@inproceedings{2008-C-BregmanCentroids-ICPR
, author={Frank Nielsen and Richard Nock}
, title={Bregman sided and symmetrized centroids}
, booktitle={International Conference on Pattern Recognition (ICPR)}
, month={December}
, year={2008}
, pages={1-4}
, address={Tampa, Florida, USA}
, doi={10.1109/ICPR.2008.4761794}
, abstract={We generalize the notions of centroids and barycenters to the broad class of information-theoretic
 distortion measures called Bregman divergences. Because Bregman divergences are
 typically asymmetric, we consider both the left-sided and right-sided centroids
 and the symmetrized centroids, and prove that all three are unique. We give closed-form
 solutions for the sided centroids that are generalized means, and design a provably
 fast and efficient approximation algorithm for the symmetrized centroid based on
 its exact geometric characterization that requires solely to walk on the geodesic
 linking the two sided centroids. }
}