%SVC_NU Support Vector Classifier: NU algorithm% % 	[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 belogs 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 classes % algorithm will typically take long time to converge (if at all). % So, it is advisable to set NU larger than expected overlap.%% Output is rescaled in a such 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 1.3 2006/03/07 16:19:34 duin Exp $function [W, J, C] = svc_nu(a,type,par,nu,mc,pd)		prtrace(mfilename);  if nargin < 2 | ~isa(type,'mapping')    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 = mapping(mfilename,{type,par,nu,mc,pd});    	W = setname(W,'Support Vector Classifier (nu version)');    	return;    end  	islabtype(a,'crisp');  	isvaldset(a,1,2); % at least 1 object per class, 2 classes  	[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 = mapping(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 = a.ident(J);  		  	else   % multi-class classifier:	    [W,J,C] = mclassc(a,mapping(mfilename,{type,par,nu,mc,pd}),'single');		end  else % execution  	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;