Tensor decomposition for analysing time-evolving social networks: an overview

Fernandes, Sofia; Fanaee-T, Hadi; Gama, João

doi:10.1007/s10462-020-09916-4

Cited by 19 publications

(11 citation statements)

References 105 publications

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“…Enron [22] consists of words of email exchanges in the form of sender-receiver-word-date quadruplets. It has been used with tensor decomposition methods for social network analysis and link prediction [23]. Flickr is a binary tensor representing user-image-tag-date quadruplets, which was first crawled by G€ orlitz et al [24] from flickr.com.…”

Section: Datasetmentioning

confidence: 99%

True Load Balancing for Matricized Tensor Times Khatri-Rao Product

Abubaker

Acer

Aykanat

2021

IEEE Trans. Parallel Distrib. Syst.

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MTTKRP is the bottleneck operation in algorithms used to compute the CP tensor decomposition. For sparse tensors, utilizing the compressed sparse fibers (CSF) storage format and the CSF-oriented MTTKRP algorithms is important for both memory and computational efficiency on distributed-memory architectures. Existing intelligent tensor partitioning models assume the computational cost of MTTKRP to be proportional to the total number of nonzeros in the tensor. However, this is not the case for the CSF-oriented MTTKRP on distributed-memory architectures. We outline two deficiencies of nonzero-based intelligent partitioning models when CSF-oriented MTTKRP operations are performed locally: failure to encode processors' computational loads and increase in total computation due to fiber fragmentation. We focus on existing fine-grain hypergraph model and propose a novel vertex weighting scheme that enables this model encode correct computational loads of processors. We also propose to augment the fine-grain model by fiber nets for reducing the increase in total computational load via minimizing fiber fragmentation. In this way, the proposed model encodes minimizing the load of the bottleneck processor. Parallel experiments with real-world sparse tensors on up to 1024 processors prove the validity of the outlined deficiencies and demonstrate the merit of our proposed improvements in terms of parallel runtimes.

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Section: Datasetmentioning

confidence: 99%

True Load Balancing for Matricized Tensor Times Khatri-Rao Product

Abubaker

Acer

Aykanat

2021

IEEE Trans. Parallel Distrib. Syst.

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“…Processing a tensor that grows in one of its modes through the streaming of new slices in a way that takes this into account and does not re-compute the model parameters from scratch for every increment in the size of the tensor first appeared in the tensor-based data mining literature [16] with the name of Incremental Tensor Analysis (ITA). ITA and its variants (Dynamic Tensor Analysis (DTA), Streaming Tensor Analysis (STA), and Windowed Tensor Analysis (WTA)) were aimed at performing TD on a sequence of tensors and were later extended to incremental higher-order singular value decomposition (HO-SVD) (based on incremental SVD) for the purposes of data mining in intelligent transportation systems [17], computer vision [18]- [22], recommendation systems (see also [23,Chapter 6]) [24], [25], handwritten digit recognition [26], and epidemics [27] and social networks [28] analysis. Pairwise interactive tensor factorization (PITF), a special case of TD, was studied in this context in [29].…”

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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“…However, the identification problem of high‐dimensional systems remains a challenging task due to many existing identification technique do not work well with the dimension of these systems. Tensor representation which can preserve multidimensional patterns and capture higher‐order interactions and couplings within multiway data has widely been applied in many fields such as social networks, 19,20 cognitive science, applied mechanics, scientific computation, and signal processing 21‐23 . Tensor decomposition techniques such as CANDECOMP/PARAFAC decomposition, 24,25 higher‐order singular value decomposition, 26,27 tensor train decomposition 28,29 help reveal such hidden patterns/redundancies to obtain a compact representation, reducing storage efforts, and enabling efficient computations.…”

Section: Introductionmentioning

confidence: 99%

An efficient recursive identification algorithm for multilinear systems based on tensor decomposition

Wang

Yang

2021

Intl J Robust & Nonlinear

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There are many important fields involving the multilinear system identification. A great number of parameters to be identified is an important challenge, leading to the need for tensorial decomposition and modeling of such systems. This article is about the parameter estimation of the higher‐order multilinear systems with non‐Gaussian noises and to explore the role of tensor algebra in the multilinear model identification. A high‐dimension system identification problem is reformulated in terms of low‐dimension problems by using the tensorial decomposition technique. Further, applying the multi‐innovation identification theory, the recursive algorithm combining with the logarithmic p‐norms is investigated for multilinear systems with non‐Gaussian noises of low computational complexity. Finally, some simulation results illustrate the effectiveness of the proposed recursive identification method.

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Tensor decomposition for analysing time-evolving social networks: an overview

Cited by 19 publications

References 105 publications

True Load Balancing for Matricized Tensor Times Khatri-Rao Product

True Load Balancing for Matricized Tensor Times Khatri-Rao Product

Online Rank-Revealing Block-Term Tensor Decomposition

An efficient recursive identification algorithm for multilinear systems based on tensor decomposition

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