Nonnegative Matrix Factorization with Zellner Penalty

TL;DR

This paper introduces Zellner NMF, a novel data-dependent constraint method for nonnegative matrix factorization, and evaluates its effectiveness in facial recognition tasks using the Cambridge ORL database.

Contribution

The paper proposes Zellner NMF, the first to incorporate data-dependent penalties into NMF, enhancing its task-specific flexibility and performance.

Findings

ZNMF improves facial recognition accuracy

Data-dependent constraints outperform traditional methods

Enhanced flexibility in NMF models

Abstract

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.