  The Bregman divergence have been the subject of several studies. We do not go
to do an exhaustive study of its subclasses, but propose a proof that shows
that the \b{eta}-divergence are subclasses of the Bregman divergences. It is in
this order of idea that we will make a proposition of demonstration which shows
that the \b{eta}-divergence are particular cases of the Bregman divergence. And
also we will propose algorithms and their applications to show the consistency
of our approach. This is of interest for numerous applications since these
divergences are widely used for instant non-negative matrix factorization
(NMF).
