A sparse rank-1 approximation algorithm for high-order tensors

DOI10.1016/j.aml.2019.106140OpenAlexW2990030052WikidataQ114210611 ScholiaQ114210611MaRDI QIDQ2187088

Manman Dong, Yi Xu, Y. J. Wang

Publication date: 2 June 2020

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2019.106140

zbMATH Keywords

proximal alternating minimization\(l_1\)-regularizationsparse rank-1 approximation

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Numerical optimization and variational techniques (65K10) Vector and tensor algebra, theory of invariants (15A72) Eigenvalues, singular values, and eigenvectors (15A18) Multilinear algebra, tensor calculus (15A69)

Related Items (6)

Existence and uniqueness of positive solution for multilinear systems with generalized strong \(\mathcal{M}\)-tensor ⋮ Best sparse rank-1 approximation to higher-order tensors via a truncated exponential induced regularizer ⋮ Several approximation algorithms for sparse best rank-1 approximation to higher-order tensors ⋮ Tensor decomposition-based alternate sub-population evolution for large-scale many-objective optimization ⋮ Practical approximation algorithms for \(\ell_1\)-regularized sparse rank-1 approximation to higher-order tensors ⋮ The low-rank approximation of fourth-order partial-symmetric and conjugate partial-symmetric tensor

Uses Software

• PMA

Cites Work

• Unnamed Item
• A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis
• Proximal alternating linearized minimization for nonconvex and nonsmooth problems
• Computing the generalized eigenvalues of weakly symmetric tensors
• Formulating an \(n\)-person noncooperative game as a tensor complementarity problem
• Enhancing sparsity by reweighted \(\ell _{1}\) minimization
• Conditions for strong ellipticity of anisotropic elastic materials
• The Drazin inverse of an even-order tensor and its application to singular tensor equations
• Tensor eigenvalues and their applications
• Parameter selection for nonnegative $l_1$ matrix/tensor sparse decomposition
• Preconditioned tensor splitting iterations method for solving multi-linear systems
• Comon's Conjecture, Rank Decomposition, and Symmetric Rank Decomposition of Symmetric Tensors
• Positive Semidefinite Generalized Diffusion Tensor Imaging via Quadratic Semidefinite Programming
• $M$-Tensors and Some Applications
• Low‐rank approximation of tensors via sparse optimization
• Provable Sparse Tensor Decomposition

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