Standard Divergence in Manifold of Dual Affine Connections
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last edited by Geo-Sci-InfoAuthor(s): Nihat Ay, Shun-Ichi Amari
DOI URL: http://dx.doi.org/10.1007/978-3-319-25040-3_35
Video: http://www.youtube.com/watch?v=Pu8M9Fu7_fM
Slides: Amari_standard divergence.pdf
Presentation: https://www.see.asso.fr/node/14289
Creative Commons Attribution-ShareAlike 4.0 InternationalAbstract:
A divergence function defines a Riemannian metric G and dually coupled affine connections (∇, ∇ ∗ ) with respect to it in a manifold M. When M is dually flat, a canonical divergence is known, which is uniquely determined from {G, ∇, ∇ ∗ }. We search for a standard divergence for a general non-flat M. It is introduced by the magnitude of the inverse exponential map, where α = -(1/3) connection plays a fundamental role. The standard divergence is different from the canonical divergence.
