# ITE / code / H_I_D / utilities / estimate_Ialpha.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 function [I_alpha] = estimate_Ialpha(Y,co) %Estimates I_alpha = \int p^{\alpha}(y)dy, the Renyi and the Tsallis entropies are simple functions of this quantity. Here, alpha:=co.alpha. % %INPUT: % Y: Y(:,t) is the t^th sample from the distribution having density p. % 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_samples] = size(Y); squared_distances = kNN_squared_distances(Y,Y,co,1); V = volume_of_the_unit_ball(d); C = ( gamma(co.k)/gamma(co.k+1-co.alpha) )^(1/(1-co.alpha)); s = sum( squared_distances(co.k,:).^(d*(1-co.alpha)/2) ); %'/2' <= squared distances I_alpha = (num_of_samples-1) / num_of_samples * V^(1-co.alpha) * C^(1-co.alpha) * s / (num_of_samples-1)^(co.alpha); 
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