# ITE / code / H_I_D_A_C / utilities / estimate_Dtemp1.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 31 32 33 34 35 36 37 38 39 function [Dtemp1] = estimate_Dtemp1(X,Y,co) %Estimates Dtemp1 = \int p^{\alpha}(u)q^{1-\alpha}(u)du, the Renyi and the Tsallis divergences 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 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)); Dtemp1 = mean( ((num_of_samplesX-1)/num_of_samplesY * (dist_k_XX./dist_k_YX).^d).^(1-co.alpha)) * B; 
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