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Decomposition of Big Tensors With Low Multilinear Rank

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arxiv 1412.1885 v2 pith:UHVCR3SP submitted 2014-12-05 cs.NA cs.DCcs.NA

Guoxu Zhou , Andrzej Cichocki , Shengli Xie This is my paper · ORCID
classification cs.NAcs.DC
keywords datatensorsdecompositionalgorithmsanalyticsdecompositionsmultilinearrank
verification ladder T0 review T1 audit T2 compute T3 formal
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Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most existing approaches are not designed to meet the major challenges posed by big data analytics. This paper attempts to improve the scalability of tensor decompositions and provides two contributions: A flexible and fast algorithm for the CP decomposition (FFCP) of tensors based on their Tucker compression; A distributed randomized Tucker decomposition approach for arbitrarily big tensors but with relatively low multilinear rank. These two algorithms can deal with huge tensors, even if they are dense. Extensive simulations provide empirical evidence of the validity and efficiency of the proposed algorithms.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Accelerating the Canonical Polyadic Alternating Least Squares Optimization via a Randomized Interpolative Decomposition

    math.NA 2026-07 conditional novelty 6.0 of 10

    Randomized QR pivots of the target tensor supply a fixed leverage-score-like sampling for CPD-ALS, reducing tensor re-sampling and storage overhead.

  2. Intrinsic Low-Tucker-Rank Theory and Unified Tensor CUR Decomposition for High-Dimensional Hyperinterpolation

    math.NA 2026-07 reject novelty 5.0 of 10

    The paper asserts low-epsilon-Tucker-rank compressibility of hyperinterpolation coefficient tensors and gives unified TCUR error bounds, but the central rank formula exceeds the tensor dimensions and the advertised pr...

  3. 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.

  4. Federated Low-Rank Tensor Estimation for Multimodal Image Reconstruction

    cs.LG 2025-02 conditional novelty 5.0 of 10

    The paper introduces CompJF and CompRandJF, federated Tucker-based reconstruction algorithms that aggregate clients via joint factorization and randomized sketching, claiming improved SSIM and communication efficiency...

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