ITE / code / H_I_D_C / base_estimators / DKL_kNN_kiTi_estimation.m

function [D] = DKL_kNN_kiTi_estimation(Y1,Y2,co)
%Estimates the Kullback-Leibler divergence (D) of Y1 and Y2 (Y1(:,t), Y2(:,t) is the t^th sample)
%using the kNN method (S={k}). The number of samples in Y1 [=size(Y1,2)] and Y2 [=size(Y2,2)] can be different. Cost parameters are provided in the cost object co.
%
%We make use of the naming convention 'D<name>_estimation', to ease embedding new divergence estimation methods.
%
%REFERENCE: 
%   Quing Wang, Sanjeev R. Kulkarni, and Sergio Verdu. Divergence estimation for multidimensional densities via k-nearest-neighbor distances. IEEE Transactions on Information Theory, 55:2392-2405, 2009.
%
%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.

[dY1,num_of_samplesY1] = size(Y1);
[dY2,num_of_samplesY2] = size(Y2);

%verification:
    if dY1~=dY2
        error('The dimension of the samples in Y1 and Y2 must be equal.');
    end

d = dY1;
k1 = floor(sqrt(num_of_samplesY1));
k2 = floor(sqrt(num_of_samplesY2));
    
co.k = k1;
squared_distancesY1Y1 = kNN_squared_distances(Y1,Y1,co,1);
    
co.k = k2;
squared_distancesY2Y1 = kNN_squared_distances(Y2,Y1,co,0);
    
dist_k_Y1Y1 = sqrt(squared_distancesY1Y1(end,:));
dist_k_Y2Y1 = sqrt(squared_distancesY2Y1(end,:));
D = d * mean(log(dist_k_Y2Y1./dist_k_Y1Y1)) + log( k1/k2 * num_of_samplesY2/(num_of_samplesY1-1) );
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