A Fast Randomized Adaptive CP Decomposition For Streaming Tensors

Thanh, Le Trung; Abed-Meraim, Karim; Trung, Nguyen Link; Hafiane, Adel

doi:10.1109/icassp39728.2021.9413554

Cited by 18 publications

(7 citation statements)

References 15 publications

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“…Accordingly, many attempts have been made to take their advantages in computation for tensor decomposition in the literature, we refer the readers to [23] for a good overview. Among them, there are a few online algorithms utilizing successfully randomized techniques to speed up the tracking process, such as [54], [60], [61], [130]. Particularly, these algorithms involve solving several overdetermined least-squares (LS) problems.…”

Section: Efficient and Scalable Tensor Trackingmentioning

confidence: 99%

A Contemporary and Comprehensive Survey on Streaming Tensor Decomposition

Thanh

Abed-Meraim

Trung

et al. 2023

IEEE Trans. Knowl. Data Eng.

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Tensor decomposition has been demonstrated to be successful in a wide range of applications, from neuroscience and wireless communications to social networks. In an online setting, factorizing tensors derived from multidimensional data streams is however non-trivial due to several inherent problems of real-time stream processing. In recent years, many research efforts have been dedicated to developing online techniques for decomposing such tensors, resulting in significant advances in streaming tensor decomposition or tensor tracking. This topic is emerging and enriches the literature on tensor decomposition, particularly from the data stream analystics perspective. Thus, it is imperative to carry out an overview of tensor tracking to help researchers and practitioners understand its development and achievements, summarise the current trends and advances, and identify challenging problems. In this article, we provide a contemporary and comprehensive survey on different types of tensor tracking techniques. We particularly categorize the state-of-the-art methods into three main groups: streaming CP decompositions, streaming Tucker decompositions, and streaming decompositions under other tensor formats (i.e., tensor-train, t-SVD, and BTD). In each group, we further divide the existing algorithms into sub-categories based on their main optimization framework and model architectures. Finally, we present several research challenges, open problems, and potential directions of tensor tracking in the future.

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Section: Efficient and Scalable Tensor Trackingmentioning

confidence: 99%

A Contemporary and Comprehensive Survey on Streaming Tensor Decomposition

Thanh

Abed-Meraim

Trung

et al. 2023

IEEE Trans. Knowl. Data Eng.

View full text Add to dashboard Cite

show abstract

“…Accordingly, many attempts have been made to take their advantages in computation for tensor decomposition in the literature, we refer the readers to [23] for a good overview. Among them, there are a few online algorithms utilizing successfully randomized techniques to speed up the tracking process, such as [57], [63], [64], [174]. Particularly, these algorithms involve solving several overdetermined least-squares (LS) problems.…”

Section: Efficient and Scalable Tensor Trackingmentioning

confidence: 99%

A Contemporary and Comprehensive Survey on Streaming Tensor Decomposition

Thanh¹,

abed-meraim²,

Linh-Trung³

et al. 2022

Preprint

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<p>Tensor decomposition has been demonstrated to be successful in a wide range of applications, from neuroscience and wireless communications to social networks. In an online setting, factorizing tensors derived from multidimensional data streams is however non-trivial due to several inherent problems of real-time stream processing. In recent years, many research efforts have been dedicated to developing online techniques for decomposing such tensors, resulting in significant advances in streaming tensor decomposition or tensor tracking. This topic is emerging and enriches the literature on tensor decomposition, particularly from the data stream analystics perspective. Thus, it is imperative to carry out an overview of tensor tracking to help researchers and practitioners understand its development and achievements, summarise the current trends and advances, and identify challenging problems. In this article, we provide a contemporary and comprehensive survey on different types of tensor tracking techniques. We particularly categorize the state-of-the-art methods into three main groups: streaming CP decompositions, streaming Tucker decompositions, and streaming decompositions under other tensor formats (i.e., tensor-train, t-SVD, and BTD). In each group, we further divide the existing algorithms into sub-categories based on their main optimization framework and model architectures. Finally, we present several research challenges, open problems, and potential directions of tensor tracking in the future.</p>

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“…[60] develops a variant of the method of [34] that employs randomized least squares to more effectively cope with large-scale tensors. A randomizationbased online CPD algorithm of the Newton type appears in [61].…”

Section: Related Workmentioning

confidence: 99%

Online Rank-Revealing Block-Term Tensor Decomposition

Rontogiannis¹,

Kofidis²,

Giampouras³

2021

Preprint

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The so-called block-term decomposition (BTD) tensor model, especially in its rank-(Lr, Lr, 1) version, has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of block components of rank higher than one, a scenario encountered in numerous and diverse applications. Its uniqueness and approximation have thus been thoroughly studied. The challenging problem of estimating the BTD model structure, namely the number of block terms (rank) and their individual (block) ranks, is of crucial importance in practice and has only recently started to attract significant attention. In data-streaming scenarios and/or big data applications, where the tensor dimension in one of its modes grows in time or can only be processed incrementally, it is essential to be able to perform model selection and computation in a recursive (incremental/online) manner. To date there is only one such work in the literature concerning the (general rank-(L, M, N )) BTD model, which proposes an incremental method, however with the BTD rank and block ranks assumed to be a-priori known and time invariant. In this preprint, a novel approach to rank-(Lr, Lr, 1) BTD model selection and tracking is proposed, based on the idea of imposing column sparsity jointly on the factors and estimating the ranks as the numbers of factor columns of nonnegligible magnitude. An online method of the alternating iteratively reweighted least squares (IRLS) type is developed and shown to be computationally efficient and fast converging, also allowing the model ranks to change in time. Its time and memory efficiency are evaluated and favorably compared with those of the batch approach. Simulation results are reported that demonstrate the effectiveness of the proposed scheme in both selecting and tracking the correct BTD model.

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A Fast Randomized Adaptive CP Decomposition For Streaming Tensors

Cited by 18 publications

References 15 publications

A Contemporary and Comprehensive Survey on Streaming Tensor Decomposition

A Contemporary and Comprehensive Survey on Streaming Tensor Decomposition

A Contemporary and Comprehensive Survey on Streaming Tensor Decomposition

Online Rank-Revealing Block-Term Tensor Decomposition

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