Results 31 to 40 of about 234,207 (337)
Skew-symmetric tensor decomposition [PDF]
Communications in Contemporary Mathematics, 2019 We introduce the “skew apolarity lemma” and we use it to give algorithms for the skew-symmetric rank and the decompositions of tensors in [Formula: see text] with [Formula: see text] and [Formula: see text]. New algorithms to compute the rank and a minimal decomposition of a tritensor are also presented.
Enrique Esteban Arrondo +3 more
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Tensor Decompositions in Deep Learning [PDF]
CoRR, 2020 The paper surveys the topic of tensor decompositions in modern machine learning applications. It focuses on three active research topics of significant relevance for the community. After a brief review of consolidated works on multi-way data analysis, we consider the use of tensor decompositions in compressing the parameter space of deep learning ...
Bacciu D., Mandic D. P.
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On the Decomposition of Tensors by Contraction [PDF]
Reviews of Modern Physics, 1949 The decomposition of tensors into irreducible representations of the orthogonal groups is calculated for three and four dimensions. The connection is shown with the problem of the allowed values of ordinary and isotopic spin for a given symmetry of the spacial eigenfunction of a nuclear system.
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Tensor Completion Using Kronecker Rank-1 Tensor Train With Application to Visual Data Inpainting
IEEE Access, 2018 The problem of data reconstruction with partly sampled elements under a tensor structure, which is referred to as tensor completion, is addressed in this paper.
Weize Sun, Yuan Chen, Hing Cheung So
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Low Tensor Rank Constrained Image Inpainting Using a Novel Arrangement Scheme
Applied SciencesEmploying low tensor rank decomposition in image inpainting has attracted increasing attention. This study exploited novel tensor arrangement schemes to transform an image (a low-order tensor) to a higher-order tensor without changing the total number of
Shuli Ma +4 more
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Geometric decomposition of the conformation tensor in viscoelastic turbulence
, 2018 This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations.
Gayme, Dennice F. +3 more
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Cohomology and Decomposition of Tensor Product Representations of SL(2,R) [PDF]
, 2002 We analyze the decomposition of tensor products between infinite dimensional (unitary) and finite-dimensional (non-unitary) representations of SL(2,R). Using classical results on indefinite inner product spaces, we derive explicit decomposition formulae,
André van Tonder +26 more
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Proof of a decomposition theorem for symmetric tensors on spaces with constant curvature
, 2008 In cosmological perturbation theory a first major step consists in the decomposition of the various perturbation amplitudes into scalar, vector and tensor perturbations, which mutually decouple.
Straumann, Norbert
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Efficient Tensor Decompositions
, 2020 This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will see how to design efficient algorithms with provable guarantees under mild assumptions, and using beyond worst ...
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A Color Image Watermarking Based on Tensor Analysis
IEEE Access, 2018 Since most of the color image watermarking methods embed the watermark information in each channel or one channel of a color image, the redundant information of the color image cannot be sufficiently utilized, resulting in the poor ability to resist ...
Haiyong Xu +3 more
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