A Riemannian geometry in the q-Exponential Banach manifold induced by q-Divergences
For 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-diverg...
- Autores:
-
Loaiza Ossa, Gabriel Ignacio
Quiceno Echavarría, Héctor Román
- Tipo de recurso:
- Fecha de publicación:
- 2013
- Institución:
- Universidad EAFIT
- Repositorio:
- Repositorio EAFIT
- Idioma:
- eng
- OAI Identifier:
- oai:repository.eafit.edu.co:10784/5244
- Acceso en línea:
- http://hdl.handle.net/10784/5244
- Palabra clave:
- ALGORITMOS
ESPACIOS DE BANACH
ESPACIOS VECTORIALES
TEOREMA DE BANACH
GEOMETRÍA DE RIEMANN
GEOMETRÍA DIFERENCIAL
ESPACIOS MÉTRICOS
MATEMÁTICAS
INTELIGENCIA ARTIFICIAL
PROCESAMIENTO DE IMÁGENES
Algorithms
Banach spaces
Vector spaces
Banach- theorem
Geometry, riemannian
Geometry, differential
Metric spaces
Mathematics
Artificial intelligence
Image processing
Espacios de Orlicz
- Rights
- License
- Springer-Verlag Berlin Heidelberg
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2015-04-24T16:18:33Z20132015-04-24T16:18:33Z0302-9743http://hdl.handle.net/10784/524410.1007/978-3-642-40020-9_82For 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 manifoldFor 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 manifoldengSpringer Berlin HeidelbergGeometric Science of Information Lecture Notes in Computer Science Volume 8085, 2013, pp 737-742http://dx.doi.org/10.1007/978-3-642-40020-9_82Springer-Verlag Berlin HeidelbergAcceso restringidohttp://purl.org/coar/access_right/c_16ecA Riemannian geometry in the q-Exponential Banach manifold induced by q-Divergencesarticleinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionpublishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1ALGORITMOSESPACIOS DE BANACHESPACIOS VECTORIALESTEOREMA DE BANACHGEOMETRÍA DE RIEMANNGEOMETRÍA DIFERENCIALESPACIOS MÉTRICOSMATEMÁTICASINTELIGENCIA ARTIFICIALPROCESAMIENTO DE IMÁGENESAlgorithmsBanach spacesVector spacesBanach- theoremGeometry, riemannianGeometry, differentialMetric spacesMathematicsArtificial intelligenceImage processingEspacios de OrliczUniversidad EAFIT. Escuela de Ciencias. Grupo de Investigación Análisis Funcional y AplicacionesGabriel Loaiza (gloaiza@eafit.edu.co)Héctor R. Quiceno (hquiceno@eafit.edu.co)Loaiza Ossa, Gabriel IgnacioQuiceno Echavarría, Héctor RománAnálisis Funcional y AplicacionesGeometric Science of Information Lecture Notes in Computer Science8085742737ORIGINALa_riemannian_geometry_in_the_q-exponential_banach_manifold_induced_by_q-divergences.pdfa_riemannian_geometry_in_the_q-exponential_banach_manifold_induced_by_q-divergences.pdfapplication/pdf351887https://repository.eafit.edu.co/bitstreams/b6ff3896-6413-4cd9-971f-bae2425d6ed3/download47d9c752a4949992b649a3ac711912c9MD52A Riemannian Geometry in the q-Exponential Banach Manifold Induced by q-Divergences.pdfA Riemannian Geometry in the q-Exponential Banach Manifold Induced by q-Divergences.pdfapplication/pdf140821https://repository.eafit.edu.co/bitstreams/6dca25b7-9a2c-45cf-831f-56c8000f6a81/downloadb666677b9e4d3d7c65c51f395d8fd7c8MD53LICENSElicense.txtlicense.txttext/plain; charset=utf-82556https://repository.eafit.edu.co/bitstreams/b9508ccb-bfab-402c-bbcf-5d6289aaf341/download76025f86b095439b7ac65b367055d40cMD5410784/5244oai:repository.eafit.edu.co:10784/52442021-09-24 16:44:19.306restrictedhttps://repository.eafit.edu.coRepositorio Institucional Universidad EAFITrepositorio@eafit.edu.co |
| dc.title.eng.fl_str_mv |
A Riemannian geometry in the q-Exponential Banach manifold induced by q-Divergences |
| title |
A Riemannian geometry in the q-Exponential Banach manifold induced by q-Divergences |
| spellingShingle |
A Riemannian geometry in the q-Exponential Banach manifold induced by q-Divergences ALGORITMOS ESPACIOS DE BANACH ESPACIOS VECTORIALES TEOREMA DE BANACH GEOMETRÍA DE RIEMANN GEOMETRÍA DIFERENCIAL ESPACIOS MÉTRICOS MATEMÁTICAS INTELIGENCIA ARTIFICIAL PROCESAMIENTO DE IMÁGENES Algorithms Banach spaces Vector spaces Banach- theorem Geometry, riemannian Geometry, differential Metric spaces Mathematics Artificial intelligence Image processing Espacios de Orlicz |
