Results 11 to 20 of about 16,615 (264)
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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Smoothed analysis of tensor decompositions [PDF]
Proceedings of the forty-sixth annual ACM symposium on Theory of computing, 2014 Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and tensors analogs of much of the matrix algebra toolkit are unlikely to exist because of hardness results.
Aditya Bhaskara +3 more
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上海师范大学学报. 自然科学版, 2021 By using the sparse scattering characteristics of the millimeter wave channel and the spatial structure of the tensor, a channel estimation method based on random grid tensor decomposition was proposed.
ZHANG Jing +3 more
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A Survey on Tensor Techniques and Applications in Machine Learning
IEEE Access, 2019 This survey gives a comprehensive overview of tensor techniques and applications in machine learning. Tensor represents higher order statistics. Nowadays, many applications based on machine learning algorithms require a large amount of structured high ...
Yuwang Ji, Qiang Wang, Xuan Li, Jie Liu
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