Results 11 to 20 of about 21,194 (269)
On the Compressibility of Tensors [PDF]
SIAM Journal on Matrix Analysis and Applications, 2021 Tensors are often compressed by expressing them in low rank tensor formats. In this paper, we develop three methodologies that bound the compressibility of a tensor: (1) Algebraic structure, (2) Smoothness, and (3) Displacement structure. For each methodology, we derive bounds on storage costs that partially explain the abundance of compressible ...
Tianyi Shi, Alex Townsend
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Foundations and Trends® in Machine Learning, 2021 The presence of multidirectional correlations in emerging multidimensional data poses a challenge to traditional regression modeling methods. Traditional modeling methods based on matrix or vector, for example, not only overlook the data’s multidimensional information and lower model performance, but also add additional computations and storage ...
Jiani Liu 0002 +3 more
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Tensor surgery and tensor rank [PDF]
computational complexity, 2018 (accepted for publication in Comm. Complexity)
M. Christandl (Matthias) +1 more
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Symmetric Tensors and Symmetric Tensor Rank [PDF]
SIAM Journal on Matrix Analysis and Applications, 2008 To appear in the SIAM Journal on Matrix Analysis and ...
Comon, Pierre +3 more
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IET Radar, Sonar & Navigation, 2021 In order to improve the accuracy and resolution for transmit beamspace (TB) multiple‐input multiple‐output (MIMO) radar, a search‐free direction‐of‐arrival (DOA) estimation method based on tensor modelling and polynomial rooting is proposed.
Feng Xu, Xiaopeng Yang, Tian Lan
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Tensor-on-Tensor Regression [PDF]
Journal of Computational and Graphical Statistics, 2018 We propose a framework for the linear prediction of a multi-way array (i.e., a tensor) from another multi-way array of arbitrary dimension, using the contracted tensor product. This framework generalizes several existing approaches, including methods to predict a scalar outcome from a tensor, a matrix from a matrix, or a tensor from a scalar.
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Tensors.jl — Tensor Computations in Julia
Journal of Open Research Software, 2019 Tensors.jl is a Julia package that provides efficient computations with symmetric and non-symmetric tensors. The focus is on the kind of tensors commonly used in e.g. continuum mechanics and fluid dynamics.
Kristoffer Carlsson, Fredrik Ekre
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Tensor Completion in Hierarchical Tensor Representations [PDF]
, 2015 Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the reconstruction of tensors of low multi-linear rank in recently introduced hierarchical tensor formats from a small number ...
Holger Rauhut +2 more
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Designs, Codes and Cryptography, 2019 To an arc $\mathcal{A}$ of $\mathrm{PG}(k-1,q)$ of size $q+k-1-t$ we associate a tensor in $\langle ν_{k,t}(\mathcal{A})\rangle^{\otimes k-1}$, where $ν_{k,t}$ denotes the Veronese map of degree $t$ defined on $\mathrm{PG}(k-1,q)$. As a corollary we prove that for each arc $\mathcal{A}$ in $\mathrm{PG}(k-1,q)$ of size $q+k-1-t$, which is not contained ...
Simeon Ball, Michel Lavrauw
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Tensor factorization via transformed tensor-tensor product for image alignment
Numerical Algorithms, 2023 In this paper, we study the problem of a batch of linearly correlated image alignment, where the observed images are deformed by some unknown domain transformations, and corrupted by additive Gaussian noise and sparse noise simultaneously. By stacking these images as the frontal slices of a third-order tensor, we propose to utilize the tensor ...
Sijia Xia, Duo Qiu, Xiongjun Zhang
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