On the Robustness of Cross-Concentrated Sampling for Matrix Completion
This work addresses robustness in matrix completion for data science applications, but it appears incremental as it builds on the existing CCS model.
The paper tackles the problem of matrix completion under cross-concentrated sampling with sparse outliers, proposing a non-convex iterative algorithm called Robust CUR Completion (RCURC) and verifying its efficiency and robustness on synthetic and real datasets.
Matrix completion is one of the crucial tools in modern data science research. Recently, a novel sampling model for matrix completion coined cross-concentrated sampling (CCS) has caught much attention. However, the robustness of the CCS model against sparse outliers remains unclear in the existing studies. In this paper, we aim to answer this question by exploring a novel Robust CCS Completion problem. A highly efficient non-convex iterative algorithm, dubbed Robust CUR Completion (RCURC), is proposed. The empirical performance of the proposed algorithm, in terms of both efficiency and robustness, is verified in synthetic and real datasets.