Robust Matrix Factorization with Grouping Effect

TL;DR

This paper introduces GRMF, a novel matrix factorization method that automatically learns grouping and sparsity structures, enhancing robustness and performance in noisy, real-world data.

Contribution

GRMF incorporates a non-convex regularization to simultaneously learn grouping and sparsity in matrix factorization without prior knowledge.

Findings

GRMF outperforms five benchmark algorithms in robustness and accuracy.

The method effectively handles outliers and contaminated noise.

GRMF can be extended to Non-negative Matrix Factorization (NMF).

Abstract

Although many techniques have been applied to matrix factorization (MF), they may not fully exploit the feature structure. In this paper, we incorporate the grouping effect into MF and propose a novel method called Robust Matrix Factorization with Grouping effect (GRMF). The grouping effect is a generalization of the sparsity effect, which conducts denoising by clustering similar values around multiple centers instead of just around 0. Compared with existing algorithms, the proposed GRMF can automatically learn the grouping structure and sparsity in MF without prior knowledge, by introducing a naturally adjustable non-convex regularization to achieve simultaneous sparsity and grouping effect. Specifically, GRMF uses an efficient alternating minimization framework to perform MF, in which the original non-convex problem is first converted into a convex problem through Difference-of-Convex (DC) programming, and then solved by Alternating Direction Method of Multipliers (ADMM). In addition, GRMF can be easily extended to the Non-negative Matrix Factorization (NMF) settings. Extensive experiments have been conducted using real-world data sets with outliers and contaminated noise, where the experimental results show that GRMF has promoted performance and robustness, compared to five benchmark algorithms.