dc.creator | Cichocki, Andrzej | es |
dc.creator | Cruces Álvarez, Sergio Antonio | es |
dc.creator | Amari, Shun-ichi | es |
dc.date.accessioned | 2016-12-01T15:13:40Z | |
dc.date.available | 2016-12-01T15:13:40Z | |
dc.date.issued | 2015-05-08 | |
dc.identifier.citation | 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. | |
dc.identifier.issn | 1099-4300 | es |
dc.identifier.uri | http://hdl.handle.net/11441/49568 | |
dc.description.abstract | 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. | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.publisher | MDPI | es |
dc.relation.ispartof | Entropy, 17 (5), 2988-3034. | es |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Similarity measures | es |
dc.subject | Generalized divergences for symmetric positive definite (covariance) matrices | es |
dc.subject | Stein’s loss | es |
dc.subject | Burg’s matrix divergence | es |
dc.subject | Affine Invariant Riemannian Metric (AIRM) | es |
dc.subject | Riemannian metric | es |
dc.subject | Geodesic distance | es |
dc.subject | Jensen-Bregman LogDet (JBLD) | es |
dc.subject | S-divergence | es |
dc.subject | LogDet Zero divergence | es |
dc.subject | Jeffrey’s KL divergence | es |
dc.subject | Symmetrized KL Divergence Metric (KLDM) | es |
dc.subject | Alpha-Beta Log-Det divergences | es |
dc.subject | Gamma divergences | es |
dc.subject | Hilbert projective metric and their extensions | es |
dc.title | Log-Determinant Divergences Revisited: Alpha-Beta and Gamma Log-Det Divergences | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/publishedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Teoría de la Señal y Comunicaciones | es |
dc.relation.publisherversion | http://dx.doi.org/10.3390/e17052988 | es |
dc.identifier.doi | 10.3390/e17052988 | es |
idus.format.extent | 47 p. | es |
dc.journaltitle | Entropy | es |
dc.publication.volumen | 17 | es |
dc.publication.issue | 5 | es |
dc.publication.initialPage | 2988 | es |
dc.publication.endPage | 3034 | es |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/49568 | |