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Tensor Decomposition Via Core Tensor Networks
ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2021Tensor decomposition (TD) has shown promising performance in image completion and denoising. Existing methods always aim to decompose one tensor into latent factors or core tensors by optimizing a particular cost function based on a specific tensor model.
Jianfu Zhang 0003 +3 more
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SIAM Journal on Scientific Computing, 2011
A simple nonrecursive form of the tensor decomposition in $d$ dimensions is presented. It does not inherently suffer from the curse of dimensionality, it has asymptotically the same number of parameters as the canonical decomposition, but it is stable and its computation is based on low-rank approximation of auxiliary unfolding matrices.
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A simple nonrecursive form of the tensor decomposition in $d$ dimensions is presented. It does not inherently suffer from the curse of dimensionality, it has asymptotically the same number of parameters as the canonical decomposition, but it is stable and its computation is based on low-rank approximation of auxiliary unfolding matrices.
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Randomized Tensor Wheel Decomposition
SIAM Journal on Scientific ComputingzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mengyu Wang, Yajie Yu, Hanyu Li
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Facial Recognition Using Tensor-Tensor Decompositions
SIAM Journal on Imaging Sciences, 2013A tensor is a multidimensional array. First-order tensors and second-order tensors can be viewed as vectors and matrices, respectively. Tensors of higher order, with the ability to include more information, appear more frequently nowadays in image and signal processing, data mining, biomedical engineering, and so on.
Ning Hao +3 more
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Shape Constrained Tensor Decompositions
2019 IEEE International Conference on Data Science and Advanced Analytics (DSAA), 2019We propose a new low-rank tensor factorization where one mode is coded as a sparse linear combination of elements from an over-complete library. Our method, Shape Constrained Tensor Decomposition (SCTD) is based upon the CANDECOMP/PARAFAC (CP) decomposition which produces r-rank approximations of data tensors via outer products of vectors in each ...
Bethany Lusch +2 more
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On the Decomposition of Modular Tensors (I)
The Annals of Mathematics, 1942The present paper is the second part of [8] (brackets refer to bibliography) referred to below as Part I. We number sections, formulae, theorems, etc. consecutively from those in Part I, and use the same notation. For instance, f is a field of characteristic p with q (?_ cc ) elements; Zi is a t-vector space of dimension n; (5 = 65(n, f) is the full ...
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Tensor Decomposition of Cooperative Games
SIAM Journal on Applied Mathematics, 1975A decomposition theory for n-person games is introduced. A “unique factorization” theorem is proved. In general, every monotonic game has a unique decomposition with a quotient that is either prime or absolutely decomposable. Finally, an application to reliability theory is suggested.
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Decomposition of Tensors of the Classical Groups
Journal of Mathematical Physics, 1967A tensor symmetrization procedure obtained in a recent publication [Phys. Rev. Letters 16, 1058 (1966)] is shown to support rather than disprove Weyl's tensor symmetrization theorem. This ``extended'' symmetrization procedure differs from Weyl's approach in that to construct a subspace irreducible under GL(n, c) one starts with a set of formal states ...
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Spectral Decomposition of the Elasticity Tensor
Journal of Applied Mechanics, 1992The elasticity tensor in anisotropic elasticity can be regarded as a symmetric linear transformation on the nine-dimensional space of second-order tensors. This allows the elasticity tensor to be expressed in terms of its spectral decomposition. The structures of the spectral decompositions are determined by the sets of invariant subspaces that are ...
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Tensor Ring decomposition for context-aware recommendation
Expert Systems With Applications, 2023Jianli Zhao, Jianli Zhao, Yujun Li
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