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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 ...
Tamara G. Kolda
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Exploring the feasibility of tensor decomposition for analysis of fNIRS signals: a comparative study with grand averaging method [PDF]
Frontiers in Neuroscience, 2023 The analysis of functional near-infrared spectroscopy (fNIRS) signals has not kept pace with the increased use of fNIRS in the behavioral and brain sciences.
Jasmine Y. Chan +4 more
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Tensor decomposition of transportation temporal and spatial big data: A brief review [PDF]
Fundamental ResearchRecent development in sensing and communication technologies has made the collection of a large amount of traffic data easy and transportation engineering has entered the big data era.
Linchao Li, Xiang Lin, Bin Ran, Bowen Du
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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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Fast Circulant Tensor Power Method for High-Order Principal Component Analysis
IEEE Access, 2021 To understand high-order intrinsic key patterns in high-dimensional data, tensor decomposition is a more versatile tool for data analysis than standard flat-view matrix models. Several existing tensor models aim to achieve rapid computation of high-order
Taehyeon Kim, Yoonsik Choe
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Block Row Kronecker-Structured Linear Systems With a Low-Rank Tensor Solution
Frontiers in Applied Mathematics and Statistics, 2022 Several problems in compressed sensing and randomized tensor decomposition can be formulated as a structured linear system with a constrained tensor as the solution.
Stijn Hendrikx +3 more
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N Dimensional Tensor Decomposition Recommendation Algorithm Based on User’s Neighbors [PDF]
Jisuanji gongcheng, 2017 Recommendation algorithm based on tensor factorization has low accuracy and data sparseness problem.Therefore,on the basic of the traditional tensor decomposition model,this paper introduces the user nearest neighbor information,and proposes N ...
CHEN Jianmei,SUN Yajun
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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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Tensor Decomposition-Inspired Convolutional Autoencoders for Hyperspectral Anomaly Detection
IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2022 Anomaly detection from hyperspectral images (HSI) is an important task in the remote sensing domain. Considering the three-order characteristics of HSI, many tensor decomposition based hyperspectral anomaly detection (HAD) models have been proposed and ...
Bangyong Sun +4 more
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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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