Smallest Enclosing Spheres and Chernoff Points in BregmanGeometry

Edelsbrunner, Herbert; Virk, Ziga; Wagner, Hubert

doi:10.4230/LIPIcs.SoCG.2018.35

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Smallest Enclosing Spheres and Chernoff Points in BregmanGeometry

Authors Herbert Edelsbrunner, Ziga Virk, Hubert Wagner

Part of: Volume: 34th International Symposium on Computational Geometry (SoCG 2018)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Symposium on Computational Geometry (SoCG)
License: Creative Commons Attribution 3.0 Unported license
Publication Date: 2018-06-08

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Document Identifiers

DOI: 10.4230/LIPIcs.SoCG.2018.35
URN: urn:nbn:de:0030-drops-87487

Subject Classification

Keywords

Bregman divergence
smallest enclosing spheres
Chernoff points
convexity
barycenter polytopes

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Abstract

Smallest enclosing spheres of finite point sets are central to methods in topological data analysis. Focusing on Bregman divergences to measure dissimilarity, we prove bounds on the location of the center of a smallest enclosing sphere. These bounds depend on the range of radii for which Bregman balls are convex.

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Herbert Edelsbrunner, Ziga Virk, and Hubert Wagner. Smallest Enclosing Spheres and Chernoff Points in BregmanGeometry. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 35:1-35:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.SoCG.2018.35

Author Details

Herbert Edelsbrunner

Ziga Virk

Hubert Wagner

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