 function [CE] = CCE_kNN_k_estimation(Y1,Y2,co)
%Estimates the crossentropy (CE) of Y1 and Y2 using the kNN method (S={k}).
%
%We use the naming convention 'C<name>_estimation' to ease embedding new cross quantity estimation methods.
%
%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. Note: the number of samples in Y1 [=size(Y1,2)] and Y2 [=size(Y2,2)] can be different.
% co: cross quantity estimator object.
%
%REFERENCE:
% Nikolai Leonenko, Luc Pronzato, and Vippal Savani. A class of Renyi information estimators for multidimensional densities. Annals of Statistics, 36(5):21532182, 2008.
%
%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.
d1 = size(Y1,1);
[d2,num_of_samples2] = size(Y2);
%verification:
if d1~=d2
error('The dimension of the samples in Y1 and Y2 must be equal.');
end
d = d1;
V = volume_of_the_unit_ball(d);
squared_distancesY1Y2 = kNN_squared_distances(Y2,Y1,co,0);
dist_k_Y1Y2 = sqrt(squared_distancesY1Y2(end,:));
CE = log(V) + log(num_of_samples2)  psi(co.k) + d * mean(log(dist_k_Y1Y2));
