Mardi 11 Mars 2008, salle à préciser
-
Orateur/Speaker :
Franck Nielsen, Sony CSL/Ecole Polytechnique
-
Titre/Title :
On the Centroids of Symmetrized Bregman Divergences
-
Résumé/Abstract :
In this talk, we generalize the notions of centroids and
barycenters to the broad class of information-theoretic distortion
measures called Bregman divergences. Bregman divergences are
versatile, and unify quadratic geometric distances with various
statistical entropic measures. 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. We report on our generic
implementation for computing entropic centers of image clusters and
entropic centers of multivariate normals, and compare our results with
former ad-hoc methods.
Code et Démo.
joint work with Richard Nock, CEREGMIA, University of Antilles-Guyane.