function [D_JS] = DJensenShannon_HShannon_estimation(Y1,Y2,co)
%Estimates the Jensen-Shannon divergence of Y1 and Y2 using the relation:
%D_JS(f_1,f_2) = H(w1*y^1+w2*y^2) - [w1*H(y^1) + w2*H(y^2)], where y^i has density f_i (i=1,2), w1*y^1+w2*y^2 is the mixture distribution of y^1 and y^2 with w1,w2 positive weights, and H denotes the Shannon entropy.
%
%Note:
% 1)We use the naming convention 'D_estimation' to ease embedding new divergence estimation methods.
% 2)This is a meta method: the Shannon entropy estimator can be arbitrary.
%
%INPUT:
% Y1: Y1(:,t) is the t^th sample from the first distribution.
% Y2: Y2(:,t) is the t^th sample from the second distribution.
% co: divergence estimator object.
%
%REFERENCE:
% Jianhua Lin. Divergence measures based on the Shannon entropy. IEEE Transactions on Information Theory, 37:145-151, 1991.
%
%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 .
%co.mult:OK.
%verification:
if size(Y1,1)~=size(Y2,1)
error('The dimension of the samples in Y1 and Y2 must be equal.');
end
w = co.w;
mixtureY = mixture_distribution(Y1,Y2,w);
D_JS = H_estimation(mixtureY,co.member_co) - (w(1)*H_estimation(Y1,co.member_co) + w(2)*H_estimation(Y2,co.member_co));