d86ea612dec96096c5e0fcc8dd42ab6d-Reviews.html

This paper considers robust principal component analysis, from the approach of transfer learning. The goal is to obtain a method that, according to the paper, can deal with not only small and/or sparse errors, but also dense large errors, in the setting where there are two data sources (two data matrices) which have some overlap in their principal components. The authors then propose a rank-constrained optimization problem that is the natural formulation, assuming sparse errors; that is, they propose an objective which balances between the L2 loss in fitting the data matrix, plus an L1 penalty on the sparse corruption. This, in principle, should allow the handling of sparse noise, and also smaller dense noise. Instead of relaxing the rank constraints, they propose a projected proximal type iterative method, where they project back to matrices of appropriate rank, at every step. There are several issues with this paper that if addressed, would significantly strengthen the contribution.