Dynamic L1-Norm Tucker Tensor Decomposition

Chachlakis, Dimitris G.; Dhanaraj, Mayur; Prater-Bennette, Ashley; Markopoulos, Panos P.

doi:10.1109/jstsp.2021.3058846

“…RACP [62] introduces a ℓ 1 -norm penalty to promote the sparsity on outliers and then uses an ADMM solver to estimate them. Under the Tucker format, ORLTM [102], OLRTR [103], and D-L1-Tucker [93] are able to deal with sparse outliers. Both ORLTM and OLRTR propose to regularize the main objective function with a ℓ 1 -norm regularization.…”

Section: Data Imperfection and Corruptionmentioning

confidence: 99%

A Contemporary and Comprehensive Survey on Streaming Tensor Decomposition

Thanh¹,

abed-meraim²,

Linh-Trung³

et al. 2022

Preprint

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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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“…Specifically, the higher value of 𝛼 𝑡 is, the faster the loading factor U (𝑛) changes. 9 Our codes are available at https://github.com/thanhtbt/Tensor_Tracking. The 𝑡-th slice 𝒳 𝑡 with missing entries is then derived from the following model:…”

Section: Experiments Setupmentioning

confidence: 99%

“…However, both algorithms are only suitable for third-order tensors. Dimitris et al have recently proposed the first robust online Tucker decomposition that can deal with streaming tensors in the presence of outliers [9]. However, it was not designed for handling missing data.…”

Section: Introductionmentioning

confidence: 99%

Tracking Online Low-Rank Approximations of Higher-Order Incomplete Streaming Tensors

Thanh¹,

abed-meraim²,

Linh-Trung³

et al. 2022

Preprint

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In this paper, we propose two new provable algorithms for tracking online low-rank approximations of higher-order streaming tensors in the presence of missing data. The first algorithm, dubbed adaptive CP decomposition (ACP), minimizes an exponentially weighted recursive least-squares cost function to obtain the tensor factors in an efficient way, thanks to the alternative minimization framework and the randomized sketching technique. Under the Tucker model, the second algorithm called adaptive Tucker decomposition (ATD), which is more flexible than the first one, first tracks the underlying low-dimensional subspaces covering the tensor factors, and then estimates the core tensor using a stochastic approximation. Both algorithms are fast, and require a low computational complexity and memory storage. A unified convergence analysis is presented for ACP and ATD to justify their performance. Experiments indicate that the two proposed algorithms are capable of the adaptive tensor decomposition problem with competitive performance on both synthetic and real data.

show abstract

“…However, both algorithms are only suitable for third-order tensors. In [18], Dimitris et al proposed the first robust online Tucker decomposition that can deal with streaming tensors in the presence of outliers. However, it was not designed for handling missing data.…”

Section: Introductionmentioning

confidence: 99%

Tracking Online Low-Rank Approximations of Higher-Order Incomplete Streaming Tensors

Thanh¹

2023

Preprint

View full text Add to dashboard Cite

In this paper, we propose two new provable algorithms for tracking online low-rank approximations of higher-order streaming tensors in the presence of missing data. The first algorithm, dubbed adaptive CP decomposition (ACP), minimizes an exponentially weighted recursive least-squares cost function to obtain the tensor factors in an efficient way, thanks to the alternative minimization framework and the randomized sketching technique. Under the Tucker model, the second algorithm called adaptive Tucker decomposition (ATD), which is more flexible than the first one, first tracks the underlying low-dimensional subspaces covering the tensor factors, and then estimates the core tensor using a stochastic approximation. Both algorithms are fast, and require a low computational complexity and memory storage. A unified convergence analysis is presented for ACP and ATD to justify their performance. Experiments indicate that the two proposed algorithms are capable of the adaptive tensor decomposition problem with competitive performance on both synthetic and real data.

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Dynamic L1-Norm Tucker Tensor Decomposition

Cited by 21 publications

References 47 publications

A Contemporary and Comprehensive Survey on Streaming Tensor Decomposition

A Contemporary and Comprehensive Survey on Streaming Tensor Decomposition

Tracking Online Low-Rank Approximations of Higher-Order Incomplete Streaming Tensors

Tracking Online Low-Rank Approximations of Higher-Order Incomplete Streaming Tensors

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