Bregman divergences from comparative convexity

Frank Nielsen*, Richard Nock

*Corresponding author for this work

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    1 Citation (Scopus)

    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.

    Original languageEnglish
    Title of host publicationGeometric Science of Information - 3rd International Conference, GSI 2017, Proceedings
    EditorsFrank Nielsen, Frederic Barbaresco, Frank Nielsen
    PublisherSpringer Verlag
    Pages639-647
    Number of pages9
    ISBN (Print)9783319684444
    DOIs
    Publication statusPublished - 2017
    Event3rd International Conference on Geometric Science of Information, GSI 2017 - Paris, France
    Duration: 7 Nov 20179 Nov 2017

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume10589 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Conference

    Conference3rd International Conference on Geometric Science of Information, GSI 2017
    Country/TerritoryFrance
    CityParis
    Period7/11/179/11/17

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