Results 1 to 10 of about 2,509 (175)
Optimal High-Order Tensor SVD via Tensor-Train Orthogonal Iteration [PDF]
IEEE Transactions on Information Theory, 2022 This paper studies a general framework for high-order tensor SVD. We propose a new computationally efficient algorithm, tensor-train orthogonal iteration (TTOI), that aims to estimate the low tensor-train rank structure from the noisy high-order tensor observation.
Yuchen Zhou, Anru R Zhang, Lili Zheng
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Exact Tensor Completion Using t-SVD [PDF]
IEEE Transactions on Signal Processing, 2017 16 pages, 5 figures, 2 ...
Shuchin Aeron
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Tensor SVD: Statistical and Computational Limits [PDF]
IEEE Transactions on Information Theory, 2018 Typos ...
Anru R Zhang, Dong Xia
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Hot-SVD: higher order t-singular value decomposition for tensors based on tensor–tensor product
Computational and Applied Mathematics, 2022 This paper considers a way of generalizing the t-SVD of third-order tensors (regarded as tubal matrices) to tensors of arbitrary order N (which can be similarly regarded as tubal tensors of order (N-1)). \color{black}Such a generalization is different from the t-SVD for tensors of order greater than three [Martin, Shafer, Larue, SIAM J. Sci.
Yuning Yang, Yang Yuning
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On the Tensor SVD and the Optimal Low Rank Orthogonal Approximation of Tensors [PDF]
SIAM Journal on Matrix Analysis and Applications, 2009 It is known that a higher order tensor does not necessarily have an optimal low rank approximation, and that a tensor might not be orthogonally decomposable (i.e., admit a tensor SVD). We provide several sufficient conditions which lead to the failure of the tensor SVD, and characterize the existence of the tensor SVD with respect to the higher order ...
Yousef Saad
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Grassmannian Optimization for Online Tensor Completion and Tracking With the t-SVD
IEEE Transactions on Signal Processing, 2022 We propose a new fast streaming algorithm for the tensor completion problem of imputing missing entries of a low-tubal-rank tensor using the tensor singular value decomposition (t-SVD) algebraic framework. We show the t-SVD is a specialization of the well-studied block-term decomposition for third-order tensors, and we present an algorithm under this ...
Kyle Gilman +2 more
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Tensor Eigenvalue and SVD from the Viewpoint of Linear Transformation
Axioms, 2023 A linear transformation from vector space to another vector space can be represented as a matrix. This close relationship between the matrix and the linear transformation is helpful for the study of matrices.
Xinzhu Zhao, Bo Dong, Bo Yu, Yan Yu
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Perivascular spaces, diffusion MRI markers and cognitive decline in cerebral small vessel disease [PDF]
Cerebral Circulation - Cognition and BehaviorBackground: MRI markers, including visible perivascular spaces (PVS), diffusion tensor image analysis along the perivascular space (DTI-ALPS) index, and peak width of skeletonized mean diffusivity (PSMD) may capture the earliest pathogenesis of cerebral ...
Gemma Solé-Guardia +11 more
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Unified transformed t-SVD using unfolding tensors for visual inpainting
Computational Visual MediaLow-rank tensor completion (LRTC) restores missing elements in multidimensional visual data; the challenge is representing the inherent structures within this data.
Mengjie Qin +5 more
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On spectral data and tensor decompositions in Finslerian framework [PDF]
AUT Journal of Mathematics and Computing, 2021 The extensions of the Riemannian structure include the Finslerian one, which provided in recent years successful models in various fields like Biology, Physics, GTR, Monolayer Nanotechnology and Geometry of Big Data.
Vladimir Balan
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