%NUSVC Support Vector Classifier: NU algorithm
%
% [W,J,NU] = NUSVC(A,KERNEL,NU)
% W = A*SVC([],KERNEL,NU)
%
% 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 (PROXM([],'p',1));
% NU Regularization parameter (0 < NU < 1): expected fraction of SV
% (optional; default: max(leave-one-out 1_NN error,0.01))
%
% OUTPUT
% W Mapping: Support Vector Classifier
% J Object indices of support objects
% NU Actual nu_value used
%
% DESCRIPTION
% Optimizes a support vector classifier for the dataset A by quadratic
% programming. The difference with the standard SVC routine is the use and
% interpretation of the regularisation parameter NU. It is an upperbound
% for the expected classification error. By default NU is estimated by the
% leave-one-error of the 1_NN rule. For NU = NaN an automatic optimisation
% is performed using REGOPTC.
%
% If KERNEL = 0 it is assumed that A is already the kernelmatrix (square).
% In this case also a kernel matrix B should be supplied at evaluation by
% B*W or MAP(B,W).
%
% There are several ways to define KERNEL, e.g. PROXM([],'r',1) for a
% radial basis kernel or by USERKERNEL for a user defined kernel.
%
% SEE ALSO
% MAPPINGS, DATASETS, SVC, NUSVO, PROXM, USERKERNEL, REGOPTC
% Copyright: S.Verzakov, s.verzakov@ewi.tudelft.nl
% Based on SVC byby: D. de Ridder, D. Tax, R.P.W. Duin, r.p.w.duin@prtools.org
% Faculty EWI, Delft University of Technology
% P.O. Box 5031, 2600 GA Delft, The Netherlands
% $Id: nusvc.m,v 1.6 2010/06/25 09:50:40 duin Exp $
function [W,J,nu,C,alginf] = nusvc(a,kernel,nu,Options)
prtrace(mfilename);
if nargin < 4
Options = [];
end
DefOptions.mean_centering = 1;
DefOptions.pd_check = 1;
DefOptions.bias_in_admreg = 1;
DefOptions.allow_ub_bias_admreg = 1;
DefOptions.pf_on_failure = 1;
DefOptions.multiclass_mode = 'single';
Options = updstruct(DefOptions,Options,1);
if nargin < 3
nu = [];
prwarning(3,'Regularization parameter nu set to NN error\n');
end
if nargin < 2 | isempty(kernel)
kernel = proxm([],'p',1);
end
if nargin < 1 | isempty(a)
W = prmapping(mfilename,{kernel,nu,Options});
W = setname(W,'nuSVM');
elseif (~ismapping(kernel) | isuntrained(kernel)) % training
pd = 1; % switches, fixed here.
mc = 1;
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
if isempty(nu)
nu = 2*min(max(testk(a,1),0.01),(0.8*min(classsizes(a))/size(a,1)));
end
% The SVC is basically a 2-class classifier. More classes are
% handled by mclassc.
if c == 2 % two-class classifier
if (isnan(nu)) % optimize trade-off parameter
defs = {proxm([],'p',1),[],[]};
parmin_max = [0,0;0.001,0.999;0,0]; % kernel and Options can not be optimised
[W,J,nu,C,alginf] = regoptc(a,mfilename,{kernel,nu,Options},defs,[2],parmin_max,testc([],'soft'));
else
% Compute the parameters for the optimization:
y = 3 - 2*nlab;
if ~isequal(kernel,0)
if mc
u = nanmean(a);
b = a -ones(m,1)*u;
else
b = a;
u = [];
end
K = b*(b*kernel);
% Perform the optimization:
[v,J,nu,C] = nusvo(+K,y,nu,Options);
s = b(J,:);
insize = k;
else % kernel is already given!
K = min(a,a'); % make sure kernel matrix is symmetric
% Perform the optimization:
[v,J,nu,C] = nusvo(+K,y,nu,Options);
u = [];
s = [];
insize = size(K,2); % ready for kernel inputs
end
% Store the results, use SVC for execution
W = prmapping('svc','trained',{u,s,v,kernel,J},getlablist(a),insize,2);
W = cnormc(W,a);
W = setcost(W,a);
alginf.svc_type = 'nu-SVM';
alginf.kernel = kernel;
alginf.C = C;
alginf.nu = nu;
alginf.nSV = length(J);
alginf.classsizes = [nnz(y==1), nnz(y==-1)];
alginf.pf = isnan(C);
end
else % multi-class classifier:
[W,J,nu,C,alginf] = mclassc(a,prmapping(mfilename,{kernel,nu,Options}),'single');
end
W = setname(W,'nuSVM');
end
return;