1. Zoltán Szabó
  2. ITE


ITE / code / H_I_D_A_C / utilities / estimate_Dtemp3.m

function [Dtemp3] = estimate_Dtemp3(Y1,Y2,co)
%Estimates Dtemp3 = \int p(u)q^{a-1}(u)du; used in Bregman distance computation.
%   Y1: Y1(:,t) is the t^th sample from the first distribution (Y1~p).
%   Y2: Y2(:,t) is the t^th sample from the second distribution (Y2~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 <http://www.gnu.org/licenses/>.

    [dY1,num_of_samplesY1] = size(Y1);
    [dY2,num_of_samplesY2] = size(Y2);
    if dY1~=dY2
        error('The dimension of the samples in Y1 and Y2 must be equal.');
d = dY1; %=dY2
a = co.alpha;
k = co.k;

squared_distancesY1Y2 = kNN_squared_distances(Y2,Y1,co,0);
V = volume_of_the_unit_ball(d);
Ca = ( gamma(k)/gamma(k+1-a) ); %C^a

Dtemp3 = num_of_samplesY2^(1-a) * Ca * V^(1-a) * mean(squared_distancesY1Y2(co.k,:).^(d*(1-a)/2)); %/2 <= squared distances