Nonnegative Matrix Factorization with Zellner Penalty
This work provides an incremental improvement to NMF algorithms for researchers and practitioners working on parts-based data decomposition, particularly in applications like facial recognition.
This paper introduces Zellner Nonnegative Matrix Factorization (ZNMF), a new variant of NMF that incorporates data-dependent auxiliary constraints. The authors evaluate ZNMF's performance for facial recognition on the Cambridge ORL database, comparing it against other constrained NMF algorithms.
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.