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-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

• Autores: Loaiza Ossa, Gabriel Ignacio; Quiceno Echavarría, Héctor Román
• 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
• License: Springer-Verlag Berlin Heidelberg