Smallest enclosing spheres and Chernoff points in Bregman geometry Conference Paper


Author(s): Edelsbrunner, Herbert; Virk, Žiga; Wagner, Hubert
Title: Smallest enclosing spheres and Chernoff points in Bregman geometry
Title Series: Leibniz International Proceedings in Information, LIPIcs
Affiliation IST Austria
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.
Keywords: spheres; topology; computational geometry; topological data analysis; polytopes; Convexity; Bregman divergence; Bregman divergences; Barycenter polytopes; Chernoff points; Smallest enclosing spheres; Bregman; Finite point sets
Conference Title: SoCG: Symposium on Computational Geometry
Volume: 99
Conference Dates: June 11 - 14, 2018
Conference Location: Budapest, Hungary
ISBN: 18688969 (ISSN); 9783959770668 (ISBN)
Publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik  
Date Published: 2018-06-11
Start Page: 351
End Page: 3513
Sponsor: This research is partially supported by the Office of Naval Research, through grant no. N62909-18-1-2038, and the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fu
DOI: 10.4230/LIPIcs.SoCG.2018.35
Open access: yes (OA journal)
IST Austria Authors
  1. Hubert Wagner
    6 Wagner
  2. Žiga Virk
    3 Virk
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