News Algorithms for tensor decomposition based on a reduced functional

DOI10.1002/nla.1875zbMath1340.65076arXiv1109.3832OpenAlexW2125655985MaRDI QIDQ5502417

Carmeliza Navasca, Stefan Kindermann

Publication date: 26 August 2015

Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.3832

zbMATH Keywords

nonlinear least squarestensor decompositiontensor rankalternating least squarescomponent matricesKhatri-Rao productbest rank-1 approximation

Mathematics Subject Classification ID

Related Items (2)

Finding a low-rank basis in a matrix subspace ⋮ The Relation Between a Tensor and Its Associated Semi-Symmetric Form

Uses Software

• Matlab
• Multilinear Engine

Cites Work

• Tensor Decompositions and Applications
• On the non-existence of optimal solutions and the occurrence of ``degeneracy in the CANDECOMP/PARAFAC model
• Perturbation theory for linear operators.
• Some convergence results on the regularized alternating least-squares method for tensor decomposition
• Degeneracy in Candecomp/Parafac explained for \(p\times p\times 2\) arrays of rank \(p+1\) or higher
• Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young decomposition
• Explicit Candecomp/Parafac solutions for a contrived 2\(\times 2\times 2\) array of rank three
• Orthogonal Tensor Decompositions
• Rank-One Approximation to High Order Tensors
• A Nonlinear GMRES Optimization Algorithm for Canonical Tensor Decomposition
• A Decomposition for Three-Way Arrays
• Multigrid Accelerated Tensor Approximation of Function Related Multidimensional Arrays
• A Method to Avoid Diverging Components in the Candecomp/Parafac Model for Generic $I\timesJ\times2$ Arrays
• A General Matrix Eigenvalue Algorithm
• A Multilinear Singular Value Decomposition
• On the Best Rank-1 and Rank-(R₁ ,R₂ ,. . .,R_N) Approximation of Higher-Order Tensors
• Low-Rank Approximation of Generic $p \timesq \times2$ Arrays and Diverging Components in the Candecomp/Parafac Model
• Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem

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