The Carroll and Chang conjecture of equal Indscal components when Candecomp/Parafac gives perfect fit

DOI10.1016/j.laa.2008.09.023zbMath1185.65073OpenAlexW2037728586WikidataQ123250571 ScholiaQ123250571MaRDI QIDQ959889

Alwin Stegeman, Mohammed Bennani Dosse, Jos M. F. ten Berge

Publication date: 12 December 2008

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2008.09.023

zbMATH Keywords

equivalencetypical rankthree-way arraysCandecompParafac\(k\)-rankindscal

Mathematics Subject Classification ID

Related Items (3)

Ranks of tensors and a generalization of secant varieties ⋮ Simplicity and typical rank results for three-way arrays ⋮ Generic and typical ranks of multi-way arrays

Cites Work

• Transforming three-way arrays to maximal simplicity
• Simplicity transformations for three-way arrays with symmetric slices, and applications to Tucker-3 models with sparse core arrays
• Some clarifications of the CANDECOMP algorithm applied to INDSCAL
• 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 \(I\times 3\times 3\)
• The assumption of proportional components when Candecomp is applied to symmetric matrices in the context of INDSCAL
• Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young decomposition

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