A Riemannian geometry in the q-Exponential Banach manifold induced by q-Divergences

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dc.citation.epage737spa
dc.citation.journalTitleGeometric Science of Information Lecture Notes in Computer Sciencespa
dc.citation.spage742spa
dc.citation.volume8085spa
dc.contributor.authorLoaiza Ossa, Gabriel Ignacio
dc.contributor.authorQuiceno Echavarría, Héctor Román
dc.contributor.departmentUniversidad EAFIT. Escuela de Ciencias. Grupo de Investigación Análisis Funcional y Aplicaciones
dc.contributor.eafitauthorGabriel Loaiza (gloaiza@eafit.edu.co)spa
dc.contributor.eafitauthorHéctor R. Quiceno (hquiceno@eafit.edu.co)spa
dc.contributor.researchgroupAnálisis Funcional y Aplicacionesspa
dc.date.accessioned2015-04-24T16:18:33Z
dc.date.available2015-04-24T16:18:33Z
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 manifoldspa
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 manifoldeng
dc.identifier.doi10.1007/978-3-642-40020-9_82
dc.identifier.issn0302-9743spa
dc.identifier.urihttp://hdl.handle.net/10784/5244
dc.language.isoengeng
dc.publisherSpringer Berlin Heidelbergspa
dc.relation.ispartofGeometric Science of Information Lecture Notes in Computer Science Volume 8085, 2013, pp 737-742spa
dc.relation.urihttp://dx.doi.org/10.1007/978-3-642-40020-9_82
dc.rightsSpringer-Verlag Berlin Heidelbergspa
dc.rights.accessrightsinfo:eu-repo/semantics/restrictedAccessspa
dc.rights.localAcceso restringidospa
dc.subject.keywordAlgorithmseng
dc.subject.keywordBanach spaceseng
dc.subject.keywordVector spaceseng
dc.subject.keywordBanach- theoremeng
dc.subject.keywordGeometry, riemannianeng
dc.subject.keywordGeometry, differentialeng
dc.subject.keywordMetric spaceseng
dc.subject.keywordMathematicseng
dc.subject.keywordArtificial intelligenceeng
dc.subject.keywordImage processingeng
dc.subject.keywordEspacios de Orliczspa
dc.subject.lembALGORITMOSspa
dc.subject.lembESPACIOS DE BANACHspa
dc.subject.lembESPACIOS VECTORIALESspa
dc.subject.lembTEOREMA DE BANACHspa
dc.subject.lembGEOMETRÍA DE RIEMANNspa
dc.subject.lembGEOMETRÍA DIFERENCIALspa
dc.subject.lembESPACIOS MÉTRICOSspa
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.typearticleeng
dc.typeinfo:eu-repo/semantics/articleeng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localArtículospa

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