Total Jensen divergences: Definition, properties and clustering

Frank Nielsen, Richard Nock

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

    33 Citations (Scopus)

    Abstract

    We present a novel class of divergences induced by a smooth convex function called total Jensen divergences that are invariant by construction to rotations, a feature inducing a conformal factor on ordinary Jensen divergences. We analyze the relationships between this novel class of total Jensen divergences and the total Bregman divergences. We then define total Jensen centroids, analyze their robustness, and prove that the k-means++ initialization that bypasses explicit centroid computations is good enough in practice to guarantee probabilistically a constant approximation factor to the optimal k-means clustering.

    Original languageEnglish
    Title of host publication2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages2016-2020
    Number of pages5
    ISBN (Electronic)9781467369978
    DOIs
    Publication statusPublished - 4 Aug 2015
    Event40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Brisbane, Australia
    Duration: 19 Apr 201424 Apr 2014

    Publication series

    NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
    Volume2015-August
    ISSN (Print)1520-6149

    Conference

    Conference40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015
    Country/TerritoryAustralia
    CityBrisbane
    Period19/04/1424/04/14

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