![]() |
ETNA - Electronic Transactions on Numerical Analysis
|
![]() |
Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
|
||||||||||||||||||||
|
DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
|

ETNA - Electronic Transactions on Numerical Analysis, pp. 247-280, 2025/07/09
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 the least-squares method 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 for alternative approaches. It uses a rank estimator to adaptively 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.
Keywords: tensor decompositions, randomized algorithms, sketching, least-squares, leverage scores, Tikhonov regularization, iterative refinement, HOSVD