A Sampling-Based Method for Tensor Ring Decomposition

TL;DR

This paper introduces a sampling-based algorithm for tensor ring decomposition that significantly speeds up computation while maintaining accuracy, leveraging leverage score sampling and providing theoretical guarantees.

Contribution

The paper presents a novel sampling-based approach for tensor ring decomposition that reduces computational complexity and offers theoretical error bounds.

Findings

Achieves 2-3 orders of magnitude speedup over existing methods.

Maintains high accuracy in tensor approximation.

Effective for rapid feature extraction.

Abstract

We propose a sampling-based method for computing the tensor ring (TR) decomposition of a data tensor. The method uses leverage score sampled alternating least squares to fit the TR cores in an iterative fashion. By taking advantage of the special structure of TR tensors, we can efficiently estimate the leverage scores and attain a method which has complexity sublinear in the number of input tensor entries. We provide high-probability relative-error guarantees for the sampled least squares problems. We compare our proposal to existing methods in experiments on both synthetic and real data. Our method achieves substantial speedup -- sometimes two or three orders of magnitude -- over competing methods, while maintaining good accuracy. We also provide an example of how our method can be used for rapid feature extraction.