Scalable and Robust Tensor Ring Decomposition for Large-scale Data

TL;DR

This paper introduces a scalable, robust tensor ring decomposition method that efficiently handles large-scale tensors with missing data and outliers, outperforming existing algorithms in speed and accuracy.

Contribution

The authors develop a novel auto-weighted steepest descent algorithm combined with fast Gram matrix computation and randomized sketching for robust, scalable tensor ring decomposition.

Findings

Outperforms existing TR methods in handling outliers.

Runs significantly faster than current robust tensor completion algorithms.

Effectively manages large-scale tensors with missing entries and corruptions.

Abstract

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.