% Copyright (c) 2002,  KULeuven-ESAT-SCD, License & help @ http://www.esat.kuleuven.ac.be/sista/lssvmlabclc;disp('This is a simple demo, solving a simple regression task using');disp('LS-SVMlab. A dataset is constructed in the right formatting. The');disp('data are represented as matrices where each row contains one');disp('datapoint: ');disp(' ');disp('press <ENTER> key'); pausedisp(' ');disp('>> X = (-3:0.2:3)'';');X = (-3:0.2:3)';disp('>> Y = sinc(X)+0.1.*randn(length(X),1);');eval('Y = sinc(X)+0.1.*randn(length(X),1);',...     'Y = sin(pi.*X+12345*eps)./(pi*X+12345*eps)+0.1.*randn(length(X),1);');disp('>> X');Xdisp('>> Y');Ydisp('In order to make an LS-SVM model, we need 2 extra parameters: gamma');disp('(gam) is the regularization parameter, determining the trade-off');disp('between the fitting error minimization and smoothness of the');disp('estimated function. sigma^2 (sig2) is the kernel function');disp('parameter of the RBF kernel:');disp(' ');disp('>> gam = 10;');gam = 10;disp('>> sig2 = 0.3;');sig2 = 0.3;disp('>> type = ''function estimation'';');type = 'function estimation';disp('>> [alpha,b] = trainlssvm({X,Y,type,gam,sig2,''RBF_kernel''});');[alpha,b] = trainlssvm({X,Y,type,gam,sig2,'RBF_kernel'});disp(' ');disp('press <ENTER> key'); pausedisp(' ');disp('The parameters and the variables relevant for the LS-SVM are');disp('passed as one cell. This cell allows for consistent default');disp('handling of LS-SVM parameters and syntactical grouping of related');disp('arguments. This definition should be used consistently throughout');disp('the use of that specific LS-SVM model');disp('The object oriented interface to LS-SVMlab leads to');disp('shorter function calls (see demomodel). ');disp('By default, the data are preprocessed by application of the function');disp('prelssvm to the raw data and the function postlssvm on the');disp('predictions of the model. This option can explicitly be switched off in');disp('the call: ');disp(' ');disp('>> [alpha,b] = trainlssvm({X,Y,type,gam,sig2,''RBF_kernel'',''original''});');[alpha,b] = trainlssvm({X,Y,type,gam,sig2,'RBF_kernel','original'});disp(' ');disp('or can be switched on (default):');disp(' ');disp('>> [alpha,b] = trainlssvm({X,Y,type,gam,sig2,''RBF_kernel'',''preprocess''});');[alpha,b] = trainlssvm({X,Y,type,gam,sig2,'RBF_kernel','preprocess'});%disp('Remember to consistently use the same option in all successive calls.');disp(' ');disp('press <ENTER> key'); pausedisp(' ');disp('To evaluate new points for this model, the function simlssvm is');disp('used. At first, test data is generated: ');disp(' ');disp('>> Xt = 3.*randn(10,1);');Xt = 3.*randn(10,1);disp(' ');disp('Then, the obtained model is simulated on the test data:'); disp(' ');disp('>> Yt = simlssvm({X,Y,type,gam,sig2,''RBF_kernel'',''preprocess''},{alpha,b},Xt);');Yt = simlssvm({X,Y,type,gam,sig2,'RBF_kernel','preprocess'},{alpha,b},Xt);disp(' ');disp('>> Y');Ydisp(' ');disp('press <ENTER> key'); pausedisp(' ');disp('The LS-SVM result can be displayed if the dimension of the input');disp('data is 1 or 2. ');disp(' ');disp('>> plotlssvm({X,Y,type,gam,sig2,''RBF_kernel'',''preprocess''},{alpha,b});');figure; plotlssvm({X,Y,type,gam,sig2,'RBF_kernel','preprocess'},{alpha,b});disp(' ');disp('All plotting is done with this simple command. It looks for the');disp('best way of displaying the result. When the real function is known,');disp('it can be displayed as follows:');disp(' ');disp('>> hold on; plot(min(X):.1:max(X),sinc(min(X):.1:max(X)),''r-.'');'); hold offXt = (min(X):.1:max(X))'; eval('Yt = sinc(Xt);',...     'Yt = sin(pi.*Xt+12345*eps)./(pi*Xt+12345*eps)+0.1.*randn(length(Xt),1);');hold on;  plot(Xt,Yt,'r-.'); hold offdisp(' ');disp(' This concludes the demo');