Smallest Enclosing Spheres and Chernoff Points in BregmanGeometry

Authors Herbert Edelsbrunner, Ziga Virk, Hubert Wagner

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Herbert Edelsbrunner
Ziga Virk
Hubert Wagner

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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)


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.
  • Bregman divergence
  • smallest enclosing spheres
  • Chernoff points
  • convexity
  • barycenter polytopes


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