A Constructive Algorithm for Decomposing a Tensor into a Finite Sum of Orthonormal Rank-1 Terms

DOI10.1137/141000658zbMath1323.65039arXiv1407.1593OpenAlexW1795389166MaRDI QIDQ2947059

No author found.

Publication date: 21 September 2015

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.1593

zbMATH Keywords

algorithmnumerical examplessingular value decompositionTucker decompositionCANDECOMP/PARAFAC decompositiontensor decompositionsmultiway arraysorthogonal rank-1 termstensor-train rank-1 series

Mathematics Subject Classification ID

Related Items (9)

SVD-Based Algorithms for the Best Rank-1 Approximation of a Symmetric Tensor ⋮ SOTT: Greedy Approximation of a Tensor as a Sum of Tensor Trains ⋮ Partial orthogonal rank-one decomposition of complex symmetric tensors based on the Takagi factorization ⋮ Orthogonal and unitary tensor decomposition from an algebraic perspective ⋮ Successive partial-symmetric rank-one algorithms for almost unitarily decomposable conjugate partial-symmetric tensors ⋮ A randomized singular value decomposition for third-order oriented tensors ⋮ Orthogonal tensor decomposition and orbit closures from a linear algebraic perspective ⋮ Symmetric tensor decomposition by an iterative eigendecomposition algorithm ⋮ An inexact augmented Lagrangian method for computing strongly orthogonal decompositions of tensors

Uses Software

• TensorToolbox
• Algorithm 862
• TKPSVD

Cites Work

• Tensor Decompositions and Applications
• Tensor-Train Decomposition
• Kruskal's polynomial for \(2 \times{}2 \times{}2\) arrays and a generalization to \(2 \times{}n \times{}n\) arrays
• A singular value decomposition of a \(k\)-way array for a principal component analysis of multiway data, \(\text{PTA-}k\)
• Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young decomposition
• Orthogonal Tensor Decompositions
• On Generic Nonexistence of the Schmidt--Eckart--Young Decomposition for Complex Tensors
• Algorithm 862
• Efficient MATLAB Computations with Sparse and Factored Tensors
• A Multilinear Singular Value Decomposition
• First-Order Perturbation Analysis of Singular Vectors in Singular Value Decomposition
• Sequential Unfolding SVD for Tensors With Applications in Array Signal Processing
• A Rank-Revealing Method with Updating, Downdating, and Applications
• Subtracting a best rank-1 approximation may increase tensor rank

This page was built for publication: A Constructive Algorithm for Decomposing a Tensor into a Finite Sum of Orthonormal Rank-1 Terms