Artículo
Log-Determinant Divergences Revisited: Alpha-Beta and Gamma Log-Det Divergences
Autor/es | Cichocki, Andrzej
Cruces Álvarez, Sergio Antonio Amari, Shun-ichi |
Departamento | Universidad de Sevilla. Departamento de Teoría de la Señal y Comunicaciones |
Fecha de publicación | 2015-05-08 |
Fecha de depósito | 2016-12-01 |
Publicado en |
|
Resumen | This work reviews and extends a family of log-determinant (log-det) divergences
for symmetric positive definite (SPD) matrices and discusses their fundamental properties.
We show how to use parameterized Alpha-Beta (AB) ... This work reviews and extends a family of log-determinant (log-det) divergences for symmetric positive definite (SPD) matrices and discusses their fundamental properties. We show how to use parameterized Alpha-Beta (AB) and Gamma log-det divergences to generate many well-known divergences; in particular, we consider the Stein’s loss, the S-divergence, also called Jensen-Bregman LogDet (JBLD) divergence, Logdet Zero (Bhattacharyya) divergence, Affine Invariant Riemannian Metric (AIRM), and other divergences. Moreover, we establish links and correspondences between log-det divergences and visualise them on an alpha-beta plane for various sets of parameters. We use this unifying framework to interpret and extend existing similarity measures for semidefinite covariance matrices in finite-dimensional Reproducing Kernel Hilbert Spaces (RKHS). This paper also shows how the Alpha-Beta family of log-det divergences relates to the divergences of multivariate and multilinear normal distributions. Closed form formulas are derived for Gamma divergences of two multivariate Gaussian densities; the special cases of the Kullback-Leibler, Bhattacharyya, Rényi, and Cauchy-Schwartz divergences are discussed. Symmetrized versions of log-det divergences are also considered and briefly reviewed. Finally, a class of divergences is extended to multiway divergences for separable covariance (or precision) matrices. |
Cita | Cichocki, A., Cruces, S.A. y Shun-ichi, A. (2015). Log-Determinant Divergences Revisited: Alpha-Beta and Gamma Log-Det Divergences. Entropy, 17 (5), 2988-3034. |
Ficheros | Tamaño | Formato | Ver | Descripción |
---|---|---|---|---|
entropy-17-02988-v2.pdf | 759.1Kb | [PDF] | Ver/ | |
Este registro aparece en las siguientes colecciones
Excepto si se señala otra cosa, la licencia del ítem se describe como: Attribution-NonCommercial-NoDerivatives 4.0 Internacional
Items relacionados
Enseñando items relacionados por título, autor, creador y materia.
-
Artículo
Generalized Alpha-Beta Divergences and Their Application to Robust Nonnegative Matrix Factorization
Cichocki, Andrzej; Cruces Álvarez, Sergio Antonio; Amari, Shun-ichi (Multidisciplinary Digital Publishing Institute, 2011)We propose a class of multiplicative algorithms for Nonnegative Matrix Factorization (NMF) which are robust with respect ...
-
Artículo
Optimization of Alpha-Beta Log-Det Divergences and their Application in the Spatial Filtering of Two Class Motor Imagery Movements
Thiyam, Deepa Beeta; Cruces Álvarez, Sergio Antonio; Olías Sánchez, Francisco Javier; Cichocki, Andrzej (MDPI, 2017-02-25)The Alpha-Beta Log-Det divergences for positive definite matrices are flexible divergences that are parameterized by two ...
-
Artículo
Convergence et divergence entre espagnol, italien et français: la traduction des Colloques de Pedro Mexía (XVIe siècle)
Rey Quesada, Santiago del (Francke Verlag, 2022-12)En este trabajo nos ocupamos de la obra de un autor español que gozó de gran éxito editorial en la Europa de su tiempo, ...