Coupled Canonical Polyadic Decompositions and (Coupled) Decompositions in Multilinear Rank- $(L_{r,n},L_{r,n},1)$ Terms---Part II: Algorithms

DOI10.1137/140956865zbMath1321.65068OpenAlexW4242200182MaRDI QIDQ5502141

Mikael Sørensen, Lieven De Lathauwer, I. Yu. Domanov

Publication date: 17 August 2015

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

Full work available at URL: https://doi.org/10.1137/140956865

zbMATH Keywords

algorithmnumerical experimentsignal processingcanonical decompositionhigher-order tensorcanonical polyadic decompositionparallel factorpolyadic decompositioncoupled matrix-tensor factorizationcoupled decompositions

Mathematics Subject Classification ID

Related Items (7)

New Uniqueness Conditions for the Canonical Polyadic Decomposition of Third-Order Tensors ⋮ Nonlinear algebra and applications ⋮ On Uniqueness and Computation of the Decomposition of a Tensor into Multilinear Rank-$(1,L_r,L_r)$ Terms ⋮ Bilinear factorizations subject to monomial equality constraints via tensor decompositions ⋮ A note on nonclosed tensor formats ⋮ Fiber Sampling Approach to Canonical Polyadic Decomposition and Application to Tensor Completion ⋮ Coupled Canonical Polyadic Decompositions and (Coupled) Decompositions in Multilinear Rank-$(L_r,n,L_r,n,1)$ Terms---Part I: Uniqueness

Uses Software

• Tensorlab

Cites Work

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• Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
• Tensor Decompositions and Applications
• A randomized algorithm for a tensor-based generalization of the singular value decomposition
• A comparison of algorithms for fitting the PARAFAC model
• Dimensionality reduction in higher-order signal processing and rank-\((R_1,R_2,\ldots,R_N)\) reduction in multilinear algebra
• Optimization-Based Algorithms for Tensor Decompositions: Canonical Polyadic Decomposition, Decomposition in Rank-$(L_r,L_r,1)$ Terms, and a New Generalization
• On the Uniqueness of the Canonical Polyadic Decomposition of Third-Order Tensors---Part I: Basic Results and Uniqueness of One Factor Matrix
• Canonical Polyadic Decomposition of Third-Order Tensors: Reduction to Generalized Eigenvalue Decomposition
• Best Low Multilinear Rank Approximation of Higher-Order Tensors, Based on the Riemannian Trust-Region Scheme
• A Decomposition for Three-Way Arrays
• Blind Separation of Exponential Polynomials and the Decomposition of a Tensor in Rank-$(L_r,L_r,1)$ Terms
• Matrix Analysis
• On the Best Rank-1 and Rank-(R₁ ,R₂ ,. . .,R_N) Approximation of Higher-Order Tensors
• Quasi-Newton Methods on Grassmannians and Multilinear Approximations of Tensors
• Coupled Canonical Polyadic Decompositions and (Coupled) Decompositions in Multilinear Rank-$(L_r,n,L_r,n,1)$ Terms---Part I: Uniqueness
• A Link between the Canonical Decomposition in Multilinear Algebra and Simultaneous Matrix Diagonalization
• Decompositions of a Higher-Order Tensor in Block Terms—Part II: Definitions and Uniqueness
• Applied Multiway Data Analysis

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