dd_kernel.m

%DD_KERNEL Kernel computation
%
%              K = DD_KERNEL(A,B,KTYPE,P);
%
% INPUT
%   A,B      Data matrices
%   KTYPE    Kernel type
%   P        Kernel parameter
%
% OUPUT
%   K        Matrix with kernel values
%
% DESCRIPTION
% Computation of a kernel function between A and B. The data A and B are
% expected to be standard Matlab matrices (NOT prtools datasets).
%
% The kernel is defined by the kernel type KTYPE, and its parameter P.
%        KTYPE   defines the kernel type
%       'linear'       | 'l': A*B'
%       'polynomial'   | 'p': sign(A*B'+1).*(A*B'+1).^P
%       'homogeneous'  | 'h': sign(A*B').*(A*B').^P
%       'exponential'  | 'e': exp(-(||A-B||)/P)
%       'radial_basis' | 'r': exp(-(||A-B||.^2)/(P*P))
%       'sigmoid'      | 's': sigm((sign(A*B').*(A*B'))/P)
%       'distance'     | 'd': ||A-B||.^P
%       'cityblock'    | 'c': ||A-B||_1
%       'negdistance'  | 'n': -||A-B||.^P
%
% When more than 1 free parameter is required, then parameter P can be a
% vector of length 2 or more.
%
% SEE ALSO
% dd_proxm, sqeucldistm

% 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
% See also: incsvdd, proxm, Wstartup, Wadd
function K = dd_kernel(A,B,ktype,kpar);

switch ktype
case {'linear' 'l'}
	K = A*B'; 
case {'polynomial' 'p'}
	K = A*B'; 
	if kpar ~= 1
		n = size(A,1);
		m = size(B,1);
		if kpar ~= round(kpar)
			K = K + ones(n,m);
			K = sign(K).*abs(K).^kpar;
		else
			K = K + ones(n,m);
			K = K.^kpar;
		end
	end
case {'homogeneous' 'h'}
	K = A*B'; 
	if kpar ~= 1
		n = size(A,1);
		m = size(B,1);
		if kpar ~= round(kpar)
			K = sign(K).*abs(K).^kpar;
		else
			K = K.^kpar;
		end
	end
case {'sigmoid' 's'}
	K = A*B'; 
	if length(kpar)>1
		K = sigm(K/kpar(1) + kpar(2));   %DXD: I need this sometimes
	else
		K = sigm(K/kpar);
	end
case {'exponential' 'e'}
	K = sqeucldistm(A,B);
	J = find(K<0);
	K(J) = zeros(size(J));
	K = exp(-sqrt(K)/kpar);
case {'radial_basis' 'r'}
	K = sqeucldistm(A,B);
	J = find(K<0);
	K(J) = zeros(size(J));
	K = exp(-K/(kpar*kpar));
case {'inv_radial_basis' 'i'}
	K = sqeucldistm(A,B);
	J = find(K<0);
	K(J) = zeros(size(J));
	K = exp(sqrt(K)/kpar);
case {'distance' 'd'}
	K = sqeucldistm(A,B);
	J = find(K<0);
	K(J) = zeros(size(J));
	if kpar ~= 2
		K = K.^(kpar/2);
	end
case {'negdistance' 'n'}
	K = sqeucldistm(A,B);
	J = find(K<0);
	K(J) = zeros(size(J));
	if kpar ~= 2
		K = K.^(kpar/2);
    end
    K = -K;
case {'cityblock', 'c'}
	n = size(A,1);
	m = size(B,1);
	K = zeros(n,m);
	for j=1:m
		K(:,j) = sum(abs(A - repmat(B(j,:),n,1)),2);
	end

otherwise
	error(sprintf('Unknown proximity type: %s',ktype))
end

return