Zoltan Szabo avatar Zoltan Szabo committed 1e31d39

Multivariate extension of Blomqvist's beta (medial correlation coefficient), average pairwise Spearman's rho: added; see 'ABlomqvist_initialization.m', 'ABlomqvist_estimation.m', 'ASpearman4_initialization.m', 'ASpearman4_estimation.m'. Definition of multivariate measure of concordance and -independence measure: added (doc). Further references: included; see 'ISW1_estimation.m', 'ISWinf_estimation.m', 'ASpearman1_estimation.m', 'ASpearman2_estimation.m', 'ASpearman3_estimation.m', +doc.

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Files changed (11)

+v0.28 (Jan 2, 2012):
+-Multivariate extension of Blomqvist's beta (medial correlation coefficient): added; see 'ABlomqvist_initialization.m', 'ABlomqvist_estimation.m'.
+-Average pairwise Spearman's rho: added; see 'ASpearman4_initialization.m', 'ASpearman4_estimation.m'.
+-Definition of the multivariate measure of concordance and -independence measure: added (doc).
+-Further references: included; see 'ISW1_estimation.m', 'ISWinf_estimation.m', 'ASpearman1_estimation.m', 'ASpearman2_estimation.m', 'ASpearman3_estimation.m', +doc.
+
 v0.27 (Dec 28, 2012):
 -Approximate correntropy independence measure estimator: added; see 'IApprCorrEntr_initialization.m', 'IApprCorrEntr_estimation.m'.
 -Correntropy induced metric, centered correntropy induced metric estimators: added; see 'ACIM_initialization.m', 'ACIM_estimation.m', 'ACCIM_initialization.m', 'ACCIM_estimation.m'.
 - `entropy (H)`: Shannon entropy, R�nyi entropy, Tsallis entropy (Havrda and Charv�t entropy), complex entropy,
 - `mutual information (I)`: generalized variance, kernel canonical correlation analysis, kernel generalized variance, Hilbert-Schmidt independence criterion, Shannon mutual information, L2 mutual information, R�nyi mutual information, Tsallis mutual information, copula-based kernel dependency, multivariate version of Hoeffding's Phi, Schweizer-Wolff's sigma and kappa, complex mutual information, Cauchy-Schwartz quadratic mutual information, Euclidean distance based quadratic mutual information, distance covariance, distance correlation, approximate correntropy independence measure,
 - `divergence (D)`: Kullback-Leibler divergence (relative entropy), L2 divergence, R�nyi divergence, Tsallis divergence, Hellinger distance, Bhattacharyya distance, maximum mean discrepancy (kernel distance, an integral probability metric), J-distance (symmetrised Kullback-Leibler divergence), Cauchy-Schwartz divergence, Euclidean distance based divergence, energy distance (specially the Cramer-Von Mises distance),
-- `association measures (A)`, including `measures of concordance`: multivariate extensions of Spearman's rho (Spearman's rank correlation coefficient, grade correlation coefficient), correntropy, centered correntropy, correntropy coefficient, correntropy induced metric, centered correntropy induced metric,
+- `association measures (A)`, including `measures of concordance`: multivariate extensions of Spearman's rho (Spearman's rank correlation coefficient, grade correlation coefficient), correntropy, centered correntropy, correntropy coefficient, correntropy induced metric, centered correntropy induced metric, multivariate extension of Blomqvist's beta (medial correlation coefficient),
 - `cross quantities (C)`: cross-entropy.
 
 ITE offers solution methods for 
 
 **Download** the latest release: 
 
-- code: [zip](https://bitbucket.org/szzoli/ite/downloads/ITE-0.27_code.zip), [tar.bz2](https://bitbucket.org/szzoli/ite/downloads/ITE-0.27_code.tar.bz2), 
-- [documentation (pdf)](https://bitbucket.org/szzoli/ite/downloads/ITE-0.27_documentation.pdf).
+- code: [zip](https://bitbucket.org/szzoli/ite/downloads/ITE-0.28_code.zip), [tar.bz2](https://bitbucket.org/szzoli/ite/downloads/ITE-0.28_code.tar.bz2), 
+- [documentation (pdf)](https://bitbucket.org/szzoli/ite/downloads/ITE-0.28_documentation.pdf).
 
