Nonnegative Tensor Completion via Low-Rank Tucker Decomposition: Model and Algorithm

Chen, Bilian; Sun, Ting; Zhou, Zhehao; Zeng, Yanjun; Cao, Lei

doi:10.1109/access.2019.2929189

Cited by 14 publications

(8 citation statements)

References 25 publications

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“…The Tucker ranks r 1 , r 2 , r 3 of X are the smallest integers such that (2.2) holds [10]. Nonnegative tensor recovery methods via Tucker decomposition can be found in [16,5].…”

Section: Cp Decomposition Tucker Decomposition and Related Tensor Ranksmentioning

confidence: 99%

“…We now investigate the ORL face data in AT & T Laboratories Cambridge [5,13,16]. Using Algorithm 1, we compute best low triple rank approximations of the tensor T f ace .…”

Section: Orl Face Datamentioning

confidence: 99%

“…We now investigate the McGill Calibrated Colour Image Data [5,12]. We choose three colour images: butterfly, flower, and grape, which are illustrated in the first column of Figure 7.…”

Section: Mcgill Calibrated Colour Image Datamentioning

confidence: 99%

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Triple Decomposition and Tensor Recovery of Third Order Tensors

Chen

Bakshi

et al. 2020

Preprint

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In this paper, we introduce a new tensor decomposition for third order tensors, which decomposes a third order tensor to three third order low rank tensors in a balanced way. We call such a decomposition the triple decomposition, and the corresponding rank the triple rank. For a third order tensor, its CP decomposition can be regarded as a special case of its triple decomposition. The triple rank of a third order tensor is not greater than the middle value of the Tucker rank, and is strictly less than the middle value of the Tucker rank for an essential class of examples. These indicate that practical data can be approximated by low rank triple decomposition as long as it can be approximated by low rank CP or Tucker decomposition. This theoretical discovery is confirmed numerically. Numerical tests show that third order tensor data from practical applications such as internet traffic and video image are of low triple ranks. A tensor recovery method based on low rank triple decomposition is proposed. Its convergence and convergence rate are established. Numerical experiments confirm the efficiency of this method.

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“…The Tucker ranks r 1 , r 2 , r 3 of X are the smallest integers such that (2.2) holds [10]. Nonnegative tensor recovery methods via Tucker decomposition can be found in [16,5].…”

Section: Cp Decomposition Tucker Decomposition and Related Tensor Ranksmentioning

confidence: 99%

“…We now investigate the ORL face data in AT & T Laboratories Cambridge [5,13,16]. Using Algorithm 1, we compute best low triple rank approximations of the tensor T f ace .…”

Section: Orl Face Datamentioning

confidence: 99%

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Triple Decomposition and Tensor Recovery of Third Order Tensors

Chen

Bakshi

et al. 2020

Preprint

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show abstract

“…Such a low-rank image completion methodology is mostly based on the concept of tensor completion issues that have been extensively studied [32][33][34][35][36]. There are many tensor decomposition models that are used for image completion tasks, including the fundamental ones, such as CANDECOMP/PARAFAC (CP) [37,38] and Tucker decomposition [39][40][41], as well as tensor networks, such as tensor ring [42], tensor train [43,44], hierarchical Tucker decomposition [45], and other tensor decomposition models [46].…”

Section: Introductionmentioning

confidence: 99%

Image Completion with Hybrid Interpolation in Tensor Representation

Zdunek¹,

Sadowski²

2020

Applied Sciences

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The issue of image completion has been developed considerably over the last two decades, and many computational strategies have been proposed to fill-in missing regions in an incomplete image. When the incomplete image contains many small-sized irregular missing areas, a good alternative seems to be the matrix or tensor decomposition algorithms that yield low-rank approximations. However, this approach uses heuristic rank adaptation techniques, especially for images with many details. To tackle the obstacles of low-rank completion methods, we propose to model the incomplete images with overlapping blocks of Tucker decomposition representations where the factor matrices are determined by a hybrid version of the Gaussian radial basis function and polynomial interpolation. The experiments, carried out for various image completion and resolution up-scaling problems, demonstrate that our approach considerably outperforms the baseline and state-of-the-art low-rank completion methods.

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“…To infer the missing data in the internet network, many research works have been developed, for instance, see [3,31] and the references therein. Using optimization technology to recover incomplete internet traffic data is a very important way, which are somewhat different from the existing methods for dealing with general data recovery [9,10,13,35,51], including Compressive Sensing (CS) [16], Singular Value Thresholding (SVT) algorithm [9] and Low-rank Matrix Fitting (LMaFit) algorithm [50], etc. Since most of the known approaches for missing internet network data are designed based on purely spatial or purely temporal information [26,43,52], sometime their data recovery performance is low.…”

Section: Introductionmentioning

confidence: 99%

A Parallelizable Method for Missing Internet Traffic Tensor Data

Chen¹,

Yu²,

Qi³

et al. 2020

Preprint

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Recovery of internet network traffic data from incomplete observed data is an important issue in internet network engineering and management. In this paper, by fully combining the temporal stability and periodicity features in internet traffic data, a new separable optimization model for internet data recovery is proposed, which is based upon the t-product and the rapid discrete Fourier transform of tensors. Moreover, by using generalized inverse matrices, an easy-to-operate and effective algorithm is proposed. In theory, we prove that under suitable conditions, every accumulation point of the sequence generated by the proposed algorithm is a stationary point of the established model. Numerical simulation results carried on the widely used real-world internet network datasets, show good performance of the proposed method. In the case of moderate sampling rates, the proposed method works very well, its effect is better than that of some existing internet traffic data recovery methods in the literature. The separable structural features presented in the optimization model provide the possibility to design more efficient parallel algorithms.

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Nonnegative Tensor Completion via Low-Rank Tucker Decomposition: Model and Algorithm

Cited by 14 publications

References 25 publications

Triple Decomposition and Tensor Recovery of Third Order Tensors

Triple Decomposition and Tensor Recovery of Third Order Tensors

Image Completion with Hybrid Interpolation in Tensor Representation

A Parallelizable Method for Missing Internet Traffic Tensor Data

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