%%  Example on toy problem of%  WMW / AUC  optimisation with linear hypothesis%  on a toy problemclear allclose allticn=4000;sigma=0.5;[x,y]=datasets('gaussian',n,0,sigma);nbtrain=100;kernel='poly';kerneloption=[1];margin=1;kppv=inf;C=100;lambda = 1e-12;  verbose=1;span=1;classcode=[1 -1];qpsize=500;kkttol=0.01;%load toydatapouetxapp=x;yapp=y;[xapp,yapp,xtest,ytest,indice]=CreateDataAppTest(x,y,nbtrain, classcode);[xapp,xtest]=normalizemeanstd(xapp,xtest);% % SVMROC[xsup,w,w0,pos,timeps,alpha,matriceind]=svmroc(xapp,yapp,C,kppv,margin,lambda,kernel,kerneloption,verbose,span,qpsize,kkttol);%[xsup,w,w0,pos,timeps,alpha,matriceind]=svmrocL2(xapp,yapp,C,kppv,margin,lambda,kernel,kerneloption,verbose,span,qpsize,kkttol);%[xsup2,w2,w02,pos,timeps,alpha2,matriceind2]=svmrocL2CS(xapp,yapp,C,kppv,margin,lambda,kernel,kerneloption,verbose,span);[AUC,tpr,fpr,w0]=svmroccurve(xapp,yapp,xsup,w,w0,kernel,kerneloption,span);[AUCtest,tprt,fprt]=svmroccurve(xtest,ytest,xsup,w,w0,kernel,kerneloption,span);[ypredapp]=svmrocval(xapp,xsup,w,w0,kernel,kerneloption,span);[Confapp,metric]=ConfusionMatrix(sign(ypredapp),yapp,[1 -1]);Confapp[ypredtest]=svmrocval(xtest,xsup,w,w0,kernel,kerneloption,span);[Conftest,metric]=ConfusionMatrix(sign(ypredtest),ytest,[1 -1]);metricAUCtestplot(xapp(yapp==1,1),xapp(yapp==1,2),'r+',xapp(yapp==-1,1),xapp(yapp==-1,2),'bx'); hold on%---------------------------------------------------------------[xsupsvm,wsvm,w0svm,possvm,timeps,alpha]=svmclassL2(xapp,yapp,C,lambda,kernel,kerneloption,verbose,span);[AUC,tpr,fpr,w0svm]=svmroccurve(xapp,yapp,xsupsvm,wsvm,w0svm,kernel,kerneloption,span);[ypredappsvm]=svmrocval(xapp,xsupsvm,wsvm,w0svm,kernel,kerneloption,span);[Confappsvm,metric]=ConfusionMatrix(sign(ypredappsvm),yapp,[1 -1]);Confappsvm%------- Building a 2D Grid for function evaluation -------------------------%------------------------Plot the optimized points--------------%indpos=(find(yapp==1));indneg=(find(yapp==-1));optpos=unique(matriceind(:,1));optneg=unique(matriceind(:,2));plot(xapp(indpos(optpos),1),xapp(indpos(optpos),2),'ro',xapp(indneg(optneg),1),xapp(indneg(optneg),2),'bo'); hold on[xtest1 xtest2]  = meshgrid([-1:.05:1]*3.5,[-1:0.05:1]*3); nn = length(xtest1); xtest = [reshape(xtest1 ,nn*nn,1) reshape(xtest2 ,nn*nn,1)]; ypred = svmrocval(xtest,xsup,w,w0,kernel,kerneloption,span); % ROC SVMypred = reshape(ypred,nn,nn); ypredsvm = svmrocval(xtest,xsupsvm,wsvm,w0svm,kernel,kerneloption,span); ypredsvm = reshape(ypredsvm,nn,nn); hold on[cc,hh1]=contour(xtest1,xtest2,ypred,20);[cc,hh1]=contour(xtest1,xtest2,ypred,[0 0],'k--');%[cc,hh2]=contour(xtest1,xtest2,ypredsvm,20);%legend([hh1(1) hh2(1)], 'SVM-ROC','SVM');%figure%plot(fpr,tpr);% xsupsvm% xsup{1},xsup{2}% w% wsvm% yapp(possvm)