Latent Schatten TT Norm for Tensor Completion

Wang, Andong; Song, Xulin; Wu, Xiyin; Lai, Zhihui

doi:10.1109/icassp.2019.8683685

Cited by 8 publications

(14 citation statements)

References 20 publications

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“…Our work is somewhat related to latent-norm based completion methods [37], [38] and Tensor-Ring based completion methods [32], [36], [39]. In [37], Tomioka et al proposed the latent nuclear norm by mode-k unfolding scheme (one mode versus the rest), and shown that it generalizes better than the overlapped nuclear norm [34] when only several modes are low-rank.…”

Section: Related Workmentioning

confidence: 99%

“…Since the mode-k unfolding scheme is significantly-unbalanced, the unfolding matrix is usually unbalanced and the rank is often too small to describe the global information of target tensor. Recently, Wang et al [38] defined a new latent nuclear norm via Tensor Train, however it may still base on the significantly-unbalanced matrix due to the unbalanced k-mode unfolding scheme. In recent years, Wang et al [32] first applied Tensor Ring decomposition by alternating least square (TR-ALS) to incomplete data.…”

Section: Related Workmentioning

confidence: 99%

“…As well-known, in tensor completion, most common definitions of the nuclear norm are overlapped nuclear norm and latent nuclear norm via Tucker/TT rank [34], [35], [37], [38]. These nuclear norms are based on mode-k unfolding scheme (one mode versus the rest) or k-modes unfolding scheme (the first k modes versus the rest), and thus may construct significantly-unbalanced unfoldings.…”

Section: Latent Tensor-ring Nuclear Norm and Frank-wolfe Based Almentioning

confidence: 99%

“…Rank-minimization based method is another type of approach to exploit the low-rank structure of incompleted tensor. Since the tensor rank minimization rank(•) is an NP-hard problem, a number of norms are defined as the convex surrogates of tensor rank, and the most commonly used ones are overlapped nuclear norm [34]- [36] and latent nuclear norm [37], [38]. In [34], the overlapped nuclear norm via Tucker rank was first proposed by assuming all modes are low-rank, while it performs poorly when the target tensor is only lowrank in a certain mode.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, for a significantly-unbalanced matrix of size m × n, the matrix rank substantially fails to capture the global information of the target tensor due to the small upper bound min{m, n}. Besides, the overlapped and latent nuclear norms via Tensor Train are proposed in [35] and [38], respectively. However, these two norms are still based on the unbalanced unfolding scheme, i.e., k-mode unfolding scheme (the first k modes versus the rest).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

An Efficient Tensor Completion Method Via New Latent Nuclear Norm

Sun

Qiu

et al. 2020

IEEE Access

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In tensor completion, the latent nuclear norm is commonly used to induce low-rank structure, while substantially failing to capture the global information due to the utilization of unbalanced unfolding schemes. To overcome this drawback, a new latent nuclear norm equipped with a more balanced unfolding scheme is defined for low-rank regularizer. Moreover, the new latent nuclear norm together with the Frank-Wolfe (FW) algorithm is developed as an efficient completion method by utilizing the sparsity structure of observed tensor. Specifically, both FW linear subproblem and line search only need to access the observed entries, by which we can instead maintain the sparse tensors and a set of small basis matrices during iteration. Most operations are based on sparse tensors, and the closed-form solution of FW linear subproblem can be obtained from rank-one SVD. We theoretically analyze the space-complexity and time-complexity of the proposed method, and show that it is much more efficient over other norm-based completion methods for higher-order tensors. Extensive experimental results of visual-data inpainting demonstrate that the proposed method is able to achieve state-of-the-art performance at smaller costs of time and space, which is very meaningful for the memory-limited equipment in practical applications. INDEX TERMS Tensor completion, tensor ring decomposition, tensor ring rank, latent nuclear norm, image/video inpainting.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Latent Tensor-ring Nuclear Norm and Frank-wolfe Based Almentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An Efficient Tensor Completion Method Via New Latent Nuclear Norm

Sun

Qiu

et al. 2020

IEEE Access

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Tensor Completion Algorithm and Its Applications to Wireless Edge Caching and Hyper- Spectral Imaging

Garg,

Liu,

Ratnarajah

2024

IEEE Access

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In this paper, we present a lightweight tensor completion algorithm with applications in wireless edge caching and hyper-spectral imaging. In wireless edge caching, content popularity's dynamic and selective nature inevitably leads to missing observations. We address this challenge by employing tensor-based models, which are notably practical for imputing missing data. We approach cooperative caching as a problem of third-order tensor completion and prediction, acknowledging the correlations across time, files, and base stations. Given the potentially large content libraries, we modify the latent norm-based Frank-Wolfe (FW) algorithm. This modification, which incorporates multi-rank updates instead of the traditional rank-1 updates, significantly reduces computational time complexity. This advancement facilitates the development of an efficient online caching algorithm. Through simulations using Movielens datasets and comparing them with the conventional FW algorithm, our proposed algorithm demonstrates a reduced computational overhead reduction and improved normalized cache hit rates within linear prediction models. Furthermore, since hyper-spectral images often have missing or corrupted data due to various noise sources, we conduct simulations on hyper-spectral images. From the Pavia University and Pavia City datasets with noisy data, our proposed tensor completion algorithm can recover the original images from heavily interfered with communication noise effectively. The effectiveness of our proposed tensor completion algorithm across various applications, including wireless edge caching and hyper-spectral imaging, accentuates its versatility and significant utility. Its ability to adeptly handle diverse challenges underscores its value as a comprehensive solution for solving intricate data recovery problems.INDEX TERMS Tensor completion, Frank-Wolfe algorithm, wireless edge caching, hyper-spectral imaging.

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

Zhou

Sun

et al. 2023

IEEE Trans. Neural Netw. Learning Syst.

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Latent Schatten TT Norm for Tensor Completion

Cited by 8 publications

References 20 publications

An Efficient Tensor Completion Method Via New Latent Nuclear Norm

An Efficient Tensor Completion Method Via New Latent Nuclear Norm

Tensor Completion Algorithm and Its Applications to Wireless Edge Caching and Hyper- Spectral Imaging

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

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