# ITE / code / H_I_D / utilities / estimate_Dalpha.m

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30``` ```function [D_alpha] = estimate_Dalpha(X,Y,co) %Estimates D_alpha = \int p^{\alpha}(x)q^{1-\alpha}(x)dx, the Rényi and the Tsallis divergences are simple functions of this quantity. % %INPUT: % X: X(:,t) is the t^th sample from the first distribution. % Y: Y(:,t) is the t^th sample from the second distribution. % 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 . [d,num_of_samplesY] = size(Y); [d,num_of_samplesX] = size(X); 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,:)); B = gamma(co.k)^2 / (gamma(co.k-co.alpha+1)*gamma(co.k+co.alpha-1)); D_alpha = mean( ((num_of_samplesX-1)/num_of_samplesY * (dist_k_XX./dist_k_YX).^d).^(1-co.alpha)) * B; ```