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RTSMS: Randomized Tucker with single-mode sketching

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arxiv 2311.14873 v1 pith:OJQLPUPS submitted 2023-11-24 math.NA cs.NA

Behnam Hashemi , Yuji Nakatsukasa This is my paper · ORCID
classification math.NAcs.NA
keywords tuckeralgorithmrandomizeddecompositionrtsmssketchingalternativeapproaches
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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.

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  1. Efficient randomized algorithms for the fixed Tucker-rank problem of Tucker decomposition with adaptive shifts

    math.NA 2025-06 conditional novelty 5.0 of 10

    Adaptively shifted power iterations are added to randomized T-HOSVD and ST-HOSVD for Tucker decomposition, with probabilistic error bounds and speedups in numerical tests.

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