%DISTMAHA Mahalanobis distance
%
% D = DISTMAHA (A,U,G)
%
% INPUT
% A Dataset
% U Mean(s) (optional; default: estimate on classes in A)
% G Covariance(s) (optional; default: estimate on classes in A)
%
% OUTPUT
% D Mahalanobis distance matrix
%
% DESCRIPTION
% Computes the M*N Mahanalobis distance matrix of all vectors in M*K dataset
% A to an N*K dataset of points U, using the covariance matrix or matrices
% G. G should be either be one K*K matrix, or a K*K*N matrix containing a
% covariance matrix for each point in U.
%
% When U and G are not specified, it estimates the C*C Mahalanobis distance
% matrix between all classes in A: the distance between the means,
% relative to the average per-class covariance matrix.
%
% SEE ALSO
% DATASETS, DISTM, PROXM, MEANCOV
% Copyright: R.P.W. Duin, r.p.w.duin@prtools.org
% Faculty EWI, Delft University of Technology
% P.O. Box 5031, 2600 GA Delft, The Netherlands
% $Id: distmaha.m,v 1.6 2004/05/16 20:40:13 duin Exp $
function d = distmaha_new (a,u,g,DirectionalFeatures)
prtrace(mfilename);
[m,k,c] = getsize(a);
if (nargin == 1 || (nargin == 4 && isempty(u) && isempty(g) ) )
% Calculate Mahalanobis distance matrix between classes in dataset:
% the distance matrix between the class means, sphered using the
% average covariance matrix of the per-class centered data.
if( isempty(DirectionalFeatures) )
u = zeros(c,k);
for i = 1:c
J = findnlab(a,i);
if (~isempty(J))
% Mean of class I.
u(i,:) = mean(a(J,:),1);
% Remove class mean, for later covariance calculation.
a(J,:) = a(J,:) - repmat(+u(i,:),length(J),1);
end
end
else
u = zeros(c,k);
for i = 1:c
J = findnlab(a,i);
if (~isempty(J))
% Mean of class I.
u(i,:) = meancov_new(+a(J,:),0,DirectionalFeatures);
% Remove class mean, for later covariance calculation.
a(J,:) = a(J,:) - repmat(+u(i,:),length(J),1);
%al quitar la media, aun los features circulares quedan
%en torno al origen y pueden considerarse features
%lineales.
end
end
end
% Sphere means and calculate distance matrix.
[E,V] = eig(covm(a));
u = u*E*sqrt(inv(V));
d = distm(u);
elseif (nargin == 2)
% Calculate Euclidean distance between data and means.
prwarning(4,'covariance matrix not specified, assuming G = I');
d = distm(a,u);
elseif (nargin == 3 || (nargin == 4 && ~isempty(u) && ~isempty(g) ) )
% Calculate distance between A and distributions specified by U and G.
% Check arguments.
[kg1,kg2,cg] = size(g); [cu,ku] = size(u);
if any([kg1,kg2,ku] ~= k) | (cu ~= cg & cg ~= 1)
error('sizes of mean(s) and covariance(s) do not match')
end
% Get labels of means if present, or assign labels 1:N. These are
% only used in the construction of the dataset D.
if (isa(u,'prdataset')), labels = getlab(u); else, labels = [1:cu]'; end
% If there is only one covariance matrix, invert it here.
if (cg == 1), g_inv = inv(g); end
d = zeros(m,cu);
for i = 1:cu
% If each mean has its own covariance matrix, invert it here.
if (cg ~= 1), g_inv = inv(g(:,:,i)); end
if( isempty(DirectionalFeatures) )
% And calculate the standard Mahalanobis distance.
d(:,i) = sum((a-repmat(+u(i,:),m,1))'.*(g_inv*(a-repmat(+u(i,:),m,1))'),1)';
else
NotDirectionalFeatures = setdiff(1:iCantFeatures, DirectionalFeatures);
if( ~isempty(NotDirectionalFeatures) )
d(:,i) = sum((a(:,NotDirectionalFeatures)-repmat(+u(i,NotDirectionalFeatures),m,1))'.*(g_inv(NotDirectionalFeatures,NotDirectionalFeatures)*(a(:,NotDirectionalFeatures)-repmat(+u(i,NotDirectionalFeatures),m,1))'),1)';
end
for ii = DirectionalFeatures
d(:,i) = d(:,i) + sum((a(:,ii)-repmat(+u(i,ii),m,1))'.*(g_inv*(a(:,ii)-repmat(+u(i,ii),m,1))'),1)';
end
end
end
% Construct the distance matrix dataset.
d = setdata(a,d,labels);
d = setname(d,'Maha Dist');
else
error('incorrect number of arguments')
end
return