  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.
