Results 11 to 20 of about 308,320 (313)
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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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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Varying Coefficient Tensor Models for Brain Imaging [PDF]
, 2005 We revisit a multidimensional varying-coefficient model (VCM), by allowing regressor coefficients to vary smoothly in more than one dimension, thereby extending the VCM of Hastie and Tibshirani.
Marx, Brian D. +2 more
core +1 more source
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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Finsler geometry on higher order tensor fields and applications to high angular resolution diffusion imaging. [PDF]
, 2009 We study 3D-multidirectional images, using Finsler geometry. The application considered here is in medical image analysis, specifically in High Angular Resolution Diffusion Imaging (HARDI) (Tuch et al. in Magn. Reson. Med.
Florack, L.M.J. +7 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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