Conformal Flattening on the Probability Simplex and Its Applications to Voronoi Partitions and Centroids

DOI10.1007/978-3-030-02520-5_4zbMath1418.53011OpenAlexW2901861155MaRDI QIDQ4967755

Atsumi Ohara

Publication date: 10 July 2019

Published in: Geometric Structures of Information (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-02520-5_4

zbMATH Keywords

affine differential geometryescort probabilitygeometric divergenceconformal flatteningconformal divergence

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Statistical aspects of information-theoretic topics (62B10) Affine differential geometry (53A15)

Cites Work

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• \(F\)-geometry and Amari's \(\alpha\)-geometry on a statistical manifold
• Geometry of distributions associated with Tsallis statistics and properties of relative entropy minimization
• Voronoi diagrams and arrangements
• Geometry of minimum contrast
• An optimal convex hull algorithm in any fixed dimension
• On the divergence of 1-conformally flat statistical manifolds
• Differential-geometrical methods in statistics
• On Conformal Divergences and Their Population Minimizers
• Introduction to Nonextensive Statistical Mechanics
• CONTINUITY OF A CLASS OF ENTROPIES AND RELATIVE ENTROPIES
• Divergence Function, Duality, and Convex Analysis
• CONFORMAL GEOMETRY OF ESCORT PROBABILITY AND ITS APPLICATIONS
• Bregman Voronoi diagrams

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