Standard Divergence in Manifold of Dual Affine Connections

28/10/2015
Publication GSI2015
OAI : oai:www.see.asso.fr:11784:14289

Résumé

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.

Standard Divergence in Manifold of Dual Affine Connections

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application/pdf Standard Divergence in Manifold of Dual Affine Connections Shun-Ichi Amari, Nihat Ay

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            <title>Standard Divergence in Manifold of Dual Affine Connections</title></titles>
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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.

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