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Log-Determinant Divergences Revisited: Alpha-Beta and Gamma Log-Det Divergences

Opened Access Log-Determinant Divergences Revisited: Alpha-Beta and Gamma Log-Det Divergences

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Autor: Cichocki, Andrzej
Cruces, Sergio A.
Amari, Shun-ichi
Departamento: Universidad de Sevilla. Departamento de Teoría de la Señal y Comunicaciones
Fecha: 2015-05-08
Publicado en: Entropy, 17 (5), 2988-3034.
Tipo de documento: Artículo
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) 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 di...
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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.
Tamaño: 759.1Kb
Formato: PDF

URI: http://hdl.handle.net/11441/49568

DOI: 10.3390/e17052988

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