% Copyright (c) 2002,  KULeuven-ESAT-SCD, License & help @ http://www.esat.kuleuven.ac.be/sista/lssvmlabdisp(' This demo illustrates the idea of fixed size LS-SVM. ');disp(' The program consists of 2 steps. In the former, one ');disp(' constructs a reduced set of support vectors base on ');disp(' an apropriate criterion on the data. In this case');disp(' the measure ''kentropy'' is optimized.');disp(' ');disp(' In the latter step, one constructs the implicit mapping');disp(' to feature space based on the eigenvalue decomposition.');disp(' A parametric linear regression is executed on the mapped');disp(' data');disp(' ');disp(' To see the used cose, use the call');disp(' ');disp('>> type demo_fixedsize ');disp(' ');disp(' or ');disp(' ');disp('>> edit demo_fixedsize ');disp(' ');disp(' A dataset is constructed at first...');%% dataset%clearfigure;randn('state',0);x = sort(2.*randn(2000,1));x0 = sort(2.*randn(2000,1));%x=(-9.95:0.1:10)';%x0=(-9.95:0.05:10)';eval('y = sinc(x)+0.05.*randn(length(x),1);',...     'y = sin(pi.*x+12345*eps)./(pi*x+12345*eps)+0.05.*randn(length(x),1);');eval('y0 = sinc(x0)+0.05.*randn(length(x0),1);',...     'y0 = sin(pi.*x0+12345*eps)./(pi*x0+12345*eps)+0.05.*randn(length(x0),1);');disp(' The parameters are initialized...');%% initiate valueskernel = 'RBF_kernel';sigma2=.75;gamma=1;crit_old=-inf;Nc=15;Xs=x(1:Nc,:);Ys=y(1:Nc,:);disp(' The optimal reduced set is constructed iteratively: ');%% iterate over data%tv = 1;for tel=1:length(x)       %  % new candidate set  %  Xsp=Xs; Ysp=Ys;  S=ceil(length(x)*rand(1));  Sc=ceil(Nc*rand(1));  Xs(Sc,:) = x(S,:);  Ys(Sc,:) = y(S);  Ncc=Nc;  %  % automaticly extract features and compute entropy  %  crit = kentropy(Xs,kernel, sigma2);    if crit <= crit_old,    crit = crit_old;    Xs=Xsp;    Ys=Ysp;  else    crit_old = crit;    %    % ridge regression        %    [features,U,lam] = AFE(Xs,kernel, sigma2,x);    [w,b,Yh] = ridgeregress(features,y,gamma,features);    %    % make-a-plot    %    plot(x,y,'*'); hold on    plot(x,Yh,'r-')    plot(Xs,Ys,'go','Linewidth',7)    xlabel('X'); ylabel('Y');     title(['Approximation by fixed size LS-SVM based on maximal entropy: ' num2str(crit)]);    hold off;  drawnow       end    %  % validate  %  %Yh0 = AFE(Xs,kernel, sigma2,x0)*w + b;  %val(tv,2) = mse(Yh0-y0); tv=tv+1;  enddisp(' The parametric linear ridge regression is calculated:');%% ridge regression    %echo on;features = AFE(Xs,kernel, sigma2,x);    % Bayesian inference of the gammatry,  [CostL3, gamma_optimal] = bay_rr(features,y,gamma,3);catch,  warning('no Bayesian optimization of the regularization parameter');  gamma_optimal = gamma;end[w,b] = ridgeregress(features,y,gamma_optimal);Yh0 = AFE(Xs,kernel, sigma2,x0)*w+b;echo off;         %% make-a-plotplot(x,y,'*'); hold onplot(x0,Yh0,'r-')plot(Xs,Ys,'go','Linewidth',7)xlabel('X'); ylabel('Y'); title(['Approximation by fixed size LS-SVM based on maximal entropy: ' num2str(crit)]);hold off;