1. Zoltán Szabó
  2. ITE


ITE / code / H_I_D / base_estimators / DKL_kNN_k_estimation.m

function [D] = DKL_kNN_k_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.
%   Fernando Perez-Cruz. Estimation of Information Theoretic Measures for Continuous Random Variables. Advances in Neural Information Processing Systems (NIPS), pp. 1257-1264, 2008.
%   Nikolai Leonenko, Luc Pronzato, and Vippal Savani. A class of Renyi information estimators for multidimensional densities. Annals of Statistics, 36(5):2153-2182, 2008.
%   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/>.


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

    if dY1~=dY2
        error('The dimension of Y1 and Y2 must be equal.');

d = dY1;
squared_distancesY1Y1 = kNN_squared_distances(Y1,Y1,co,1);
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(num_of_samplesY2/(num_of_samplesY1-1));