 function [H] = HShannon_kNN_k_estimation(Y,co)
%Estimates the Shannon differential entropy (H) of Y (Y(:,t) is the t^th sample)
%using the kNN method (and neighbors S={k}). Cost parameters are provided in the cost object co.
%
%We make use of the naming convention 'H<name>_estimation', to ease embedding new entropy estimation methods.
%
%REFERENCE:
% M. N. Goria, Nikolai N. Leonenko, V. V. Mergel, and P. L. Novi Inverardi. A new class of random vector entropy estimators and its applications in testing statistical hypotheses. Journal of Nonparametric Statistics, 17: 277�297, 2005. (S={k})
% Harshinder Singh, Neeraj Misra, Vladimir Hnizdo, Adam Fedorowicz and Eugene Demchuk. Nearest neighbor estimates of entropy. American Journal of Mathematical and Management Sciences, 23, 301321, 2003. (S={k})
% L. F. Kozachenko and Nikolai N. Leonenko. A statistical estimate for the entropy of a random vector. Problems of Information Transmission, 23:9�16, 1987. (S={1})
%
%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/>.
[d,num_of_samples] = size(Y);
squared_distances = kNN_squared_distances(Y,Y,co,1);
%co.mult:OK.
%H estimation:
V = volume_of_the_unit_ball(d);
H = log(num_of_samples1)  psi(co.k) + log(V) + d / num_of_samples * sum(log(sqrt(squared_distances(co.k,:)))); %sqrt <= squared_distances,
