Tracking Tensor Ring Decompositions of Streaming Tensors

TL;DR

This paper introduces efficient algorithms for tracking tensor ring decompositions in streaming tensors, utilizing randomized techniques and sketching, with theoretical guarantees and improved computational performance over batch methods.

Contribution

It proposes novel algorithms for streaming tensor ring decomposition, including a randomized version that leverages sketching and offers theoretical analysis.

Findings

Algorithms outperform batch methods in computation time

Maintains similar accuracy to existing methods

Provides theoretical bounds on sketch size

Abstract

Tensor ring (TR) decomposition is an efficient approach to discover the hidden low-rank patterns for higher-order tensors, and streaming tensors are becoming highly prevalent in real-world applications. In this paper, we investigate how to track TR decompositions of streaming tensors. An efficient algorithm is first proposed. Then, based on this algorithm and randomized techniques, we present a randomized streaming TR decomposition. The proposed algorithms make full use of the structure of TR decomposition, and the randomized version can allow any sketching type. Theoretical results on sketch size are provided. In addition, the complexity analyses for the obtained algorithms are also given. We compare our proposals with the existing batch methods using both real and synthetic data. Numerical results show that they have better performance in computing time with maintaining similar accuracy.