ITE / code / H_I_D / base_estimators / DKL_kNN_kiTi_estimation.m

function [D] = DKL_kNN_kiTi_estimation(X,Y,co)
%Estimates the Kullback-Leibler divergence (D) of X and Y (X(:,t), Y(:,t) is the t^th sample)
%using the kNN method (S={k}). The number of samples in X [=size(X,2)] and Y [=size(Y,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.

[dX,num_of_samplesX] = size(X);
[dY,num_of_samplesY] = size(Y);

if dX~=dY
    disp('Error: the dimension of X and Y must be equal.');
else
    d = dX;
    k1 = floor(sqrt(num_of_samplesX));
    k2 = floor(sqrt(num_of_samplesY));
    
    co.k = k1;
    squared_distancesXX = kNN_squared_distances(X,X,co,1);
    
    co.k = k2;
    squared_distancesYX = kNN_squared_distances(Y,X,co,0);
    
    dist_k_XX = sqrt(squared_distancesXX(end,:));
    dist_k_YX = sqrt(squared_distancesYX(end,:));
    D = d * mean(log(dist_k_YX./dist_k_XX)) + log( k1/k2 * num_of_samplesY/(num_of_samplesX-1) );
end
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