 

code/H_I_D_A_C/base_estimators/ABlomqvist_estimation.m

+function [A] = ABlomqvist_estimation(Y,ds,co)
+%Estimates the multivariate extension of Blomqvist's beta (medial correlation coefficient). 
+%
+%We use the naming convention 'A<name>_estimation' to ease embedding new association estimator methods.
+%
+%INPUT:
+%   Y: Y(:,t) is the t^th sample.
+%  ds: subspace dimensions.
+%  co: association estimator object.
+%
+%REFERENCE: 
+%   Friedrich Schmid, Rafael Schmidt, Thomas Blumentritt, Sandra Gaiser, and Martin Ruppert. Copula Theory and Its Applications, Chapter Copula based Measures of Multivariate Association. Lecture Notes in Statistics. Springer, 2010. (multidimensional case, length(ds)>=2)
+%   Manuel Ubeda-Flores. Multivariate versions of Blomqvist's beta and Spearman's footrule. Annals of the Institute of Statistical Mathematics, 57:781-788, 2005.
+%   Nils Blomqvist. On a measure of dependence between two random variables. The Annals of Mathematical Statistics, 21:593-600, 1950. (2D case, statistical properties)
+% Frederick Mosteller. On some useful ''inefficient'' statistics. Annals of Mathematical Statistics, 17:377--408, 1946. (2D case, def)
+%
+%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/>.
+
+%co.mult:OK.
+
+%verification:
+    if sum(ds) ~= size(Y,1);
+        error('The subspace dimensions are not compatible with Y.');
+    end
+    if ~one_dimensional_problem(ds)
+        error('The subspaces must be one-dimensional for this estimator.');
+    end
+
+[d,num_of_samples] = size(Y);
+U = copula_transformation(Y);
+
+h = 2^(d-1) / (2^(d-1)-1); %h(d)
+C1 = mean(all(U<=1/2,1)); %C(1/2)
+C2 = mean(all(U>1/2,1)); %\bar{C}(1/2)
+A = h * ( C1 + C2 - 2^(1-d) );

code/H_I_D_A_C/base_estimators/ABlomqvist_initialization.m

+function [co] = ABlomqvist_initialization(mult)
+%Initialization of the estimator of the multivariate extension of Blomqvist's beta (medial correlation coefficient).
+%
+%Note:
+%   1)The estimator is treated as a cost object (co).
+%   2)We use the naming convention 'A<name>_initialization' to ease embedding new association estimator methods.
+%
+%INPUT:
+%   mult: is a multiplicative constant relevant (needed) in the estimation; '=1' means yes, '=0' no.
+%OUTPUT:
+%   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/>.
+
+%mandatory fields:
+    co.name = 'Blomqvist';
+    co.mult = mult;
+ 

code/H_I_D_A_C/base_estimators/ASpearman1_estimation.m

 %
 %REFERENCE:
 %   Friedrich Shmid, Rafael Schmidt, Thomas Blumentritt, Sandra Gaiser, and Martin Ruppert. Copula Theory and Its Applications, Chapter Copula based Measures of Multivariate Association. Lecture Notes in Statistics. Springer, 2010.
+%   Friedrich Schmid and Rafael Schmidt. Multivariate extensions of Spearman's rho and related statistics. Statistics & Probability Letters, 77:407-416, 2007.
+%   Roger B. Nelsen. Nonparametric measures of multivariate association. Lecture Notes-Monograph Series, Distributions with Fixed Marginals and Related Topics, 28:223-232, 1996.
+%   Edward F. Wolff. N-dimensional measures of dependence. Stochastica, 4:175-188, 1980.
 %   C. Spearman. The proof and measurement of association between two things. The American Journal of Psychology, 15:72-101, 1904.
 %
 %Copyright (C) 2012 Zoltan Szabo ("http://nipg.inf.elte.hu/szzoli", "szzoli (at) cs (dot) elte (dot) hu")

code/H_I_D_A_C/base_estimators/ASpearman2_estimation.m

 %
 %REFERENCE:
 %   Friedrich Shmid, Rafael Schmidt, Thomas Blumentritt, Sandra Gaiser, and Martin Ruppert. Copula Theory and Its Applications, Chapter Copula based Measures of Multivariate Association. Lecture Notes in Statistics. Springer, 2010.
+%   Friedrich Schmid and Rafael Schmidt. Multivariate extensions of Spearman's rho and related statistics. Statistics & Probability Letters, 77:407-416, 2007.
+%   Roger B. Nelsen. Nonparametric measures of multivariate association. Lecture Notes-Monograph Series, Distributions with Fixed Marginals and Related Topics, 28:223-232, 1996.
+%   Harry Joe. Multivariate concordance. Journal of Multivariate Analysis, 35:12-30, 1990.
 %   C. Spearman. The proof and measurement of association between two things. The American Journal of Psychology, 15:72-101, 1904.
 %
 %Copyright (C) 2012 Zoltan Szabo ("http://nipg.inf.elte.hu/szzoli", "szzoli (at) cs (dot) elte (dot) hu")

code/H_I_D_A_C/base_estimators/ASpearman3_estimation.m

 %
 %REFERENCE:
 %   Friedrich Shmid, Rafael Schmidt, Thomas Blumentritt, Sandra Gaiser, and Martin Ruppert. Copula Theory and Its Applications, Chapter Copula based Measures of Multivariate Association. Lecture Notes in Statistics. Springer, 2010.
+%   Roger B. Nelsen. An Introduction to Copulas (Springer Series in Statistics). Springer, 2006.
+%   Roger B. Nelsen. Distributions with Given Marginals and Statistical Modelling, chapter Concordance and copulas: A survey, pages 169-178. Kluwer Academic Publishers, Dordrecht, 2002.
 %   C. Spearman. The proof and measurement of association between two things. The American Journal of Psychology, 15:72-101, 1904.
 %
 %Copyright (C) 2012 Zoltan Szabo ("http://nipg.inf.elte.hu/szzoli", "szzoli (at) cs (dot) elte (dot) hu")

