Robust to Rank Selection: Low-Rank Sparse Tensor-Ring Completion

Yu, Jinshi; Zhou, Guoxu; Sun, Weijun; Xie, Shengli

doi:10.1109/tnnls.2021.3106654

Cited by 10 publications

(5 citation statements)

References 59 publications

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“…By exploring the low-rank tensorring structure via optimizing model ( 12), the complete graph tensor S, in turn, can be obtained. However, as shown in references [41,46], the TR decomposition is easily afected by its TR-rank selection during the tensor completion process. To overcome this drawback, following the work in [46], we further add the Frobenius norm of TR-core, i.e.…”

Section: Low-rank High-order Relationship Explorationmentioning

confidence: 99%

“…However, as shown in references [41,46], the TR decomposition is easily afected by its TR-rank selection during the tensor completion process. To overcome this drawback, following the work in [46], we further add the Frobenius norm of TR-core, i.e. μ/2􏽐 3 k�1 ‖G (k) ‖‖ 2 F , to reduce the sensitivity of the TR decomposition to its TR-rank selection, which has been verifed to can achieve rather good completion results even when the selected TR-rank increases and more details can be found in [46].…”

Section: Low-rank High-order Relationship Explorationmentioning

confidence: 99%

“…To overcome this drawback, following the work in [46], we further add the Frobenius norm of TR-core, i.e. μ/2􏽐 3 k�1 ‖G (k) ‖‖ 2 F , to reduce the sensitivity of the TR decomposition to its TR-rank selection, which has been verifed to can achieve rather good completion results even when the selected TR-rank increases and more details can be found in [46]. In order to do this, the recovery model might be further defned as (1) , S (2) , .…”

Section: Low-rank High-order Relationship Explorationmentioning

confidence: 99%

See 2 more Smart Citations

Incomplete Multiview Clustering via Low-Rank Tensor Ring Completion

Huang

Duan

et al. 2023

International Journal of Intelligent Systems

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Since real-world multiview data frequently contains numerous samples that are not observed from some viewpoints, the incomplete multiview clustering (IMC) issue has received a great deal of attention recently. However, most existing IMC methods choose to zero-fill the missing instances, which leads to the failure to exploit information hidden in the missing instances, and high-order interactions between various views. To tackle these problems, we proposed an effective IMC method using low-rank tensor ring completion, which was demonstrated to be powerful in exploiting high-order correlation. Specifically, we first stack the incomplete similarity graphs of all views into a 3rd-order incomplete tensor and then restore it via the tensor ring decomposition. Next, using an adaptive weighting technique, we apply multiview spectral clustering to all entire graphs in order to balance the contributions of different viewpoints and identify the consensus representation for grouping. Finally, we employ the alternating direction method of multipliers (ADMM) to optimize the suggested model. Numerous experimental findings on numerous different datasets show that the suggested approach is superior to other cutting-edge approaches.

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Section: Low-rank High-order Relationship Explorationmentioning

confidence: 99%

Section: Low-rank High-order Relationship Explorationmentioning

confidence: 99%

Section: Low-rank High-order Relationship Explorationmentioning

confidence: 99%

See 1 more Smart Citation

Incomplete Multiview Clustering via Low-Rank Tensor Ring Completion

Huang

Duan

et al. 2023

International Journal of Intelligent Systems

Self Cite

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“…However, the matrices unfolding along each mode of tensor are unbalanced, which is accused of making it difficult to obtain promising recovery performance [17,18]. Recently, some new definitions of tensor rank have been proposed to solve TC problem, including tensor tubal rank [19], tensor train (TT) rank [20][21][22] and tensor ring (TR) rank [23][24][25][26][27][28]. Tensor singular value decomposition (t-SVD) decomposes a 3-order tensor into a f-diagonal tensor and two orthogonal tensors, where the number of non-zero tubes in f-diagonal is called tensor tubal rank.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Robust Tensor Ring Model for Incomplete Multiway Data

Huang¹,

Zhou²,

Qiu³

2022

Preprint

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Low-rank tensor completion aims to recover missing entries from the observed data. However, the observed data may be disturbed by noise and outliers. Therefore, robust tensor completion (RTC) is proposed to solve this problem. The recently proposed tensor ring (TR) structure is applied to RTC due to its superior abilities in dealing with high-dimensional data with predesigned TR rank. To avoid manual rank selection and achieve a balance between low-rank component and sparse component, in this paper, we propose a Bayesian robust tensor ring (BRTR) decomposition method for RTC problem. Furthermore, we develop a variational Bayesian (VB) algorithm to infer the probability distribution of posteriors. During the learning process, the frontal slices of previous tensor and horizontal slices of latter tensor shared with the same TR rank with zero components are pruned, resulting in automatic rank determination. Compared with existing methods, BRTR can automatically learn TR rank without manual fine-tuning of parameters. Extensive experiments indicate that BRTR has better recovery performance and ability to remove noise than other state-of-the-art methods.

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“…Many studies [12], [13], [14], [15], [16], [17] have proven that completion methods directly modeling tensors could better preserve the high-dimensional structure information than the ones modeling the tensor matricization. In the literature, two common LR TC methods are LR tensor decomposition-based methods and tensor rank minimization-based methods, respectively.…”

mentioning

confidence: 99%

Tensor Completion Using Bilayer Multimode Low-Rank Prior and Total Variation

Zeng

Chen

Liu

et al. 2024

IEEE Trans. Neural Netw. Learning Syst.

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In this article, we propose a novel bilayer low-rankness measure and two models based on it to recover a low-rank (LR) tensor. The global low rankness of underlying tensor is first encoded by LR matrix factorizations (MFs) to the all-mode matricizations, which can exploit multiorientational spectral low rankness. Presumably, the factor matrices of all-mode decomposition are LR, since local low-rankness property exists in within-mode correlation. In the decomposed subspace, to describe the refined local LR structures of factor/subspace, a new low-rankness insight of subspace: a double nuclear norm scheme is designed to explore the so-called secondlayer low rankness. By simultaneously representing the bilayer low rankness of the all modes of the underlying tensor, the proposed methods aim to model multiorientational correlations for arbitrary N-way (N ≥ 3) tensors. A block successive upper-bound minimization (BSUM) algorithm is designed to solve the optimization problem. Subsequence convergence of our algorithms can be established, and the iterates generated by our algorithms converge to the coordinatewise minimizers in some mild conditions. Experiments on several types of public datasets show that our algorithm can recover a variety of LR tensors from significantly fewer samples than its counterparts.

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Robust to Rank Selection: Low-Rank Sparse Tensor-Ring Completion

Cited by 10 publications

References 59 publications

Incomplete Multiview Clustering via Low-Rank Tensor Ring Completion

Incomplete Multiview Clustering via Low-Rank Tensor Ring Completion

Bayesian Robust Tensor Ring Model for Incomplete Multiway Data

Tensor Completion Using Bilayer Multimode Low-Rank Prior and Total Variation

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