Results 11 to 20 of about 23,770 (308)
Random Tensor Theory for Tensor Decomposition
Proceedings of the AAAI Conference on Artificial Intelligence, 2022 International audienceWe propose a new framework for tensor decomposition based on trace invariants, which are particular cases of tensor networks. In general, tensor networks are diagrams/graphs that specify a way to "multiply" a collection of tensors ...
Rivasseau, Vincent +2 more
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Symmetric tensor decomposition [PDF]
Linear Algebra and its Applications, 2009 International audienceWe present an algorithm for decomposing a symmetric tensor of dimension n and order d as a sum of of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for symmetric tensors of dimension 2. We exploit the
Mourrain, Bernard +10 more
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Time-Aware Tensor Decomposition for Sparse Tensors
2021 IEEE 8th International Conference on Data Science and Advanced Analytics (DSAA), 2021 © 2021 IEEE.Given a sparse time-evolving tensor, how can we effectively factorize it to accurately discover latent patterns? Tensor decomposition has been extensively utilized for analyzing various multidimensional real-world data.
Ahn, Dawon, Kang, U, Jang, Jun-Gi
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Hermitian Tensor Decompositions [PDF]
SIAM Journal on Matrix Analysis and Applications, 2020 Hermitian tensors are generalizations of Hermitian matrices, but they have very different properties. Every complex Hermitian tensor is a sum of complex Hermitian rank-1 tensors. However, this is not true for the real case. We study basic properties for Hermitian tensors such as Hermitian decompositions and Hermitian ranks. For canonical basis tensors,
Jiawang Nie, Zi Yang
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Counting Tensor Rank Decompositions [PDF]
Universe, 2021 Tensor rank decomposition is a useful tool for geometric interpretation of the tensors in the canonical tensor model (CTM) of quantum gravity. In order to understand the stability of this interpretation, it is important to be able to estimate how many tensor rank decompositions can approximate a given tensor.
Dennis Obster, Naoki Sasakura
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Orthogonal decomposition of tensor trains [PDF]
Linear and Multilinear Algebra, 2021 In this paper we study the problem of decomposing a given tensor into a tensor train such that the tensors at the vertices are orthogonally decomposable. When the tensor train has length two, and the orthogonally decomposable tensors at the two vertices are symmetric, we recover the decomposition by considering random linear combinations of slices ...
Karim Halaseh +2 more
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On the optimization landscape of tensor decompositions [PDF]
Mathematical Programming, 2020 Best paper in the NIPS 2016 Workshop on Nonconvex Optimization for Machine Learning: Theory and Practice.
Rong Ge 0001, Tengyu Ma 0001
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Decomposition Algorithms for Tensors and Polynomials
SIAM Journal on Applied Algebra and Geometry, 2023 19 ...
Antonio Laface +2 more
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Legendre decomposition for tensors*
Journal of Statistical Mechanics: Theory and Experiment, 2019 Abstract We present a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the reconstructed tensor is unique and always minimizes the KL divergence from an input tensor ...
Mahito Sugiyama +2 more
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Orthogonal Tensor Decompositions [PDF]
SIAM Journal on Matrix Analysis and Applications, 2001 The singular value decomposition of a real \(m\times n\) matrix can be reformulated as an orthogonal decomposition in the tensor product \(\mathbb{R}^m \otimes \mathbb{R}^n\). The present paper is concerned with possible generalizations to multiple tensor products \(\mathbb{R}^{m_1} \otimes\cdots \otimes \mathbb{R}^{m_k}\), a prime consideration being ...
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