Bregman Divergences from Comparative Convexity View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2017-10-24

AUTHORS

Frank Nielsen , Richard Nock

ABSTRACT

Comparative convexity is a generalization of ordinary convexity based on abstract means instead of arithmetic means. We define and study the Bregman divergences with respect to comparative convexity. As an example, we consider the convexity induced by quasi-arithmetic means, report explicit formulas, and show that those Bregman divergences are equivalent to conformal ordinary Bregman divergences on monotone embeddings. More... »

PAGES

639-647

References to SciGraph publications

  • 2016. Information Geometry and Its Applications in NONE
  • 2007-07. Bregman divergence as relative operator entropy in ACTA MATHEMATICA HUNGARICA
  • 2010-09. Bregman Voronoi Diagrams in DISCRETE & COMPUTATIONAL GEOMETRY
  • 1998-05. Lagrangian means in AEQUATIONES MATHEMATICAE
  • 2006. Convex Functions and Their Applications, A Contemporary Approach in NONE
  • Book

    TITLE

    Geometric Science of Information

    ISBN

    978-3-319-68444-4
    978-3-319-68445-1

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-68445-1_74

    DOI

    http://dx.doi.org/10.1007/978-3-319-68445-1_74

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1092381059


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