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 definiteness structure. We interpret the required structure in terms of cumulants 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 language||English (US)|
|Title of host publication||Proceedings of the 2013 SIAM International Conference on Data Mining, SDM 2013|
|Editors||Joydeep Ghosh, Zoran Obradovic, Jennifer Dy, Zhi-Hua Zhou, Chandrika Kamath, Srinivasan Parthasarathy|
|Number of pages||9|
|State||Published - 2013|
|Event||SIAM International Conference on Data Mining, SDM 2013 - Austin, United States|
Duration: May 2 2013 → May 4 2013
|Name||Proceedings of the 2013 SIAM International Conference on Data Mining, SDM 2013|
|Other||SIAM International Conference on Data Mining, SDM 2013|
|Period||5/2/13 → 5/4/13|
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