Robust low-rank optimization for large scale problems

In this paper, we propose using smooth robust loss functions to formulate robust low-rank optimization problem in the presence of outliers. The objective of the problem is to recover a low-rank data matrix from noisy entries. Our main contributions are i) providing two smooth robust loss functions to handle respectively two different types of outliers, i.e., the universal outliers with unknown statistical distribution and the sparse spike-like outliers; ii) an efficient algorithm doing parallel minimization instead of alternating update. Numerical results show that the proposed algorithm obtains a better solution at a faster convergence rate than the state-of-art algorithms.