A Symmetric Rank-one Quasi Newton Method for Non-negative Matrix Factorization

TL;DR

This paper introduces a novel symmetric rank-one quasi-Newton method for non-negative matrix factorization that accelerates convergence and improves approximation quality, demonstrated through experiments on synthetic, image, and text data.

Contribution

The paper proposes a new symmetric rank-one quasi-Newton algorithm for NMF that enhances convergence speed and accuracy over existing methods.

Findings

Faster decrease of the objective function compared to other NMF methods

Improved approximation accuracy demonstrated on various datasets

Numerical experiments confirm the effectiveness of the proposed method

Abstract

As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix approximation is proposed. This method mainly bases on the active set and the quasi-Newton type algorithm, by using the symmetric rank-one and negative curvature direction technologies to approximate the Hessian matrix. Our method improves the recent results of those methods in [Pattern Recognition, 45(2012)3557-3565; SIAM J. Sci. Comput., 33(6)(2011)3261-3281; Neural Computation, 19(10)(2007)2756-2779, etc.]. Moreover, the object function decreases faster than many other NMF methods. In addition, some numerical experiments are presented in the synthetic data, imaging processing and text clustering. By comparing with the other six nonnegative matrix approximation methods, our experiments confirm to our analysis.