%NMSC Nearest Mean Scaled Classifier
%
% W = NMSC(A)
% W = A*NMSC
%
% INPUT
% A Trainign dataset
%
% OUTPUT
% W Nearest Mean Scaled Classifier mapping
%
% DESCRIPTION
% Computation of the linear discriminant for the classes in the dataset A
% assuming normal distributions with zero covariances and equal class variances.
% The use of soft labels is supported.
%
% The difference with NMC is that NMSC is based on an assumption of normal
% distributions and thereby automatically scales the features and is
% sensitive to class priors. NMC is a plain nearest mean classifier that is
% feature scaling sensitive and unsensitive to class priors.
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% DATASETS, MAPPINGS, NMC, LDC ,FISHERC, QDC, UDC
% Copyright: R.P.W. Duin, duin@ph.tn.tudelft.nl
% Faculty of Applied Physics, Delft University of Technology
% P.O. Box 5046, 2600 GA Delft, The Netherlands
% $Id: nmsc.m,v 1.7 2008/01/25 10:20:07 duin Exp $
function w = nmsc(varargin)
mapname = 'S-NearestMean';
argin = setdefaults(varargin,[]);
if mapping_task(argin,'definition')
w = define_mapping(argin,'untrained',mapname);
elseif mapping_task(argin,'training') % Train a mapping.
a = argin;
islabtype(a,'crisp','soft');
isvaldfile(a,1,2); % at least 1 object per class, 2 classes
[m,k,c] = getsize(a);
p = getprior(a);
a = setprior(a,p);
[U,GG] = meancov(a);
% All class covariance matrices are assumed to be diagonal. They are
% weighted by the priors, unlike the standard nearest mean classifier (NMC).
G = zeros(c,k);
for j = 1:c
G(j,:) = diag(GG(:,:,j))';
end
G = p*G;
% The two-class case is special, as it can be conveniently stored as an
% affine mapping.
if (c == 2)
ua = +U(1,:); ub = +U(2,:);
R = G*(ua - ub)';
R = ((ua - ub)./G)';
offset = ((ub./G)*ub' - (ua./G)*ua')/2 + log(p(1)/p(2));
w = affine(R,offset,a,getlablist(a),k,c);
w = cnormc(w,a);
else
pars.mean = +U; pars.cov = G; pars.prior = p;
w = normal_map(pars,getlab(U),k,c);
end
w = setname(w,mapname);
w = setcost(w,a);
end
return