RTSMS: randomized Tucker with single-mode sketching

Journal article

We propose RTSMS (Randomized Tucker with 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. RTSMS essentially only sketches one mode at a time, so the sketch matrices are significantly smaller than alternative approaches. It uses a rank estimator to adap7 tively find an appropriate rank for the Tucker decomposition, without requiring it as input. RTSMS is demonstrated to be competitive with existing methods, sometimes outperforming them by a large margin.

Authors: Hashemi, B; Nakatsukasa, Y

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Kent State University Library
• Journal: Electronic Transactions on Numerical Analysis
• Volume: 63
• Pages: 247-280
• Publication date: 2025-07-11
• Acceptance date: 2025-06-02
• DOI: 10.1553/etna_vol63s247
• EISSN: 1097-4067
• ISSN: 1068-9613
• Language: English
• Keywords: tensor decompositions; randomized algorithms; sketching; least-squares; leverage scores; Tikhonov regularization; iterative refinement; HOSVD