  Robust matrix completion aims to recover a low-rank matrix from a subset of
noisy entries perturbed by complex noises, where traditional methods for matrix
completion may perform poorly due to utilizing $l_2$ error norm in
optimization. In this paper, we propose a novel and fast robust matrix
completion method based on maximum correntropy criterion (MCC). The correntropy
based error measure is utilized instead of using $l_2$-based error norm to
improve the robustness to noises. Using the half-quadratic optimization
technique, the correntropy based optimization can be transformed to a weighted
matrix factorization problem. Then, two efficient algorithms are derived,
including alternating minimization based algorithm and alternating gradient
descend based algorithm. The proposed algorithms do not need to calculate
singular value decomposition (SVD) at each iteration. Further, the adaptive
kernel selection strategy is proposed to accelerate the convergence speed as
well as improve the performance. Comparison with existing robust matrix
completion algorithms is provided by simulations, showing that the new methods
can achieve better performance than existing state-of-the-art algorithms.
