Plot the data, the original function, and the trained network functions. plotvals = [x(1):0.01:x(end)]'; inputvals = (plotvals-mu)./sigma; y = rbffwd(net, inputvals); y2 = rbffwd(net2, inputvals); y3 = rbffwd(net3, inputvals); fh1 = figure;   plot(x, t, 'ob') hold on xlabel('Input') ylabel('Target') axis([x(1) x(end) -1.5 1.5]) [fx, fy] = fplot('sin(2*pi*x)', [x(1) x(end)]); plot(fx, fy, '-r', 'LineWidth', 2) plot(plotvals, y, '--g', 'LineWidth', 2) plot(plotvals, y2, 'k--', 'LineWidth', 2) plot(plotvals, y3, '-.c', 'LineWidth', 2) legend('data', 'function', 'Gaussian RBF', 'Thin plate spline RBF', ... 'r^4 log r RBF'); hold off   disp('RBF training errors are'); disp(['Gaussian ', num2str(rbferr(net, tr_in, t)), ' TPS ', ... num2str(rbferr(net2, tr_in, t)), ' R4logr ', num2str(rbferr(net3, tr_in, t))]);   disp(' ') disp('Press any key to end.') pause close(fh1); clear all;

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Merci.