%LKC Trainable linear kernel classifier
%
% W = LKC(A,KERNEL)
% W = A*LKC([],KERNEL)
% W = A*LKC(KERNEL)
%
% INPUT
% A Dataset
% KERNEL Mapping to compute kernel by A*MAP(A,KERNEL)
% or string to compute kernel by FEVAL(KERNEL,A,A)
% or cell array with strings and parameters to compute kernel by
% FEVAL(KERNEL{1},A,A,KERNEL{2:END})
% Default: linear kernel (PROXM('P',1))
%
% OUTPUT
% W Mapping: Support Vector Classifier
%
% DESCRIPTION
% This is a fall-back routine for other kernel procedures like SVC, RBSVC
% and LIBSVC. If they fail due to optimization problems they may fall back
% to this routine which computes a linear classifier in kernelspace using
% the pseudo-inverse of the kernel.
%
% The kernel may be supplied in KERNEL by
% - an untrained mapping, e.g. a call to PROXM like W = LIBSVC(A,PROXM('R',1))
% - a string with the name of the routine to compute the kernel from A
% - a cell-array with this name and additional parameters.
% This will be used for the evaluation of a dataset B by B*W or PRMAP(B,W) as
% well.
%
% If KERNEL = 0 it is assumed that A is already the kernel matrix (square).
% In this also a kernel matrix should be supplied at evaluation by B*W or
% PRMAP(B,W).
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% MAPPINGS, DATASETS, SVC, PROXM
% 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
function W = lkc(varargin)
mapname = 'LKC Classifier';
argin = shiftargin(varargin,{'prmapping','char'});
argin = setdefaults(argin,[],proxm('p',1));
if mapping_task(argin,'definition')
W = define_mapping(argin,'fixed',mapname);
elseif mapping_task(argin,'training') % Train a mapping.
[a,kernel] = deal(argin{:});
islabtype(a,'crisp');
isvaldfile(a,1,2); % at least 1 object per class, 2 classes
a = testdatasize(a,'objects');
[m,k,c] = getsize(a);
nlab = getnlab(a);
K = compute_kernel(a,a,kernel);
K = min(K,K'); % make sure kernel is symmetric
targets = gettargets(setlabtype(a,'targets'));
v = prpinv([K ones(m,1); ones(1,m) 0])*[targets; zeros(1,c)];
lablist = getlablist(a);
W = prmapping(mfilename,'trained',{v,a,kernel},lablist,size(a,2),c);
W = setname(W,mapname);
W = cnormc(W,a);
W = setcost(W,a);
else % Evaluation
[a,w] = deal(argin{1:2});
[v,s,kernel] = getdata(w);
m = size(a,1);
K = compute_kernel(a,s,kernel); % kernel testset
% Data is mapped by the kernel, now we just have a linear
% classifier w*x+b:
d = [K ones(m,1)]*v;
if size(d,2) == 1, d = [d -d]; end
W = setdat(a,d,w);
end
return;
function K = compute_kernel(a,s,kernel)
% compute a kernel matrix for the objects a w.r.t. the support objects s
% given a kernel description
if isstr(kernel) % routine supplied to compute kernel
K = feval(kernel,a,s);
elseif iscell(kernel)
K = feval(kernel{1},a,s,kernel{2:end});
elseif ismapping(kernel)
K = a*prmap(s,kernel);
elseif kernel == 0 % we have already a kernel
K = a;
else
error('Do not know how to compute kernel matrix')
end
K = +K;
return