ITE / code / H_I_D_A_C / base_estimators / IdCor_estimation.m

function [I] = IdCor_estimation(Y,ds,co)
%Estimates distance correlation (I) using pairwise distances of the sample points. 
%We use the naming convention 'I<name>_estimation' to ease embedding new mutual information estimation methods.
%   Y: Y(:,t) is the t^th sample.
%  ds: subspace dimensions.
%  co: mutual information estimator object.
%   Gabor J. Szekely and Maria L. Rizzo and. Brownian distance covariance. The Annals of Applied Statistics, 3:1236-1265, 2009.
%   Gabor J. Szekely, Maria L. Rizzo, and Nail K. Bakirov. Measuring and testing dependence by correlation of distances. The Annals of Statistics, 35:2769-2794, 2007.
%Copyright (C) 2012 Zoltan Szabo ("", "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); %dimension, number of samples

    if sum(ds)~=d;
        error('The subspace dimensions are not compatible with Y.');
    if length(ds)~=2
        error('There must be two subspaces for this estimator.');
A = compute_dCov_dCor_statistics(Y(1:ds(1),:),co.alpha);
B = compute_dCov_dCor_statistics(Y(ds(1)+1:ds(1)+ds(2),:),co.alpha);

n = sum(sum(A.*B)); %numerator
d1 = sum(sum(A.^2));%denumerator-1 (without sqrt)
d2 = sum(sum(B.^2));%denumerator-2 (without sqrt)

if (d1*d2)==0 %(at least) one of the random variables is constant
    I = 0;
    I = n/sqrt(d1*d2); %<A,B> / sqrt(<A,A><B,B>)
    I = sqrt(I);