function [model,b] = robustlssvm(model,ab,X,Y) % Robust training in the case of non-Gaussian noise or outliers% % >> [alpha, b] = robustlssvm({X,Y,type,gam,sig2,kernel})% >> model     = robustlssvm(model)% % Robustness towards outliers can be achieved by reducing the% influence of support values corresponding to large errors.%% % Full syntax% %     1. Using the functional interface:% % >> [alpha, b] = robustlssvm({X,Y,type,gam,sig2}, {alpha,b})% >> [alpha, b] = robustlssvm({X,Y,type,gam,sig2,kernel}, {alpha,b})% >> [alpha, b] = robustlssvm({X,Y,type,gam,sig2,kernel,preprocess}, {alpha,b})% >> [alpha, b] = robustlssvm({X,Y,type,gam,sig2,kernel,preprocess})%%       Outputs    %         alpha         : N x m matrix with support values of the robust LS-SVM%         b             : 1 x m vector with bias term(s) of the robust LS-SVM%       Inputs    %         X             : N x d matrix with the inputs of the training data%         Y             : N x 1 vector with the outputs of the training data%         type          : 'function estimation' ('f') or 'classifier' ('c')%         gam           : Regularization parameter%         sig2          : Kernel parameter (bandwidth in the case of the 'RBF_kernel')%         kernel(*)     : Kernel type (by default 'RBF_kernel')%         preprocess(*) : 'preprocess'(*) or 'original'%         alpha(*)      : Support values obtained from training%         b(*)          : Bias term obtained from training% %%     2. Using the object oriented interface:% % >> model = robustlssvm(model)% %       Outputs    %         model : Robustly trained object oriented representation of the LS-SVM model%       Inputs    %         model : Object oriented representation of the LS-SVM model% % See also:%   trainlssvm, tunelssvm, crossvalidate% Copyright (c) 2002,  KULeuven-ESAT-SCD, License & help @ http://www.esat.kuleuven.ac.be/sista/lssvmlabif iscell(model),  func = 1;  model = initlssvm(model{:});else   func = 0;endif model.type(1)~='f',  error('Robustly weighted least squares only implemented for regression case...');endif nargin>1,  if iscell(ab) & ~isempty(ab),    model.alpha = ab{1};    model.b = ab{2};    model.status = 'trained';    if nargin>=4,      model = trainlssvm(model,X,Y);    end  else    model = trainlssvm(model,ab,X);  endelse  model = trainlssvm(model);end% defaults for c1 and c2c1=2.5;c2=3;% model errorsek = model.alpha./model.gam';%% robust estimation of the variance%%vare = iqr(ek)/1.349;vare = 1.483*median(abs((ek)-median(ek)));%% robust re-estimation of the alpha's and the b%cases = reshape(abs(ek./vare),1,model.nb_data);dc = c2-c1;gam = model.gam.*(cases<=c1) + ...      model.gam.*(cases<=c2 & cases>c1).*((c2-cases)./dc) + ...      model.gam.*(cases>c2).*10e-4;model = changelssvm(model,'gam',gam);model = changelssvm(model,'implementation','MATLAB');model = trainlssvm(model);%figure;plot(ek,model.gam,'*');if func & nargout~=1,  b = model.b;  model = model.alpha;end