Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is hindered by prevalent large data sizes, missing entries, and corruption with outliers. In this work, we propose a scalable and robust TR decomposition algorithm capable of handling large-scale tensor data with missing entries and gross corruptions. We first develop a novel auto-weighted steepest descent method that can adaptively fill the missing entries and identify the outliers during the decomposition process. Further, taking advantage of the tensor ring model, we develop a novel fast Gram matrix computation (FGMC) approach and a randomized subtensor sketching (RStS) strategy which yield significant reduction in storage and computational complexity. Experimental results demonstrate that the proposed method outperforms existing TR decomposition methods in the presence of outliers, and runs significantly faster than existing robust tensor completion algorithms.

翻译：张量环（TR）分解因其在高阶张量上出色的表达能力而近期受到广泛关注。然而，传统TR分解算法在实际应用中的适用性受到普遍存在的大数据规模、缺失条目以及异常值污染的阻碍。本文提出了一种可扩展且稳健的TR分解算法，能够处理含有缺失条目和严重污染的大规模张量数据。我们首先开发了一种新颖的自适应加权最速下降法，该方法能够在分解过程中自适应地填补缺失条目并识别异常值。此外，利用张量环模型的优势，我们开发了一种快速格拉姆矩阵计算（FGMC）方法以及一种随机子张量草图（RStS）策略，从而显著降低了存储需求和计算复杂度。实验结果表明，所提出方法在处理异常值时优于现有TR分解方法，并且运行速度显著快于现有的稳健张量补全算法。