function model = bsvm2( data, options )
% BSVM2 Multi-class BSVM with L2-soft margin.
%
% Synopsis:
% model = bsvm2( data, options )
%
% Description:
% This function trains the multi-class SVM classifier based
% on BSVM formulation (bias added to the objective function) and
% L2-soft margin penalization of misclassifications [Franc02][Hsu02].
% The quadratic programming criterion can be optimzed by one of the
% following algorithms:
% mdm ... Mitchell-Demyanov-Malozemov
% kozinec ... Kozinec's algorithm.
% npa ... Nearest Point Algorithm.
%
% Input:
% data [struct] Training data:
% .X [dim x num_data] Training vectors.
% .y [1 x num_data] Labels (1,2,...,nclass).
%
% options [struct] Control parameters:
% .ker [string] Kernel identifier. See 'help kernel'.
% .arg [1 x nargs] Kernel argument(s).
% .C [1x1] Regularization constant.
% .solver [string] Used QP solver: 'kozinec', 'mdm', 'npa' (default).
% .tmax [1x1] Maximal number of iterations.
% .tolabs [1x1] Absolute tolerance stopping condition (default 0.0).
% .tolrel [1x1] Relative tolerance stopping condition (default 0.001).
%
% Output:
% model [struct] Multi-class SVM classifier:
% .Alpha [nsv x nclass] Weights.
% .b [nclass x 1] Biases.
% .sv.X [dim x nsv] Support vectors.
% .nsv [1x1] Number of support vectors.
% .options [struct] Copy of input options.
% .t [1x1] Number of iterations.
% .UB [1x1] Upper bound on the optimal solution.
% .LB [1x1] Lower bound on the optimal solution.
% .History [2 x (t+1)] UB and LB with respect to t.
%
% Example:
% data = load('pentagon');
% options = struct('ker','rbf','arg',1,'C',10,'solver','npa');
% model = bsvm2( data, options )
% figure;
% ppatterns(data); ppatterns( model.sv.X, 'ok',12);
% pboundary( model );
%
% See also
% SVMCLASS, OAASVM, OAOSVM.
%
% 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:
% 31-may-2004, VF
% 23-jan-2003, VF
data=c2s(data);
if nargin < 2, options=[]; else options=c2s(options); end
if ~isfield(options,'ker'), options.ker='linear'; end
if ~isfield(options,'arg'), options.arg=1; end
if ~isfield(options,'C'), options.C=inf; end
if ~isfield(options,'tmax'), options.tmax=inf; end
if ~isfield(options,'tolabs'), options.tolabs=0; end
if ~isfield(options,'tolrel'), options.tolrel=0.001; end
if ~isfield(options,'solver'), options.solver='npa'; end
[dim,num_data]=size(data.X);
[Alpha,b,exitflag,kercnt,trnerr,t,UB,LB,History] = bsvm2_mex(...
data.X,...
data.y,...
options.ker,...
options.arg,...
options.C,...
options.solver,...
options.tmax,...
options.tolabs, ...
options.tolrel);
sv_inx = find( sum(abs(Alpha),1) ~= 0 );
Alpha = Alpha(:,sv_inx)';
for i = 1:size(Alpha,2),
inx = find( data.y(sv_inx) ~= i);
Alpha(inx,i) = -Alpha(inx,i);
end
model.Alpha = Alpha;
model.b = b;
model.sv.X = data.X(:,sv_inx);
model.sv.y = data.y(sv_inx);
model.sv.inx = sv_inx;
model.nsv = length(sv_inx);
model.options = options;
model.exitflag = exitflag;
model.trnerr = trnerr;
model.kercnt = kercnt;
model.t = t;
model.UB = UB;
model.LB = LB;
model.LB_History = History(1,:);
model.UB_History = History(2,:);
model.fun = 'svmclass';
return;