A Riemannian Geometry in the q-Exponential Banach Manifold Induced by q-Divergences

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dc.contributor.authorLoaiza Ossa, Gabriel Ignacio
dc.contributor.authorQuiceno Echavarría, Héctor Román
dc.contributor.departmentUniversidad EAFIT. Departamento de Ciencias
dc.contributor.researchgroupAnálisis Funcional y Aplicacionesspa
dc.date.accessioned2015-10-02T21:53:07Z
dc.date.available2015-10-02T21:53:07Z
dc.date.issued2013
dc.description.abstractFor the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built. In this paper, the geometry induced on this manifold is characterized by q-divergence functionals. This geometry turns out to be a generalization of the geometry given by Fisher information metric and Levi-Civita connections. Moreover, the classical Amari’s α-connections appears as special case of the q −connections ∇ (q). The main result is the expected one, namely the zero curvature of the manifold. Loading... Geometric Science of InformationGeometric Science of Information Look Inside Chapter Metrics Downloads1K Provided by Bookmetrix Other actions Export citation About this Book Reprints and Permissions Add to Papers Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIneng
dc.identifier.doi10.1007/978-3-642-40020-9_82
dc.identifier.urihttp://hdl.handle.net/10784/7411
dc.language.isoengeng
dc.publisherSpringer Berlin Heidelberg
dc.relation.ispartofGeometric Science of Information. First International Conference, GSI 2013, Paris, France, August 28-30, 2013. Proceedings, pp 737-742spa
dc.relation.ispartofseriesLecture Notes in Computer Sciencespa
dc.relation.isversionofhttp://dx.doi.org/10.1007/978-3-642-40020-9_82spa
dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.rights.localAcceso abiertospa
dc.subject.keywordAlgorithmseng
dc.subject.keywordBanach spaceseng
dc.subject.keywordGeometry, riemannianeng
dc.subject.keywordMetric spaceseng
dc.subject.keywordMathematicseng
dc.subject.keywordArtificial intelligenceeng
dc.subject.keywordImage processingeng
dc.subject.keywordEspacios de Orliczspa
dc.subject.lembESPACIOS DE BANACHspa
dc.subject.lembESPACIOS VECTORIALESspa
dc.subject.lembTEOREMA DE BANACHspa
dc.subject.lembGEOMETRÍA DIFERENCIALspa
dc.subject.lembESPACIOS MÉTRICOSspa
dc.subject.lembALGORITMOSspa
dc.subject.lembMATEMÁTICASspa
dc.subject.lembINTELIGENCIA ARTIFICIALspa
dc.subject.lembPROCESAMIENTO DE IMÁGENESspa
dc.titleA Riemannian Geometry in the q-Exponential Banach Manifold Induced by q-Divergenceseng
dc.typeinfo:eu-repo/semantics/conferencePapereng
dc.typeconferencePapereng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localDocumento de conferenciaspa

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