Geometric Science of Information: First International by Shun-ichi Amari (auth.), Frank Nielsen, Frédéric Barbaresco

By Shun-ichi Amari (auth.), Frank Nielsen, Frédéric Barbaresco (eds.)

This booklet constitutes the refereed lawsuits of the 1st overseas convention on Geometric technology of data, GSI 2013, held in Paris, France, in August 2013. The approximately a hundred papers awarded have been conscientiously reviewed and chosen from quite a few submissions and are equipped into the next thematic classes: Geometric information on Manifolds and Lie teams, Deformations healthy areas, Differential Geometry in sign Processing, Relational Metric, Discrete Metric areas, Computational info Geometry, Hessian details Geometry I and II, Computational facets of knowledge Geometry in records, Optimization on Matrix Manifolds, optimum delivery concept, chance on Manifolds, Divergence Geometry and Ancillarity, Entropic Geometry, Tensor-Valued Mathematical Morphology, Machine/Manifold/Topology studying, Geometry of Audio Processing, Geometry of Inverse difficulties, Algebraic/Infinite dimensional/Banach details Manifolds, details Geometry Manifolds, and Algorithms on Manifolds.

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Geometric Science of Information: First International Conference, GSI 2013, Paris, France, August 28-30, 2013. Proceedings

This ebook constitutes the refereed complaints of the 1st overseas convention on Geometric technological know-how of data, GSI 2013, held in Paris, France, in August 2013. The approximately a hundred papers offered have been conscientiously reviewed and chosen from quite a few submissions and are geared up into the next thematic classes: Geometric facts on Manifolds and Lie teams, Deformations suit areas, Differential Geometry in sign Processing, Relational Metric, Discrete Metric areas, Computational info Geometry, Hessian details Geometry I and II, Computational features of knowledge Geometry in facts, Optimization on Matrix Manifolds, optimum shipping idea, chance on Manifolds, Divergence Geometry and Ancillarity, Entropic Geometry, Tensor-Valued Mathematical Morphology, Machine/Manifold/Topology studying, Geometry of Audio Processing, Geometry of Inverse difficulties, Algebraic/Infinite dimensional/Banach details Manifolds, info Geometry Manifolds, and Algorithms on Manifolds.

Extra info for Geometric Science of Information: First International Conference, GSI 2013, Paris, France, August 28-30, 2013. Proceedings

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Definition 4. We define two one-to-one mappings: the parameterization or patch ep : Sp → E (p), ep (u) = eu−Kp (u) · p and the chart sp : E (p) → Sp , sp (q) = log (f racqp) − Ep log q p . Proposition 6. If p1 , p2 ∈ E (p), then the transition mapping sp2 ◦ ep1 : Sp1 → Sp2 is the restriction of an affine function from Bp1 → Bp2 u → u + log p1 p2 − Ep2 u + log p1 p2 . The derivative of the transition map sp2 ◦ ep1 is the isomorphism of Bp1 onto Bp2 Bp1 u → u − Ep2 [u] = e Upp21 ∈ Bp2 . Definition 5. The exponential manifold is defined by the atlas of charts in Def.

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