%NUSVC Support Vector Classifier: NU algorithm% % 	[W,J] = NUSVC(A,KERNEL,NU)% 	[W,J] = NUSVC(A,TYPE,PAR,NU)%    W    = A*SVC([],KERNEL,NU)%    W    = A*SVC([],TYPE,PAR,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));%   TYPE    Kernel type (see PROXM)%   PAR     Kernel parameter (see PROXM)%   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		%% 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 1.4 2008/01/25 10:20:55 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 = mapping(mfilename,{kernel,nu,Options});	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		% 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 mc          u = mean(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);        % Store the results, use SVC for execution      	W = mapping('svc','trained',{u,b(J,:),v,kernel},getlablist(a),k,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,mapping(mfilename,{kernel,nu,Options}),'single');		end		 		W = setname(W,'Support Vector Classifier (nu version)');	end	  return;