Abstract
A divergence function defines a Riemannian metric G and dually coupled affine connections \(\left( \nabla , \nabla ^{*}\right) \) with respect to it in a manifold M. When M is dually flat, a canonical divergence is known, which is uniquely determined from \(\left\{ G, \nabla , \nabla ^{*}\right\} \). We search for a standard divergence for a general non-flat M. It is introduced by the magnitude of the inverse exponential map, where \(\alpha =-(1/3)\) connection plays a fundamental role. The standard divergence is different from the canonical divergence.
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Amari, Si., Ay, N. (2015). Standard Divergence in Manifold of Dual Affine Connections. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_35
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DOI: https://doi.org/10.1007/978-3-319-25040-3_35
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