function W = dlpdd(x,nu,usematlab)%DLPDD Distance Linear Programming Data Description%%       W = DLPDD(D,NU)%% This one-class classifier works directly on the distance (dissimilarity) % matrix D(X,R). Every entry of D is a dissimilarity between an object from % X and an object from R. X consists either of target examples or of both% target and outlier examples. The same holds for R, however, for logical% reasons, it might be better if R contains the targets only.% The distance matrix D does not need to be square. The distance itself % does not need to be metric.%% The DLPDD is constructed as a hyperplane in the so-called dissimilarity% space D(X,R), such that it is attracted towards the origin. The data are,% therefore, suppressed from above by this hyperplane. See the reference % paper for details. %% The NU parameter gives the fraction of error on the target set. % If NU = 0 and D is a square target distance matrix, then DLPDD and DLPDDA % tend to give the same results.%% Although it is more or less assumed that the data is in the positive quadrant, % you can put other data in as well and see how it may or may not work.%% EXAMPLE: % X = OC_SET(GENDATB([40 20]),'1');% I = FIND_TARGET(X);% D = SQRT(DISTM(X,X(I,:)));		% R <-- X(I,:), D is now 60 x 40% W = DLPDD(D,0.05);%% SEE ALSO: % LPDD, DD_EX5, DLPDDA%% @inproceedings{Pekalska2002,%	author    = {Pekalska, E. and Tax, D.M.J. and Duin, R.P.W.},%	title     = {One-class {LP} classifier for dissimilarity representations},%	booktitle = {Advances in Neural Information Processing Systems},%	year      = {2003},%	pages     = {761-768},% editor    = {S.~Becker and S.~Thrun and K.~Obermayer},% volume    = {15},% publisher = {MIT Press: Cambridge, MA}%}% Copyright: D.M.J. Tax, D.M.J.Tax@prtools.org% Faculty EWI, Delft University of Technology% P.O. Box 5031, 2600 GA Delft, The Netherlands% first set up the parametersif nargin < 3, usematlab = 0; endif nargin < 2 | isempty(nu), nu = 0.05; endif nargin < 1 | isempty(x) % empty	W = mapping(mfilename,{nu});	W = setname(W,'Distance Linear Programming Distance-data description');	returnend% trainingif ~ismapping(nu)	% work directly on the distance matrix	[n,d] = size(x);	% maybe we have example outliers...	if isocset(x)		labx = getoclab(x);	else		labx = ones(n,1);	end	x = +x; % no dataset please.	% scale the distances to avoid numerical issues (thanks Ela!):	sc = mean(x(:));	x = x./sc;	% set up the LP problem:  if (nu > 0) & (nu <= 1),  % allow error on the training data		C = 1./(n*nu);		f = [1 -1 zeros(1,d) repmat(C,1,n)]';		A = [-labx labx repmat(labx,1,d).*x  -eye(n)];		b = zeros(n,1); 		Aeq = [0 0 ones(1,d) zeros(1,n)];		beq = 1;		N = n + d + 2;		lb = zeros(N,1);		ub = repmat(inf,N,1);  elseif nu == 0,       % don't allow errors on the training data		f = [1 -1 zeros(1,d)]';		A = [-labx labx repmat(labx,1,d).*x];		b = zeros(n,1); 		Aeq = [0 0 ones(1,d)];		beq = 1;		N = d + 2;		lb = zeros(N,1);		ub = repmat(inf,N,1);  else		error ('Illegal nu.');  end	% optimize::	if (exist('glpkmex')>0) & (usematlab==0)		% the cplex optimizer:		ctype = [repmat('S',size(Aeq,1),1);		         repmat('U',size(A,1),1)];		vartype = repmat('C',size(f,1),1);		[alf,fmin] = glpkmex(1,f,[Aeq;A],[beq;b], ctype, lb,ub, vartype);	else		% or the good old Matlab optimizer:		alf = linprog(f,A,b,Aeq,beq,lb,ub);	end	% store the results	paramalf = alf(3:2+d);	W.I = find(paramalf>1e-8);	W.w = paramalf(W.I);	W.sc = sc;	W.threshold = alf(1)-alf(2)+1e-12;	W = mapping(mfilename,'trained',W,str2mat('target','outlier'),d,2);	W = setname(W,'Distance Linear Programming Distance-data description');else                               %testing	% get the data:	W = getdata(nu);	m = size(x,1);	% and here we go:	D = +x(:,W.I)./W.sc;	% annoying prtools:	newout = [D*W.w repmat(W.threshold,m,1)];	% Store the distance as output:	W = setdat(x,-newout,nu);	W = setfeatdom(W,{[-inf 0] [-inf 0]});endreturn