Bregman sided and symmetrized centroids

@article{Nielsen2008BregmanSA,
  title={Bregman sided and symmetrized centroids},
  author={Frank Nielsen and Richard Nock},
  journal={2008 19th International Conference on Pattern Recognition},
  year={2008},
  pages={1-4}
}
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… CONTINUE READING

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