Two Efficient Algorithms for Orthogonal Nonnegative Matrix Factorization

Jing Wu,Tao Han,Bin Chen,Predrag S Stanimirović

doi:10.1155/2021/8490147

Abstract

Nonnegative matrix factorization (NMF) is a popular method for the multivariate analysis of nonnegative data. It involves decomposing a data matrix into a product of two factor matrices with all entries restricted to being nonnegative. Orthogonal nonnegative matrix factorization (ONMF) has been introduced recently. This method has demonstrated remarkable performance in clustering tasks, such as gene expression classification. In this study, we introduce two convergence methods for solving ONMF. First, we design a convergent orthogonal algorithm based on the Lagrange multiplier method. Second, we propose an approach that is based on the alternating direction method. Finally, we demonstrate that the two proposed approaches tend to deliver higher-quality solutions and perform better in clustering tasks compared with a state-of-the-art ONMF.

Highlights

Nonnegative matrix factorization (NMF) has been investigated by many researchers, such as Paatero and Tapper [1]
Because NMF algorithms based on the alternating direction method are more efficient than multiplicative update algorithms, we propose another convergence algorithm for solving the Orthogonal nonnegative matrix factorization (ONMF) problem by combining the ADM approach with our convergence algorithm
We use examples of ONMF arising in image processing to analyze the quality of the solutions

Summary

Introduction

Nonnegative matrix factorization (NMF) has been investigated by many researchers, such as Paatero and Tapper [1]. In a study conducted by Pompili et al [18], the authors proposed a method working the opposite way: at each iteration, a projected gradient scheme is used to ensure that the orthogonal factor iterates are orthogonal but not necessarily nonnegative. These algorithms still are not convergent algorithms for ONMF. Because NMF algorithms based on the alternating direction method are more efficient than multiplicative update algorithms, we propose another convergence algorithm for solving the ONMF problem by combining the ADM approach with our convergence algorithm.

Related Algorithms

Alternating Direction Algorithm for ONMF

Experiments and Results

Conclusion