Scalable Robust Matrix Factorization with Nonconvex Loss
For practitioners dealing with large-scale matrix completion with outliers, this work offers a more robust and scalable solution.
This paper proposes a scalable robust matrix factorization method using nonconvex loss to improve robustness over the ℓ1-loss, achieving superior accuracy and scalability compared to state-of-the-art RMF-MM algorithm.
Robust matrix factorization (RMF), which uses the $\ell_1$-loss, often outperforms standard matrix factorization using the $\ell_2$-loss, particularly when outliers are present. The state-of-the-art RMF solver is the RMF-MM algorithm, which, however, cannot utilize data sparsity. Moreover, sometimes even the (convex) $\ell_1$-loss is not robust enough. In this paper, we propose the use of nonconvex loss to enhance robustness. To address the resultant difficult optimization problem, we use majorization-minimization (MM) optimization and propose a new MM surrogate. To improve scalability, we exploit data sparsity and optimize the surrogate via its dual with the accelerated proximal gradient algorithm. The resultant algorithm has low time and space complexities and is guaranteed to converge to a critical point. Extensive experiments demonstrate its superiority over the state-of-the-art in terms of both accuracy and scalability.