Scalable and Robust Tensor Ring Decomposition for Large-Scale Data With Missing Data and Outliers

Tensor ring (TR) decomposition demonstrates superior performance in handling high-order tensors. However, traditional TR-based decomposition algorithms face limitations in real-world applications due to large data sizes, missing entries, and outlier corruption. To address these challenges, we propose a scalable and robust TR decomposition algorithm for large-scale tensor data that effectively handles missing entries and gross corruptions. Our method introduces a novel auto-weighted scaled steepest descent approach that adaptively identifies outliers and completes missing entries during decomposition. Additionally, leveraging the tensor ring decomposition model, we develop a Fast Gram Matrix Computation (FGMC) technique and a Randomized Subtensor Sketching (RStS) strategy, significantly reducing storage and computational complexity. Experimental results demonstrate that the proposed method outperforms existing TR decomposition and tensor completion methods.