%SVC_NU Support Vector Classifier: NU algorithm
%
% This routine is outdated, use NUSVC instead
%
% [W,J,C] = SVC(A,TYPE,PAR,NU,MC,PD)
%
% INPUT
% A Dataset
% TYPE Type of the kernel (optional; default: 'p')
% PAR Kernel parameter (optional; default: 1)
% NU Regularization parameter (0 < NU < 1): expected fraction of SV
% (optional; default: max(leave-one-out 1_NN error,0.05))
%
% MC Do or do not data mean-centering (optional; default: 1 (to do))
% PD Do or do not the check of the positive definiteness (optional; default: 1 (to do))
%
% OUTPUT
% W Mapping: Support Vector Classifier
% J Object identifiers of support objects
% C Equivalent C regularization parameter of SVM-C algorithm
%
% DESCRIPTION
% Optimizes a support vector classifier for the dataset A by
% quadratic programming. The classifier can be of one of the types
% as defined by PROXM. Default is linear (TYPE = 'p', PAR = 1). In J
% the identifiers of the support objects in A are returned.
%
% NU belongs to the interval (0,1). NU close to 1 allows for more class overlap.
% Default NU = 0.25.
%
% NU is bounded from above by NU_MAX = (1 - ABS(Lp-Lm)/(Lp+Lm)), where
% Lp (Lm) is the number of positive (negative) samples. If NU > NU_MAX is supplied
% to the routine it will be changed to the NU_MAX.
%
% If NU is less than some NU_MIN which depends on the overlap between the classes
% the algorithm will typically take a long time to converge (if at all).
% So, it is advisable to set NU larger than expected overlap.
%
% Output is rescaled in such a manner as if it were returned by SVC with the parameter C.
%
%
% SEE ALSO
% SVO_NU, SVO, SVC, MAPPINGS, DATASETS, PROXM
% Copyright: S.Verzakov, s.verzakov@ewi.tudelft.nl
% Based on SVC.M by D.M.J. Tax, D. de Ridder, R.P.W. Duin
% Faculty EWI, Delft University of Technology
% P.O. Box 5031, 2600 GA Delft, The Netherlands
% $Id: svc_nu.m,v 1.6 2009/01/31 18:43:11 duin Exp $
function [W, J, C] = svc_nu(a,type,par,nu,mc,pd)
warning('SVC_NU is outdated, use NUSVC instead')
if nargin < 2 | ~isa(type,'prmapping')
if nargin < 6
pd = 1;
end
if nargin < 5
mc = 1;
end
if nargin < 4 | isempty(nu)
nu = [];
prwarning(3,'Regularization parameter nu set to NN error\n');
end
if nargin < 3 | isempty(par)
par = 1;
prwarning(3,'Kernel parameter par set to 1\n');
end
if nargin < 2 | isempty(type)
type = 'p';
prwarning(3,'Polynomial kernel type is used\n');
end
if nargin < 1 | isempty(a)
W = prmapping(mfilename,{type,par,nu,mc,pd});
W = setname(W,'Support Vector Classifier (nu version)');
return;
end
islabtype(a,'crisp');
isvaldfile(a,1,2); % at least 1 object per class, 2 classes
a = testdatasize(a,'objects');
[m,k,c] = getsize(a);
nlab = getnlab(a);
if isempty(nu), nu = max(testk(a,1),0.01); end
% The SVC is basically a 2-class classifier. More classes are
% handled by mclassc.
if c == 2 % two-class classifier
% Compute the parameters for the optimization:
y = 3 - 2*nlab;
if mc
u = mean(a);
a = a -ones(m,1)*u;
else
u = [];
end
K = a*proxm(a,type,par);
% Perform the optimization:
[v,J,C] = svo_nu(+K,y,nu,pd);
% Store the results:
W = prmapping(mfilename,'trained',{u,a(J,:),v,type,par},getlablist(a),k,2);
%W = cnormc(W,a);
W = setname(W,'Support Vector Classifier (nu version)');
W = setcost(W,a);
J = getident(a,J);
%J = a.ident(J);
else % multi-class classifier:
[W,J,C] = mclassc(a,prmapping(mfilename,{type,par,nu,mc,pd}),'single');
end
else % execution
nodatafile(a);
w = +type;
m = size(a,1);
% The first parameter w{1} stores the mean of the dataset. When it
% is supplied, remove it from the dataset to improve the numerical
% precision. Then compute the kernel matrix using proxm:
if isempty(w{1})
d = a*proxm(w{2},w{4},w{5});
else
d = (a-ones(m,1)*w{1})*proxm(w{2},w{4},w{5});
end
% Data is mapped by the kernel, now we just have a linear
% classifier w*x+b:
d = [d ones(m,1)] * w{3};
d = sigm([d -d]);
W = setdat(a,d,type);
end
return;