Computational Information Geometry Wonderland

ICASSP [web] is currently being held in Pragues. Olivier is presenting a poster on our experiments of clustering with alpha-divergences. It is well-known that f-divergences are the invariant statistical divergences [by reparameterization with sufficient statistics or monotonous embedding]. Kullback-Leibler yields flat geometry [equivalent to Bregman divergence for exponential families], and alpha-divergences (although flat on positive measure spaces) are canonical information-geometric divergences for constant curvature curved spaces. We carried out a series of experiments to investigate the choice of alpha in practice. See paper . It was first investigation, and we still get our hands on...

Frank.

In this note alphadivergencemeans.pdf, we summarize the following work

• Shun-ichi Amari, Integration of Stochastic Models by Minimizing \alpha-Divergence, Neural Computation (NECO), (19)10:2780-2796, October 2007.

• F. Nielsen and R. Nock, The dual Voronoi diagrams with respect to representational Bregman divergences, International Symposium on Voronoi Diagrams (ISVD), June 2009.

• F. Nielsen and R. Nock, Sided and Symmetrized Bregman Centroids, IEEE transactions on information theory (2009), vol. 55, no. 6, pp. 2882-2904