This paper studies the robust matrix completion problem and a computationally efficient non-convex method called ARMC has been proposed. This method is developed by introducing subspace projection to a singular value thresholding based method when updating the low rank part. Numerical experiments on synthetic and real data show that ARMC is superior to existing non-convex RMC methods. Through a refined analysis based on the leave-one-out technique, we have established the theoretical guarantee for ARMC subject to both sparse outliers and stochastic noise. The established bounds for the sample complexity and outlier sparsity are better than those established for a convex approach that also considers both outliers and stochastic noise.

翻译：本文研究了鲁棒矩阵补全问题，并提出了一种计算高效的非凸方法ARMC。该方法通过在更新低秩部分时向基于奇异值阈值的算法引入子空间投影而发展。在合成数据与真实数据上的数值实验表明，ARMC优于现有的非凸RMC方法。基于留一法技术的精细分析，我们为ARMC建立了针对稀疏异常值和随机噪声的理论保证。所建立的样本复杂度与异常值稀疏性边界优于同样考虑异常值与随机噪声的凸优化方法所建立的边界。