lpdd.m

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function W = lpdd(x,nu,dtype,par1,par2)
% W = lpdd(x,nu,dtype,p1,p2)
% 
% One-class classifier put into a linear programming framework. From
% the data x the distance matrix is computed, and on this the linear
% machine is trained. The parameter nu gives the possible error on the
% target class.
%
% Several distances dtype can be used: see ddistm to see the
% possibilities and the definition of the parameters par1 and par2. 
%

% Copyright: D. Tax, E. Pekalska, [e-mail]
% Faculty of Applied Physics, Delft University of Technology
% P.O. Box 5046, 2600 GA Delft, The Netherlands


% first set up the parameters
if nargin < 5 | isempty(par2), par2 = 1; end
if nargin < 4 | isempty(par1), par1 = 2; end
if nargin < 3 | isempty(dtype), dtype = 'lp'; end
if nargin < 2 | isempty(nu), nu = 0.05; end
if nargin < 1 | isempty(x) % empty
  W = mapping('lpdd',{nu,dtype,par1,par2});
  return
end

% training
if isa(nu,'double')

  % do some trick to compute the distances later:
  W.x = x;
  [N,d_org] = size(x);
  % maybe we have example outliers...
  if is_ocset(x)
    labx = -ones(N,1);
    labx(find_target(x)) = 1;
  else
    labx = ones(N,1);
  end

%  x = +x; % no dataset please.
  x = ddistm(+x,+x,dtype,par1,par2);
  [N,d] = size(x);

  % set up the LP problem:
  f = [ones(N,1)/(nu*N); 1; zeros(d,1)];
  A = [-eye(N) -labx repmat(labx,1,d).*x];
  b = zeros(N,1);
  Aeq = [zeros(1,N+1) ones(1,d)];
  beq = 1;
  lb = [zeros(N,1); -inf; zeros(d,1)];
  ub = inf*ones(N+d+1,1);

  % optimize, use the mex-interface if available, else the Matlab
  % optimizer:
  if exist('lp_solve')>0
%    if ~exist('lpenv') lpenv=cplex_init; end
%    [alf,y_upd_,how_upd_,p_lp]=...
%      lp_solve(lpenv, f, sparse([Aeq;A]), [beq;b], lb, ub, 1, 0);
    newf = [f;-1];
    newA = [A +labx];
    newb = [b; 0];
    newAeq = [Aeq 0];
    e = [0; -ones(N,1)];
    [v,alf] = lp_solve(-newf,sparse([newAeq;newA]),[beq;b],e);
    alf(N+1) = -(alf(N+1) + alf(end));
    alf(end) = [];
    alf1 = linprog(f,A,b,Aeq,beq,lb,ub);
  else
    alf = linprog(f,A,b,Aeq,beq,lb,ub);
  end

  % store the results
  W.dtype = dtype;
  W.par1 = par1;
  W.par2 = par2;
  W.rho = alf(N+1);
  W.w = alf((N+2):end);

  W = mapping('lpdd',W,str2mat('target','outlier'),d_org,2);
else                               %testing

  [W,classlist,type,k,c] = mapping(nu);  % unpack
  [nlab,lablist,m,k,c,p] = dataset(x);

  % and here we go:
  D = ddistm(+x,W.x,W.dtype,W.par1,W.par2);
  % the official output:
%  out = W.rho - D*W.w;
%  newout = [out -out];
  % but I choose for:
  newout = [-D*W.w -repmat(W.rho,m,1)];

  W = dataset(newout,getlab(x),classlist,p,lablist);
end
return