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Robust matrix completion via Novel M-estimator Functions
  • Zhi-Yong Wang ,
  • Hing Cheung so
Zhi-Yong Wang
City University of Hong Kong

Corresponding Author:[email protected]

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Hing Cheung so
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M-estmators including the Welsch and Cauchy have been widely adopted for robustness against outliers, but they also down-weigh the uncontaminated data. To address this issue, we devise a framework to generate a class of nonconvex functions which only down-weigh outlier-corrupted observations. Our framework is then applied to the Welsch, Cauchy and lp-norm functions to produce the corresponding robust loss functions. Targeting on the application of robust matrix completion, efficient algorithms based on these functions are developed and their convergence is analyzed. Finally, extensive numerical results demonstrate that the proposed methods are superior to the competitors in terms of recovery accuracy and runtime.