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L1-Norm Tucker Tensor Decomposition [PDF]
IEEE Access, 2019 Tucker decomposition is a standard multi-way generalization of Principal-Component Analysis (PCA), appropriate for processing tensor data. Similar to PCA, Tucker decomposition has been shown to be sensitive against faulty data, due to its L2-norm-based ...
Dimitris G. Chachlakis +2 more
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Interpretable nonconvex submodule clustering algorithm using ℓr-induced tensor nuclear norm and ℓ2,p column sparse norm with global convergence guarantees. [PDF]
PLoS ONETensor-based subspace clustering algorithms have garnered significant attention for their high efficiency in clustering high-dimensional data. However, when dealing with 2D image data, traditional vectorization operations in most algorithms tend to ...
Ming Yang +3 more
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Spectral norm of random tensors [PDF]
, 2014 We show that the spectral norm of a random $n_1\times n_2\times \cdots \times n_K$ tensor (or higher-order array) scales as $O\left(\sqrt{(\sum_{k=1}^{K}n_k)\log(K)}\right)$ under some sub-Gaussian assumption on the entries.
Suzuki, Taiji, Tomioka, Ryota
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Norm-Attaining Tensors and Nuclear Operators [PDF]
Mediterranean Journal of Mathematics, 2022 25 pages.
Sheldon Dantas +3 more
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Traffic Data Restoration Method Based on Tensor Weighting and Truncated Nuclear Norm [PDF]
Jisuanji kexue, 2023 The problem of missing data seriously affects a series of activities in intelligent transportation systems,such as monitoring traffic dynamics,predicting traffic flow,and deploying traffic planning through data.Therefore,a traffic flow data ...
WU Jiangnan, ZHANG Hongmei, ZHAO Yongmei, ZENG Hang, HU Gang
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Weighted t-Schatten-p Norm Minimization for Real Color Image Denoising
IEEE Access, 2020 In this paper, to fully exploit the spatial and spectral correlation information, we present a new real color image denoising scheme using tensor Schatten-p norm (t-Schatten-p norm) minimization based on t-SVD to recover the underlying low-rank tensor ...
Min Liu, Xinggan Zhang, Lan Tang
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Dynamic L1-Norm Tucker Tensor Decomposition [PDF]
IEEE Journal of Selected Topics in Signal Processing, 2020 <p>Tucker decomposition is a standard method for processing multi-way (tensor) measurements and finds many applications in machine learning and data mining, among other fields. When tensor measurements arrive in a streaming fashion or are too many to jointly decompose, incremental Tucker analysis is preferred.
Panos P. Markopoulos +3 more
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Hyper-Laplacian Regularized Multi-View Subspace Clustering With a New Weighted Tensor Nuclear Norm
IEEE Access, 2021 In this paper, we present a hyper-Laplacian regularized method WHLR-MSC with a new weighted tensor nuclear norm for multi-view subspace clustering. Specifically, we firstly stack the subspace representation matrices of the different views into a tensor ...
Qingjiang Xiao +4 more
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Nonlinear Transform Induced Tensor Nuclear Norm for Tensor Completion
Journal of Scientific Computing, 2022 Nonlinear transform, tensor nuclear norm, proximal alternating minimization, tensor ...
Ben-Zheng Li +4 more
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The Ideal of σ-Nuclear Operators and Its Associated Tensor Norm
Mathematics, 2020 We introduce a new tensor norm ( σ -tensor norm) and show that it is associated with the ideal of σ -nuclear operators. In this paper, we investigate the ideal of σ -nuclear operators and the σ -tensor norm.
Ju Myung Kim, Keun Young Lee
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