Beta-divergence as a subclass of Bregman divergence

Romain Hennequin (1) , Bertrand David (1) , Roland Badeau (1)

1 LTCI - Laboratoire Traitement et Communication de l'Information

In this paper, we present a complete proof that the beta-divergence is a particular case of Bregman divergence. This little-known result makes it possible to straightforwardly apply theorems about Bregman divergences to beta-divergences. This is of interest for numerous applications since these divergences are widely used, for instance in non-negative matrix factorization (NMF).

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Romain Hennequin, Bertrand David, Roland Badeau. Beta-divergence as a subclass of Bregman divergence. IEEE Signal Processing Letters, 2011, 18 (2), pp.83--86. ⟨hal-00945202⟩