Robust matrix completion aims to recover a low-rank matrix from a subset of noisy entries perturbed by complex noises. Traditional matrix completion algorithms are always based on $l_2$-norm minimization and are sensitive to non-Gaussian noise with outliers. In this paper, we propose a novel robust and fast matrix completion method based on the maximum correntropy criterion (MCC). The correntropy-based error measure is utilized instead of the $l_2$-based error norm to improve robustness against noise. By using the half-quadratic optimization technique, the correntropy-based optimization can be transformed into a weighted matrix factorization problem. Two efficient algorithms are then derived: an alternating minimization-based algorithm and an alternating gradient descent-based algorithm. These algorithms do not require the singular value decomposition (SVD) to be calculated for each iteration. Furthermore, an adaptive kernel width selection strategy is proposed to accelerate the convergence speed as well as improve the performance. A comparison with existing robust matrix completion algorithms is provided by simulations and shows that the new methods can achieve better performance than the existing state-of-the-art algorithms.

中文翻译：

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通过最大相关熵准则和半二次优化的稳健矩阵完成

稳健矩阵补全旨在从受复杂噪声扰动的噪声条目子集中恢复低秩矩阵。传统的矩阵补全算法总是基于$l_2$-范数最小化并且对具有异常值的非高斯噪声敏感。在本文中，我们提出了一种基于最大相关熵准则（MCC）的新型鲁棒且快速的矩阵补全方法。使用基于相关熵的误差度量而不是$l_2$基于误差范数以提高对噪声的鲁棒性。通过使用半二次优化技术，基于相关熵的优化可以转化为加权矩阵分解问题。然后推导出两种有效的算法：基于交替最小化的算法和基于交替梯度下降的算法。这些算法不需要为每次迭代计算奇异值分解 (SVD)。此外，提出了一种自适应内核宽度选择策略，以加快收敛速度​​并提高性能。仿真提供了与现有稳健矩阵完成算法的比较，表明新方法可以实现比现有最先进算法更好的性能。