| title_short |
A Riemannian geometry in the q-Exponential Banach manifold induced by q-Divergences |
| title_full |
A Riemannian geometry in the q-Exponential Banach manifold induced by q-Divergences |
| title_fullStr |
A Riemannian geometry in the q-Exponential Banach manifold induced by q-Divergences |
| title_full_unstemmed |
A Riemannian geometry in the q-Exponential Banach manifold induced by q-Divergences |
| title_sort |
A Riemannian geometry in the q-Exponential Banach manifold induced by q-Divergences |
| dc.creator.fl_str_mv |
Loaiza Ossa, Gabriel Ignacio Quiceno Echavarría, Héctor Román |
| dc.contributor.department.none.fl_str_mv |
Universidad EAFIT. Escuela de Ciencias. Grupo de Investigación Análisis Funcional y Aplicaciones |
| dc.contributor.eafitauthor.spa.fl_str_mv |
Gabriel Loaiza (gloaiza@eafit.edu.co) Héctor R. Quiceno (hquiceno@eafit.edu.co) |
| dc.contributor.author.none.fl_str_mv |
Loaiza Ossa, Gabriel Ignacio Quiceno Echavarría, Héctor Román |
| dc.contributor.researchgroup.spa.fl_str_mv |
Análisis Funcional y Aplicaciones |
| dc.subject.lemb.spa.fl_str_mv |
ALGORITMOS ESPACIOS DE BANACH ESPACIOS VECTORIALES TEOREMA DE BANACH GEOMETRÍA DE RIEMANN GEOMETRÍA DIFERENCIAL ESPACIOS MÉTRICOS MATEMÁTICAS INTELIGENCIA ARTIFICIAL PROCESAMIENTO DE IMÁGENES |
| topic |
ALGORITMOS ESPACIOS DE BANACH ESPACIOS VECTORIALES TEOREMA DE BANACH GEOMETRÍA DE RIEMANN GEOMETRÍA DIFERENCIAL ESPACIOS MÉTRICOS MATEMÁTICAS INTELIGENCIA ARTIFICIAL PROCESAMIENTO DE IMÁGENES Algorithms Banach spaces Vector spaces Banach- theorem Geometry, riemannian Geometry, differential Metric spaces Mathematics Artificial intelligence Image processing Espacios de Orlicz |
| dc.subject.keyword.eng.fl_str_mv |
Algorithms Banach spaces Vector spaces Banach- theorem Geometry, riemannian Geometry, differential Metric spaces Mathematics Artificial intelligence Image processing |
| dc.subject.keyword.spa.fl_str_mv |
Espacios de Orlicz |
| description |
For 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 |
| publishDate |
2013 |
| dc.date.issued.none.fl_str_mv |
2013 |
| dc.date.available.none.fl_str_mv |
2015-04-24T16:18:33Z |
| dc.date.accessioned.none.fl_str_mv |
2015-04-24T16:18:33Z |
| dc.type.eng.fl_str_mv |
article info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion publishedVersion |
| dc.type.coarversion.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
| dc.type.coar.fl_str_mv |
http://purl.org/coar/resource_type/c_6501 http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.type.local.spa.fl_str_mv |
Artículo |
| status_str |
publishedVersion |
| dc.identifier.issn.spa.fl_str_mv |
0302-9743 |
| dc.identifier.uri.none.fl_str_mv |
http://hdl.handle.net/10784/5244 |
| dc.identifier.doi.none.fl_str_mv |
10.1007/978-3-642-40020-9_82 |
| identifier_str_mv |
0302-9743 10.1007/978-3-642-40020-9_82 |
| url |
http://hdl.handle.net/10784/5244 |
| dc.language.iso.eng.fl_str_mv |
eng |
| language |
eng |
| dc.relation.ispartof.spa.fl_str_mv |
Geometric Science of Information Lecture Notes in Computer Science Volume 8085, 2013, pp 737-742 |
| dc.relation.uri.none.fl_str_mv |
http://dx.doi.org/10.1007/978-3-642-40020-9_82 |
| dc.rights.spa.fl_str_mv |
Springer-Verlag Berlin Heidelberg |
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http://purl.org/coar/access_right/c_16ec |
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Acceso restringido |
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Springer-Verlag Berlin Heidelberg Acceso restringido http://purl.org/coar/access_right/c_16ec |
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Springer Berlin Heidelberg |
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Universidad EAFIT |
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