  Nonnegative matrix factorization (NMF) is a relatively new unsupervised
learning algorithm that decomposes a nonnegative data matrix into a
parts-based, lower dimensional, linear representation of the data. NMF has
applications in image processing, text mining, recommendation systems and a
variety of other fields. Since its inception, the NMF algorithm has been
modified and explored by numerous authors. One such modification involves the
addition of auxiliary constraints to the objective function of the
factorization. The purpose of these auxiliary constraints is to impose
task-specific penalties or restrictions on the objective function. Though many
auxiliary constraints have been studied, none have made use of data-dependent
penalties. In this paper, we propose Zellner nonnegative matrix factorization
(ZNMF), which uses data-dependent auxiliary constraints. We assess the facial
recognition performance of the ZNMF algorithm and several other well-known
constrained NMF algorithms using the Cambridge ORL database.
