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dc.creatorCichocki, Andrzejes
dc.creatorCruces Álvarez, Sergio Antonioes
dc.creatorAmari, Shun-ichies
dc.date.accessioned2016-12-01T15:13:40Z
dc.date.available2016-12-01T15:13:40Z
dc.date.issued2015-05-08
dc.identifier.citationCichocki, 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.issn1099-4300es
dc.identifier.urihttp://hdl.handle.net/11441/49568
dc.description.abstractThis 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.formatapplication/pdfes
dc.language.isoenges
dc.publisherMDPIes
dc.relation.ispartofEntropy, 17 (5), 2988-3034.es
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectSimilarity measureses
dc.subjectGeneralized divergences for symmetric positive definite (covariance) matriceses
dc.subjectStein’s losses
dc.subjectBurg’s matrix divergencees
dc.subjectAffine Invariant Riemannian Metric (AIRM)es
dc.subjectRiemannian metrices
dc.subjectGeodesic distancees
dc.subjectJensen-Bregman LogDet (JBLD)es
dc.subjectS-divergencees
dc.subjectLogDet Zero divergencees
dc.subjectJeffrey’s KL divergencees
dc.subjectSymmetrized KL Divergence Metric (KLDM)es
dc.subjectAlpha-Beta Log-Det divergenceses
dc.subjectGamma divergenceses
dc.subjectHilbert projective metric and their extensionses
dc.titleLog-Determinant Divergences Revisited: Alpha-Beta and Gamma Log-Det Divergenceses
dc.typeinfo:eu-repo/semantics/articlees
dcterms.identifierhttps://ror.org/03yxnpp24
dc.type.versioninfo:eu-repo/semantics/publishedVersiones
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses
dc.contributor.affiliationUniversidad de Sevilla. Departamento de Teoría de la Señal y Comunicacioneses
dc.relation.publisherversionhttp://dx.doi.org/10.3390/e17052988es
dc.identifier.doi10.3390/e17052988es
idus.format.extent47 p.es
dc.journaltitleEntropyes
dc.publication.volumen17es
dc.publication.issue5es
dc.publication.initialPage2988es
dc.publication.endPage3034es
dc.identifier.idushttps://idus.us.es/xmlui/handle/11441/49568

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Attribution-NonCommercial-NoDerivatives 4.0 Internacional
Except where otherwise noted, this item's license is described as: Attribution-NonCommercial-NoDerivatives 4.0 Internacional