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% SVMOCAS Train linear SVM classifier using OCAS solver.
%
% Synopsis:
% [W,W0,stat] = svmocas(X,X0,y,C,Method,TolRel,TolAbs,QPBound,BufSize,nExamples,MaxTime);
%
% [W,W0,stat] = svmocas(data_file,X0,C,Method,TolRel,TolAbs,QPBound,BufSize,nExamples,MaxTime);
%
% Desription:
% This function trains linear SVM classifier by solving
%
% W,W0 = argmin 0.5*(w'*w+w0^2) + C*sum max( 0, 1-y(i)*(w'*X(:,i)+w0*X0) )
% w,w0 i=1:nExamples
%
% The function accepts examples either in Matlab matrix X (both sparse and dense) and
% a dense vector y or as path to a file in SVM^light format.
%
% Reference:
% V. Franc, S. Sonnenburg. OCAS optimized cutting plane algorithm for Support Vector
% Machines. In Proceedings of ICML. Omnipress, 2008.
% http://ida.first.fraunhofer.de/~franc/papers/Franc-OCAS-ICML08.pdf
%
% Input:
% data_file [string] Training examples stored in SVM^light format.
%
% X [nDim x nExamples] training inputs (sparse or dense matrix).
% X0 [1x1] constant coordinate (implicitly) added to all examples;
% this allows training biased decision rule.
% y [nExamples x 1] labels (+1/-1).
% C [1x1] or [nExamples x 1] C [1x1] is a regularization constant common for all examples;
% if C is a vector [nExamples x 1] then each example has its own (possibly different)
% regularization constant.
% Method [1x1] 0..cutting plane; 1..OCAS (default 1)
% TolRel [1x1] halts if Q_P-Q_D <= abs(Q_P)*TolRel (default 0.01)
% TolAbs [1x1] halts if Q_P-Q_D <= TolAbs (default 0)
% QPValue [1x1] halts if Q_P <= QPBpound (default 0)
% BufSize [1x1] Initial size of active constrains buffer (default 2000)
% nExaples [1x1] Number of examples used for training; must be >0 and <= size(X,2).
% If nExamples = inf then nExamples is set to size(X,2).
% MaxTime [1x1] halts if time used by solver (data loading time is not counted) exceeds
% MaxTime given in seconds. Use MaxTime=inf (default) to switch off this stopping condition.
%
% Output:
% W [nDim x 1] Paramater vectors of decision rule sign(W'*X+W0)
% W0 [1x1] Bias term of the decision rule.
% stat [struct] Optimizer statistics (field names are self-explaining).
%
% Example:
% % loading data directly from file in SVM^light format
% [W,W0,stat] = svmocas('./data/riply_trn.light',1,1);
%
% % using data loaded to Matlab
% load('./data/riply_trn','X','y');
% [W,W0,stat] = svmocas(X,1,y,1);
%
% % classification
% load('riply_tst','X','y');
% ypred = sign(W'*X + W0);
% sum(ypred ~= y)/length(y)
%
%
% Copyright (C) 2008, 2009 Vojtech Franc, xfrancv@cmp.felk.cvut.cz
% Soeren Sonnenburg, soeren.sonnenburg@first.fraunhofer.de
%
% This program is free software; you can redistribute it and/or
% modify it under the terms of the GNU General Public
% License as published by the Free Software Foundation;
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