Reviews: Scalable Robust Matrix Factorization with Nonconvex Loss

In this paper, an algorithm for matrix factorization (MF) is proposed, which provide better robustness to outlier's behavior compared to state of the art algorithms for Robust MF (RMF). Another nice property of the new algorithm is that it is suitable for sparse data matrices which is a clear advantage when it is compared against previous approaches to RMF. Basically, the authors propose to replace the l1 penalty with a nonconvex regularizer and provide results for various selections of regularizers. Since the optimization in this case is not simple, the authors propose to use a Majorization Minimization (MM) optimization approach with a definition of a new MM surrogate. The paper provides a nice introduction to the problem of robust matrix factorization, providing a complete overview of the state of the art and giving good motivations for the development of a new algorithm. I found the paper well written, technically sounded and having a nice structure.