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, 2019 This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry.
Verdoolaege, Geert
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Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems [PDF]
Entropy, 2021 Information theory provides an interdisciplinary method to understand important phenomena in many research fields ranging from astrophysical and laboratory fluids/plasmas to biological systems.
Eun-jin Kim
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Information Geometry of Nonlinear Stochastic Systems [PDF]
Entropy, 2018 We elucidate the effect of different deterministic nonlinear forces on geometric structure of stochastic processes by investigating the transient relaxation of initial PDFs of a stochastic variable x under forces proportional to -xn (n=3,5,7) and ...
Rainer Hollerbach +2 more
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Connecting Information Geometry and Geometric Mechanics [PDF]
Entropy, 2017 The divergence function in information geometry, and the discrete Lagrangian in discrete geometric mechanics each induce a differential geometric structure on the product manifold Q × Q .
Melvin Leok, Jun Zhang
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Information Geometry for the Working Information Theorist [PDF]
CoRR, 2023 12 pages, 3 figures, 1 ...
Kumar Vijay Mishra +2 more
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Categorical Information Geometry [PDF]
, 2023 Information geometry is the study of interactions between random variables by means of metric, divergences, and their geometry. Categorical probability has a similar aim, but uses algebraic structures, primarily monoidal categories, for that purpose.
Perrone, Paolo
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Information Geometry for Covariance Estimation in Heterogeneous Clutter with Total Bregman Divergence [PDF]
Entropy, 2018 This paper presents a covariance matrix estimation method based on information geometry in a heterogeneous clutter. In particular, the problem of covariance estimation is reformulated as the computation of geometric median for covariance matrices ...
Xiaoqiang Hua +3 more
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Information Geometry of κ-Exponential Families: Dually-Flat, Hessian and Legendre Structures [PDF]
Entropy, 2018 In this paper, we present a review of recent developments on the κ -deformed statistical mechanics in the framework of the information geometry.
Antonio M. Scarfone +2 more
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Information Geometry of Randomized Quantum State Tomography [PDF]
Entropy, 2018 Suppose that a d-dimensional Hilbert space H ≃ C d admits a full set of mutually unbiased bases | 1 ( a ) 〉 , ⋯ , | d ( a ) 〉 , where a = 1 , ⋯ , d + 1 .
Akio Fujiwara, Koichi Yamagata
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Capturing Outlines of Planar Generic Images by Simultaneous Curve Fitting and Sub-division [PDF]
Journal of Artificial Intelligence and Data Mining, 2020 In this paper, a new technique has been designed to capture the outline of 2D shapes using cubic B´ezier curves. The proposed technique avoids the traditional method of optimizing the global squared fitting error and emphasizes the local control of data ...
A.R. Ebrahimi +2 more
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