Robust Low-Rank Matrix Recovery via Hybrid Ordinary-Welsch Function

As a widely-used tool to resist outliers, the correntropy criterion or Welsch function has recently been exploited for robust matrix recovery. However, it down-weighs all observations including uncontaminated data. On the other hand, its implicit regularizer (IR) cannot achieve sparseness, which is a desirable property in many practical scenarios. To address these two issues, we devise a novel M-estimator called hybrid ordinary-Welsch (HOW) function, which only down-weighs the outlier-contaminated data, and the IR generated by the HOW can attain sparseness. To verify the effectiveness of the HOW function, we apply it to robust matrix completion and principal component analysis. An efficient algorithm is developed and we prove that any generated limit point is a critical point. Finally, extensive experimental results based on synthetic and real-world data demonstrate that the proposed approach outperforms the state-of-the-art methods in terms of recovery accuracy and runtime.