Kruskal's condition for uniqueness in Candecomp/Parafac when ranks and \(k\)-ranks coincide

DOI10.1016/j.csda.2004.07.015zbMath1429.62225OpenAlexW2137415203MaRDI QIDQ959148

Jos M. F. ten Berge, Alwin Stegeman

Publication date: 11 December 2008

Published in: Computational Statistics and Data Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.csda.2004.07.015

zbMATH Keywords

uniquenessthree-way arraysCandecompParafac\(k\)-rank

Mathematics Subject Classification ID

Computational methods for problems pertaining to statistics (62-08) Factor analysis and principal components; correspondence analysis (62H25) Multilinear algebra, tensor calculus (15A69)

Related Items (6)

The Optimization Landscape for Fitting a Rank-2 Tensor with a Rank-1 Tensor ⋮ On Kruskal's uniqueness condition for the Candecomp/Parafac decomposition ⋮ Simplicity and typical rank results for three-way arrays ⋮ 2nd special issue on matrix computations and statistics ⋮ Sufficient conditions for uniqueness in Candecomp/Parafac and Indscal with random component matrices ⋮ On uniqueness conditions for Candecomp/Parafac and Indscal with full column rank in one mode

Uses Software

• PARAFAC

Cites Work

• On uniqueness in CANDECOMP/PARAFAC
• Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics
• Typical rank and indscal dimensionality for symmetric three-way arrays of order \(I\times 2\times 2\) or \(I\times 3\times 3\)
• Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young decomposition
• Kruskal's Permutation Lemma and the Identification of CANDECOMP/PARAFAC and Bilinear Models with Constant Modulus Constraints

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