%SVCINFO More information on Support Vector Classifiers
%
% [W,J,C,NU,ALGINF] = SVC(A,KERNEL,C,OPTIONS)
% W = A*SVC([],KERNEL,C,OPTIONS)
% [W,J,NU,C,ALGINF] = NUSVC(A,KERNEL,NU,OPTIONS)
% W = A*SVC([],KERNEL,NU,OPTIONS)
%
% INPUT
% A Dataset
% KERNEL - Untrained mapping to compute kernel by A*(A*KERNEL) during
% training, or B*(A*KERNEL) during testing with dataset B.
% - string to compute kernel matrices by FEVAL(KERNEL,B,A)
% Default: linear kernel (KERNELM([],'p',1));
% C Regularization parameter (optional; default: 1)
% NU Regularization parameter (0 < NU < 1): expected fraction of SV
% (optional; default: max(leave-one-out 1_NN error,0.01))
% OPTIONS Additional options, see below.
%
% OUTPUT
% W Mapping: Support Vector Classifier
% J Object indices of support objects
% C Regularization parameter which gives the same classifier by SVC
% NU NU parameter which gives the same classifier by NUSVC
% ALGINF Structure with additional training information
%
% DESCRIPTION
% Optimizes a support vector classifier for the dataset A by quadratic
% programming. The non-linearity is determined by the kernel.
% If KERNEL = 0 it is assumed that A is already the kernelmatrix (square).
% In this case also a kernel matrix should be supplied at evaluation by B*W
% or PRMAP(B,W).
%
% If C or NU is NaN this regularisation parameter is optimised by REGOPTC.
%
% The quadratic optimisation is controlled by routines SVO and NUSVO. They make use
% of one of the following routines, if available:
% - QLD.DLL (Windows) or QLD.MEXxxx under Linux
% - QUADPROG.M in Matlab's optimisation toolbox
% - Matlab's QP.M
%
% The following options are available for fine-tuning the SVC routines
% OPTIONS
% .MEAN_CENTRING subtract data mean before the kernel computation (default: 1)
% .PD_CHECK force positive definiteness of the kernel by adding a small constant
% to a kernel diagonal (default: 1)
% .BIAS_IN_ADMREG it may happen that bias of svc (b term) is not defined, then
% if BIAS_IN_ADMREG == 1, b will be pu in the midpoint of its admissible
% region, otherwise (BIAS_IN_ADMREG == 0) the situation will be considered
% as an optimization failure and treated accordingly (default: 1)
% .ALLOW_UB_BIAS_ADMREG (NUSVC only)
% it may happen that bias admissible region is unbounded;
% if ALLOW_UB_BIAS_ADMREG == 1, b will be heuristically taken
% from its admissible region, otherwise (ALLOW_UB_BIAS_ADMREG == 0)
% the situation will be considered as an optimization failure and
% treated accordingly (default: 1)
% .PF_ON_FAILURE if optimization failed (or bias is undefined and BIAS_IN_ADMREG is 0)
% and PF_ON_FAILURE == 1, then Pseudo Fisher classifier will be computed,
% otherwise (PF_ON_FAILURE == 0) an error will be issued (default: 1)
% .MULTICLASS_MODE if the multiclass problem has to be solved, MULTICLASS_MODE defines
% how it is going to be split in 2-class subproplems: 'single' means
% one-against-the rest and 'multi' means
% one-against-one (default: 'single')