# Scalable Robust Matrix Factorization with Nonconvex Loss

arXiv: https://arxiv.org/abs/1710.07205 · HTML: https://mlsanity.com/paper/1710.07205/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2017.

## Built on by (most cited first, 2 of 2)

- [SYNTHESIS: A Semi-Asynchronous Path-Integrated Stochastic Gradient Method for Distributed Learning in Computing Clusters](https://mlsanity.com/paper/2208.08425/) (2022)
- [Robust Matrix Factorization with Grouping Effect](https://mlsanity.com/paper/2106.13681/) (2021)

## Abstract (arXiv)

Robust matrix factorization (RMF), which uses the ℓ1-loss, often outperforms standard matrix factorization using the ℓ2-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) ℓ1-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.