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This paper studies the matrix completion problems when the entries are contaminated by non-Gaussian noise or outliers. The proposed approach employs a nonconvex loss function induced by the maximum correntropy criterion. With the help of this loss function, we develop a rank constrained, as well as a nuclear norm regularized model, which is resistant to non-Gaussian noise and outliers. However, its non-convexity also leads to certain difficulties. To tackle this problem, we use the simpledoi:10.3390/e20030171 pmid:33265262 fatcat:aqeqhe5mqzfvfbyi6zj7lg57oq