Practical Sketching-Based Randomized Tensor Ring Decomposition

TL;DR

This paper introduces two novel randomized algorithms for tensor ring decomposition using sketching techniques, offering efficient and accurate solutions with theoretical guarantees and empirical validation.

Contribution

It presents new randomized algorithms for tensor ring decomposition based on sketching, with theoretical analysis and empirical comparison to existing methods.

Findings

Algorithms achieve competitive accuracy and speed.

Theoretical bounds on sketch size and complexity are established.

Numerical experiments validate practical effectiveness.

Abstract

Based on sketching techniques, we propose two randomized algorithms for tensor ring (TR) decomposition. Specifically, by defining new tensor products and investigating their properties, we apply the Kronecker sub-sampled randomized Fourier transform and TensorSketch to the alternating least squares problems derived from the minimization problem of TR decomposition to devise the randomized algorithms. From the former, we find an algorithmic framework based on random projection for randomized TR decomposition. Theoretical results on sketch size and complexity analyses for the two algorithms are provided. We compare our proposals with the state-of-the-art method using both synthetic and real data. Numerical results show that they have quite decent performance in accuracy and computing time