function [Dtemp2] = estimate_Dtemp2(X,Y,co) %Estimates Dtemp2 = \int p^a(u)q^b(u)p(u)du; the Hellinger distance and the Bhattacharyya distance are simple functions of this quantity. % %INPUT: % X: X(:,t) is the t^th sample from the first distribution (X~p). % Y: Y(:,t) is the t^th sample from the second distribution (Y~q). % co: cost object (structure). % %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 . %initialization: [dY,num_of_samplesY] = size(Y); [dX,num_of_samplesX] = size(X); %verification: if dX~=dY error('The dimension of the samples in X and Y must be equal.'); end %initialization - continued: d = dX; %=dY a = co.a; b = co.b; k = co.k; squared_distancesXX = kNN_squared_distances(X,X,co,1); squared_distancesYX = kNN_squared_distances(Y,X,co,0); dist_k_XX = sqrt(squared_distancesXX(end,:)); dist_k_YX = sqrt(squared_distancesYX(end,:)); c = volume_of_the_unit_ball(d); B = c^(-(a+b)) * gamma(k)^2 / (gamma(k-a)*gamma(k-b)); Dtemp2 = (num_of_samplesX-1)^(-a) * num_of_samplesY^(-b) * B * mean(dist_k_XX.^(-d*a).*dist_k_YX.^(-d*b));