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Titlebook: Geometric Structures of Information; Frank Nielsen Book 2019 Springer Nature Switzerland AG 2019 Hessian Information Geometry.Shape Space.

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樓主
發(fā)表于 2025-3-21 18:28:07 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Geometric Structures of Information
編輯Frank Nielsen
視頻videohttp://file.papertrans.cn/384/383613/383613.mp4
概述Features new and fruitful interactions between several branches of science: information science, mathematics and physics.Addresses interrelations between different mathematical domains like shape spac
叢書名稱Signals and Communication Technology
圖書封面Titlebook: Geometric Structures of Information;  Frank Nielsen Book 2019 Springer Nature Switzerland AG 2019 Hessian Information Geometry.Shape Space.
描述.This book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different mathematical domains like shape spaces, probability/optimization & algorithms on manifolds, relational and discrete metric spaces, computational and Hessian information geometry, algebraic/infinite dimensional/Banach information manifolds, divergence geometry, tensor-valued morphology, optimal transport theory, manifold & topology learning, and applications like geometries of audio-processing, inverse problems and signal processing...The book collects the most important contributions to the conference GSI’2017 – Geometric Science of Information..
出版日期Book 2019
關(guān)鍵詞Hessian Information Geometry; Shape Space; Monotone Embedding; Stochastic Geometric Mechanics; Riemannia
版次1
doihttps://doi.org/10.1007/978-3-030-02520-5
isbn_ebook978-3-030-02520-5Series ISSN 1860-4862 Series E-ISSN 1860-4870
issn_series 1860-4862
copyrightSpringer Nature Switzerland AG 2019
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沙發(fā)
發(fā)表于 2025-3-21 21:35:17 | 只看該作者
1860-4862 tions between different mathematical domains like shape spac.This book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. I
板凳
發(fā)表于 2025-3-22 04:13:37 | 只看該作者
,Metrische Dualit?t in der isotropen Ebene,characteristic Function, Koszul Forms, and affine representation of Lie Algebra and Lie Group. The 2nd Koszul form is an extension of classical Fisher metric. Koszul theory of hessian structures and Koszul forms could be considered as main foundation and pillars of Information Geometry.
地板
發(fā)表于 2025-3-22 04:52:16 | 只看該作者
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發(fā)表于 2025-3-22 12:15:24 | 只看該作者
Models of Body Image for Boys and Mene coordinates. Finally, we demonstrate applications of the flattening to nonextensive statistical physics, Voronoi partitions and weighted centroids on the probability simplex with respect to ., which are not necessarily of Bregman type.
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發(fā)表于 2025-3-22 13:53:14 | 只看該作者
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發(fā)表于 2025-3-22 19:57:32 | 只看該作者
Conformal Flattening on the Probability Simplex and Its Applications to Voronoi Partitions and Cente coordinates. Finally, we demonstrate applications of the flattening to nonextensive statistical physics, Voronoi partitions and weighted centroids on the probability simplex with respect to ., which are not necessarily of Bregman type.
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發(fā)表于 2025-3-22 23:03:57 | 只看該作者
Some Universal Insights on Divergences for Statistics, Machine Learning and Artificial Intelligenceg. Furthermore, we discuss some specificalities, subtleties as well as pitfalls when e.g. one “moves away” from the probability context. Several subcases and examples are given, including a new approach to obtain parameter estimators in continuous models which is based on noisy divergence minimization.
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發(fā)表于 2025-3-23 04:06:27 | 只看該作者
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發(fā)表于 2025-3-23 08:00:18 | 只看該作者
Temperaturbeanspruchte Scheiben und Platten,m classical information theory generalize to this setting. Moreover, viewing the Fourier transform for noncommutative unimodular Lie groups as a matrix-valued function, relationships between trace inequalities, diffusion processes, and convolution are examined.
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