RTSMS: Randomized Tucker with single-mode sketching

TL;DR

RTSMS introduces a novel randomized algorithm for low-rank Tucker tensor decomposition that efficiently sketches one mode at a time, reducing computational costs while maintaining competitive accuracy.

Contribution

It presents a new single-mode sketching approach for Tucker decomposition, improving efficiency over existing methods.

Findings

RTSMS is competitive with state-of-the-art algorithms.

RTSMS can outperform existing methods significantly.

The approach reduces sketch size and computational complexity.

Abstract

We propose RTSMS (Randomized Tucker via Single-Mode-Sketching), a randomized algorithm for approximately computing a low-rank Tucker decomposition of a given tensor. It uses sketching and least-squares to compute the Tucker decomposition in a sequentially truncated manner. The algorithm only sketches one mode at a time, so the sketch matrices are significantly smaller than alternative approaches. The algorithm is demonstrated to be competitive with existing methods, sometimes outperforming them by a large margin.