Bregman divergences and triangle inequality

Sreangsu Acharyya, Arindam Banerjee, Daniel L Boley

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

While Bregman divergences have been used for clustering and embedding problems in recent years, the facts that they are asymmetric and do not satisfy triangle inequality have been a major concern. In this paper, we investigate the relationship between two families of symmetrized Bregman divergences and metrics that satisfy the triangle inequality. The first family can be derived from any well-behaved convex function. The second family generalizes the Jensen-Shannon divergence, and can only be derived from convex functions with certain conditional positive defmiteness structure. We interpret the required structure in terms of cumulant s of infinitely divisible distributions, and related results in harmonic analysis. We investigate kmeans-type clustering problems using both families of symmetrized divergences, and give efficient algorithms for the same.

Original languageEnglish (US)
Title of host publicationSIAM International Conference on Data Mining 2013, SMD 2013
PublisherSociety for Industrial and Applied Mathematics Publications
Pages476-484
Number of pages9
ISBN (Electronic)9781627487245
StatePublished - Jan 1 2013
Event13th SIAM International Conference on Data Mining, SMD 2013 - Austin, United States
Duration: May 2 2013May 4 2013

Publication series

NameSIAM International Conference on Data Mining 2013, SMD 2013

Other

Other13th SIAM International Conference on Data Mining, SMD 2013
Country/TerritoryUnited States
CityAustin
Period5/2/135/4/13

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