Robust matrix completion via Novel M-estimator Functions
- Zhi-Yong Wang ,
- Hing Cheung so
Abstract
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.