function [model,Z]=greedykpca(X,options)% GREEDYKPCA Greedy Kernel Principal Component Analysis.%% Synopsis:%  model = greedykpca(X)%  model = greedykpca(X,options)%% Description:%  This function implements a greedy kernel PCA algorithm. %  The input data X are first approximated by GREEDYKPCA in the %  feature space and second the ordinary PCA is applyed on the %  approximated data. This algorithm has the same objective function %  as the ordinary Kernel PCA but, in addition, the number of data in %  the resulting kernel expansion is limited. %%  For more info refer to V.Franc: Optimization Algorithms for Kernel %  Methods. Research report. CTU-CMP-2005-22. CTU FEL Prague. 2005.%  ftp://cmp.felk.cvut.cz/pub/cmp/articles/franc/Franc-PhD.pdf .%  % Input:%  X [dim x num_data] Input column vectors.%  %  options [struct] Control parameters:%   .ker [string] Kernel identifier. See 'help kernel' for more info.%   .arg [1 x narg] Kernel argument.%   .m [1x1] Maximal number of base vectors (Default m=0.25*num_data).%   .p [1x1] Depth of search for the best basis vector (p=m).%   .mserr [1x1] Desired mean squared reconstruction errors of approximation.%   .maxerr [1x1] Desired maximal reconstruction error of approximation.%     See 'help greedyappx' for more info about the stopping conditions.%   .verb [1x1] If 1 then some info is displayed (default 0).% % Output:%  model [struct] Kernel projection:%   .Alpha [nsv x new_dim] Multipliers defining kernel projection.%   .b [new_dim x 1] Bias the kernel projection.%   .sv.X [dim x num_data] Seleted subset of the training vectors..%   .nsv [1x1] Number of basis vectors.%   .kercnt [1x1] Number of kernel evaluations.%   .MaxErr [1 x nsv] Maximal reconstruction error for corresponding%     number of base vectors.%   .MsErr [1 x nsv] Mean square reconstruction error for corresponding%     number of base vectors.% % Example:%  X = gencircledata([1;1],5,250,1);%  model = greedykpca(X,struct('ker','rbf','arg',4,'new_dim',2));%  X_rec = kpcarec(X,model);             %  figure; %  ppatterns(X); ppatterns(X_rec,'+r');%  ppatterns(model.sv.X,'ob',12);%% See also %   KERNELPROJ, KPCA, GREEDYAPPX.%% About: Statistical Pattern Recognition Toolbox% (C) 1999-2003, Written by Vojtech Franc and Vaclav Hlavac% <a href="http://www.cvut.cz">Czech Technical University Prague</a>% <a href="http://www.feld.cvut.cz">Faculty of Electrical Engineering</a>% <a href="http://cmp.felk.cvut.cz">Center for Machine Perception</a>% Modifications:% 09-sep-2005, VF% 19-feb-2005, VF% 10-jun-2004, VF% 05-may-2004, VF% 14-mar-2004, VFstart_time = cputime;[dim,num_data]=size(X);% process input arguments%------------------------------------if nargin < 2, options = []; else options=c2s(options); endif ~isfield(options,'ker'), options.ker = 'linear'; endif ~isfield(options,'arg'), options.arg = 1; endif ~isfield(options,'m'), options.m = fix(0.25*num_data); endif ~isfield(options,'p'), options.p = options.m; endif ~isfield(options,'maxerr'), options.maxerr = 1e-6; endif ~isfield(options,'mserr'), options.mserr = 1e-6; endif ~isfield(options,'verb'), options.verb = 0; end% greedy algorithm to select subset of training data%-------------------------------------------------------[inx,Alpha,Z,kercnt,MsErr,MaxErr] = ...  greedyappx(X,options.ker,options.arg,...            options.m,options.p,options.mserr,options.maxerr,options.verb);   % apply ordinary PCA%------------------------------mu = sum(Z,2)/num_data;Z=Z-mu*ones(1,num_data);S = Z*Z';[U,D,V]=svd(S);model.eigval=diag(D);sum_eig = triu(ones(size(Z,1),size(Z,1)),1)*model.eigval;model.MsErr = MsErr(end)+sum_eig/num_data;options.new_dim = min([options.new_dim,size(Z,1)]);V = V(:,1:options.new_dim);% fill up the output model%-------------------------------------model.Alpha = Alpha'*V;model.nsv = length(inx);  model.b = -V'*mu;model.sv.X= X(:,inx);model.sv.inx = inx;model.kercnt = kercnt;model.GreedyMaxErr = MaxErr;model.GreedyMsErr = MsErr;model.options = options;model.cputime = cputime - start_time;model.fun = 'kernelproj';return;% EOF