2017/10/19 by Quanming Yao, Yao, Quanming, James T. Kwok +1
Computer Science · Engineering · #Blind Source Separation Techniques #FOS: Mathematics #Medical Image Segmentation Techniques #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1710.07205
openalex publication_date 2017/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.