kwhiten.m

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%KWHITEN Whiten the data in kernel space.
% 
%       W = kwhiten(A,dim,ktype,par1)
% 
% Apply a kernel PCA and retain dim dimensions, or a fraction dim of
% the total variance. The data is then rescaled to unit variance in
% the feature space. The kernel space is defined by the kernel
% function ktype, with the free parameter par1.
% 
%       W = kwhiten(A,dim,ktype,par1,reg)
% 
% In some cases the kernel matrix has to be regularized. In that case
% the parameter reg has to be filled.
% 
% See also datasets, mappings

% Copyright: D. Tax, R.P.W. Duin, [e-mail]
% Faculty of Applied Physics, Delft University of Technology
% P.O. Box 5046, 2600 GA Delft, The Netherlands
  
function [W,orglambda] = kwhiten(a,dim,ktype,par1,reg)

if nargin < 5, reg = []; end
if nargin < 4, par1 = 2; end
if nargin < 3, ktype = 'p'; end
if nargin < 2 | isempty(dim), dim = 0.95; end
if nargin < 1 | isempty(a) 
  error('Sorry, no empty kwithen implemented yet');
  return
end

if isa(dim,'double')           %training

  if ~isa(a,'dataset')              %train on training set
    error('I need a dataset to train');
  end
  x = target_class(a);     % only use the target class
  [nlab,lablist,m,k,c,prob,featlist] = dataset(x);

  % train it:
  wK = proxm(x,ktype,par1);
  K = +(x*wK);
  % hm hm, maybe some regularization?:
  if ~isempty(reg)
    K = K + eye(m)*reg;
  end
  W.Korg = K;  % we have to store this for later.
  K = center(K,K);
  % find eigenvectors and eigenvalues:
  [alf,D] = eig(K);
  lambda = abs(diag(D));
  % sort them according to size:
  [lambda I] = sort(-lambda);
  lambda = -lambda;
  alf = alf(:,I);
  % ok, have eigenvalues larger than 0 or get a specific number of
  % dimensions:  (magic)
  orglambda = lambda;
  if (dim<1)
    I = find(cumsum(lambda)<=(dim*sum(lambda)));
    alf=alf(:,I);
    lambda = lambda(I);
  else
    I = I(1:dim);
    alf = alf(:,I);
    lambda = lambda(I);
  end
%  fprintf('%d-D\n',length(I));
  % normalize the eigen vectors;
  alength = sum(alf.*alf,1);  % in matlab already normalized a.a=1
  ascale = 1./(lambda'.*sqrt(alength));
  alf= repmat(ascale,m,1).*alf;

  %and save all useful data:
  W.wK = wK;
  W.alf = alf;
  W = mapping(mfilename,W,[],k,length(I),1,[],0);

else                               %testing/mapping

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

  %compute the mapping
  n = size(W.alf,2);
  % compute the kernel matrix and center it
  K = +(a*W.wK);
  K = center(K,W.Korg);
  % map the data on the eigenvectors:
  mapped = zeros(m,n);
  for i=1:n
    mp = repmat(W.alf(:,i)',m,1).*K;
    mapped(:,i) = sum(mp,2);
  end

  W = dataset(mapped,getlab(a));
end
return