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.

**Read or Download Geometric Science of Information: First International Conference, GSI 2013, Paris, France, August 28-30, 2013. Proceedings PDF**

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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.

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

**Sample text**

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.

Statistical mechanics in the context of special relativity. ii. Phys. Rev. E 72(3), 036108 (2005) 61. : An inﬁnite-dimensional statistical manifold modelled on Hilbert space. J. Funct. Anal. 263(6), 1661–1681 (2012) 62. : On the φ-family of probability distributions. Journal of Theoretical Probability (2011) (online ﬁrst) 63. : On real Hilbertian info-manifolds. In: Disordered and Complex Systems (London, 2000). AIP Conf. Proc. Amer. Inst. , Melville, NY, vol. 553, pp. 153–158 (2001) 64. : Tubular modelling approach to statistical method for observational studies.

Ann. Inst. Statist. Math. 59(1), 27–56 (2007) 34 G. Pistone 12. : An information geometry perspective on estimation of distribution algorithms: boundary analysis. In: GECCO 2008: Proceedings of the 2008 GECCO Conference Companion on Genetic and Evolutionary Computation, pp. 2081–2088. ACM, New York (2008) 13. : Exponential models and Fisher information. Geometry and applications. PhD thesis, DIMAT Politecnico di Torino (2008) 14. : Projecting the Fokker-Planck equation onto a ﬁnite dimensional exponential family.