 function [I] = IdCov_estimation(Y,ds,co)
%Estimates distance covariance (I) using pairwise distances of the sample points.
%
%We use the naming convention 'I<name>_estimation' to ease embedding new mutual information estimation methods.
%
%INPUT:
% Y: Y(:,t) is the t^th sample.
% ds: subspace dimensions.
% co: mutual information estimator object.
%
%REFERENCE:
% Gabor J. Szekely and Maria L. Rizzo and. Brownian distance covariance. The Annals of Applied Statistics, 3:12361265, 2009.
% Gabor J. Szekely, Maria L. Rizzo, and Nail K. Bakirov. Measuring and testing dependence by correlation of distances. The Annals of Statistics, 35:27692794, 2007.
%
%Copyright (C) 2012 Zoltan Szabo ("http://nipg.inf.elte.hu/szzoli", "szzoli (at) cs (dot) elte (dot) hu")
%
%This file is part of the ITE (Information Theoretical Estimators) Matlab/Octave toolbox.
%
%ITE is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by
%the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
%
%This software is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
%MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
%
%You should have received a copy of the GNU General Public License along with ITE. If not, see <http://www.gnu.org/licenses/>.
%co.mult:OK.
[d,num_of_samples] = size(Y); %dimension, number of samples
%verification:
if sum(ds)~=d;
error('The subspace dimensions are not compatible with Y.');
end
if length(ds)~=2
error('There must be two subspaces for this estimator.');
end
A = compute_dCov_dCor_statistics(Y(1:ds(1),:),co.alpha);
B = compute_dCov_dCor_statistics(Y(ds(1)+1:ds(1)+ds(2),:),co.alpha);
I = sqrt(sum(sum(A.*B))) / num_of_samples;
