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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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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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Randomized CP tensor decomposition
Machine Learning: Science and Technology, 2020 Abstract The CANDECOMP/PARAFAC (CP) tensor decomposition is a popular dimensionality-reduction method for multiway data. Dimensionality reduction is often sought after since many high-dimensional tensors have low intrinsic rank relative to the dimension of the ambient measurement space.
N. Benjamin Erichson +3 more
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Tensor-CUR Decompositions for Tensor-Based Data [PDF]
SIAM Journal on Matrix Analysis and Applications, 2006 Motivated by numerous applications in which the data may be modeled by a variable subscripted by three or more indices, we develop a tensor-based extension of the matrix CUR decomposition. The tensor-CUR decomposition is most relevant as a data analysis tool when the data consist of one mode that is qualitatively different from the others. In this case,
Michael W. Mahoney +2 more
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DAO-CP: Data-Adaptive Online CP decomposition for tensor stream
PLoS ONE, 2022 How can we accurately and efficiently decompose a tensor stream? Tensor decomposition is a crucial task in a wide range of applications and plays a significant role in latent feature extraction and estimation of unobserved entries of data. The problem of
Sangjun Son +3 more
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CoRR, 2016 Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the complicated tensor networks.
Qibin Zhao +4 more
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IEEE Access, 2018 Reliable detection and recovery of a microseismic event in large volume of passive monitoring data is usually a challenging task due to the low signal-to-noise ratio environment.
Naveed Iqbal +5 more
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