%KERNELM Trainable kernel mapping, dissimilarity representation
%
% [W,J] = KERNELM(A,KERNEL,SELECT,P1,P2 , ...)
% W = A*KERNELM([],KERNEL,SELECT,P1,P2 , ...)
% W = A*KERNELM(KERNEL,SELECT,P1,P2 , ...)
% K = B*W
%
% INPUT
% A,B Datasets
% KERNEL Untrained kernel / dissimilarity representation,
% a mapping computing proximities between objects.
% default: Euclidean dissimilarities: PROXM('d',1)
% SELECT Name of object selection procedure, see below
% P1,P2, ... Additional parameters for SELECT
%
% OUTPUT
% W Mapping
% J Vector with indices of selected objects for representation
% K Kernel matrix, dissimilarity representation,
% size [SIZE(B,1) LENGTH(J)]
%
% DESCRIPTION
% Computes the kernel mapping W for the representation objects in A. The
% computation of the kernel matrix, which is a proximity matrix (similarities
% or dissimilarities) should be defined in KERNEL by an untrained mapping
% like PROXM for predefined proximities or USERKERNEL for user specified
% proximities.
% A*KERNEL should 'train' the kernel, i.e. specify A as representation set.
% B*(A*KERNEL) should compute the kernel matrix: a dataset.
%
% The only advantage of this routine over kernel mappings defined by PROXM
% or USERKERNEL is that it includes some options for object selection
% (prototype selection) of the initial representation set.
%
% Initially, the kernel mapping has a size [SIZE(A,2) SIZE(A,1)]. For
% increased efficiency or accuracy the representation set may be reduced
% by a routine given by the string SELECT to select to objects J, using
% possibly additional parameters P1, P2, etcetera.
%
% The following choices for SELECT are supported:
%
% 'random' random selection of P1 objects, maximum P2
% 'gendat' [X,Y,J] = GENDAT(A,P1)
% 'kcentres' [LAB,J] = KCENTRES(DISTM(A),P1,P2)
% 'modeseek' [LAB,J] = MODESEEK(DISTM(A),P1)
% 'edicon' J = EDICON(DISTM(A),P1,P2,P3)
% 'featsel' J = +FEATSELM(A*KERNELM(A,TYPE,P),P1,P2,P3)
%
% REFERENCES
% 1. E.Pekalska, R.P.W.Duin, P.Paclik, Prototype selection for dissimilarity-
% based classification, Pattern Recognition, vol. 39, no. 2, 2006, 189-208.
% 2. E.Pekalska and R.P.W.Duin, The Dissimilarity Representation for Pattern
% Recognition, Foundations and Applications, World Scientific, 2005, 1-607.
%
% EXAMPLE
% a = gendatb;
% w = (scalem*kernelm([],'random',5)*fisherc);
% scatterd(a)
% plotc(a*w)
% plotc(a*w,'r')
% plotc(a*w,'b')
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% DATASETS, MAPPINGS, PROXM, USERKERNEL, KERNELC
% Copyright: R.P.W. Duin, r.p.w.duin@37steps.com
% Faculty EWI, Delft University of Technology
% P.O. Box 5031, 2600 GA Delft, The Netherlands
% $Id: kernelm.m,v 1.7 2007/07/10 08:25:29 duin Exp $
function w = kernelm(varargin)
argin = shiftargin(varargin,'prmapping');
argin = shiftargin(varargin,'char',2);
argin = setdefaults(argin,[],proxm([],'d',1),[],[],[],[]);
if mapping_task(argin,'definition')
w = define_mapping(argin,'untrained');
w = setname(w,'Kernel mapping');
else % training
varargin = cell(1,numel(argin)-3);
[a,kernel,select,varargin{:}] = deal(argin{:});
if isstr(kernel) % old format of call: kernelm(a,type,p,n), training
type = kernel;
p = select;
if ~isempty(varargin)
if length(varargin) > 1
error('Wrong parameters supplied')
end
n = varargin{1};
else
n = [];
end
[m,k] = size(a);
kernel = proxm([],type,p);
w = prmapping(mfilename,'trained',{a*kernel},getlab(a),k,m);
if ~isempty(n)
w = w*pcam(a*w,n);
end
w = setname(w,'Kernel Mapping');
elseif isa(kernel,'prmapping') && ...
~strcmp(getmapping_file(kernel),mfilename) % training
a = testdatasize(a);
a = testdatasize(a,'objects');
isuntrained(kernel);
[m,k] = size(a);
%w = prmapping('kernelm','trained',{a*kernel},getlab(a),k,m);
if isempty(select)
w = prmapping('kernelm','trained',{a*kernel},getlab(a),k,m);
elseif ismapping(select)
r = a*select;
w = prmapping('kernelm','trained',{r*kernel},getlab(a),k,size(r,1));
else
switch select
case 'random'
J = randperm(m);
n = varargin{1};
if isempty(n) | n > m
error('Number of objects to be selected not given or too large')
end
if n < 1, n = ceil(n*m); end % fraction given
if ~isempty(varargin{2})
n = min(n,varargin{2});
end
J = J(1:n);
case 'gendat'
[x,y,J] = gendat(a,varargin{1});
case 'kcentres'
[lab,J] = kcentres(distm(a),varargin{1:2});
case 'modeseek'
[lab,J] = modeseek(distm(a),varargin{1});
case 'edicon'
J = edicon(distm(a),varargin{1:3});
case 'featsel'
w = prmapping('kernelm','trained',{a*kernel},getlab(a),k,m);
J = +featselm(a*w,varargin{1:3});
otherwise
error('Unknown choice for object selection')
end
% redefine mapping with reduced representation set
labels_out = getlab(a);
w = prmapping('kernelm','trained',{a(J,:)*kernel},labels_out(J,:),k,length(J));
end
w = setname(w,'Kernel Mapping');
else % Execution of the mapping, w will be a dataset.
kern = getdata(kernel,1); % trained kernel is stored in datafield
K = a*kern;
w = setdat(a,K,kern);
end
end
return