code/H_I_D_A_C/base_estimators/ASpearman4_estimation.m

+function [A] = ASpearman4_estimation(Y,ds,co)
+%Estimates the fourth multivariate extension of Spearman's rho, the average of pairwise Spearman's rho using empirical copulas.
+%
+%We use the naming convention 'A<name>_estimation' to ease embedding new association measure estimator methods.
+%
+%INPUT:
+%   Y: Y(:,t) is the t^th sample.
+%  ds: subspace dimensions.
+%  co: association measure estimator object.
+%
+%REFERENCE:
+%   Friedrich Schmid, Rafael Schmidt, Thomas Blumentritt, Sandra Gaiser, and Martin Ruppert. Copula Theory and Its Applications, Chapter Copula based Measures of Multivariate Association. Lecture Notes in Statistics. Springer, 2010.
+%   Friedrich Schmid and Rafael Schmidt. Multivariate extensions of Spearman's rho and related statistics. Statistics & Probability Letters, 77:407-416, 2007.
+%   Maurice G. Kendall. Rank correlation methods. London, Griffin, 1970.
+%   C. Spearman. The proof and measurement of association between two things. The American Journal of Psychology, 15:72-101, 1904.
+%
+%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/>.
+
+%co.mult:OK.
+
+%verification:
+    if sum(ds) ~= size(Y,1);
+        error('The subspace dimensions are not compatible with Y.');
+    end
+    if ~one_dimensional_problem(ds)
+        error('The subspaces must be one-dimensional for this estimator.');
+    end
+    
+[d,num_of_samples] = size(Y); %dimension, number of samples
+U = copula_transformation(Y);
+
+M_triu = triu(ones(d),1);%upper triangular mask
+b = nchoosek(d,2);
+A = 12 * sum(sum(((1-U)*(1-U).').*M_triu)) / (b*num_of_samples) -3;
+

code/H_I_D_A_C/base_estimators/ASpearman4_initialization.m

+function [co] = ASpearman4_initialization(mult)
+%Initialization of the fourth multivariate extension of Spearman's rho estimator, the average of pairwise Spearman's rho.
+%
+%Note:
+%   1)The estimator is treated as a cost object (co).
+%   2)We use the naming convention 'A<name>_initialization' to ease embedding new association measure estimator methods.
+%
+%INPUT:
+%   mult: is a multiplicative constant relevant (needed) in the estimation; '=1' means yes, '=0' no.
+%OUTPUT:
+%   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/>.
+
+%mandatory fields:
+    co.name = 'Spearman4';
+    co.mult = mult;
+    
+   

code/H_I_D_A_C/base_estimators/ISW1_estimation.m

 %
 %REFERENCE:
 %  Sergey Kirshner and Barnabas Poczos. ICA and ISA Using Schweizer-Wolff Measure of Dependence. International Conference on Machine Learning (ICML), pages 464-471, 2008.
-%  B. Schweizer and E. F. Wolff. On Nonparametric Measures of Dependence for Random Variables. The Annals of Statistics 9:879-885, 1981.
+%  Edward F. Wolff. N-dimensional measures of dependence. Stochastica, 4:175-188, 1980.
+%  B. Schweizer and Edward F. Wolff. On Nonparametric Measures of Dependence for Random Variables. The Annals of Statistics 9:879-885, 1981.
 %
 %Copyright (C) 2012 Zoltan Szabo ("http://nipg.inf.elte.hu/szzoli", "szzoli (at) cs (dot) elte (dot) hu")
 %

code/H_I_D_A_C/base_estimators/ISWinf_estimation.m

 %
 %REFERENCE:
 %  Sergey Kirshner and Barnabas Poczos. ICA and ISA Using Schweizer-Wolff Measure of Dependence. International Conference on Machine Learning (ICML), pages 464-471, 2008.
-%  B. Schweizer and E. F. Wolff. On Nonparametric Measures of Dependence for Random Variables. The Annals of Statistics 9:879-885, 1981.
+%  Edward F. Wolff. N-dimensional measures of dependence. Stochastica, 4:175-188, 1980.
+%  B. Schweizer and Edward F. Wolff. On Nonparametric Measures of Dependence for Random Variables. The Annals of Statistics 9:879-885, 1981.
 %
 %Copyright (C) 2012 Zoltan Szabo ("http://nipg.inf.elte.hu/szzoli", "szzoli (at) cs (dot) elte (dot) hu")
 %
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