Simplicity transformations for three-way arrays with symmetric slices, and applications to Tucker-3 models with sparse core arrays
DOI10.1016/j.laa.2008.09.020zbMath1274.62413OpenAlexW2131795393MaRDI QIDQ999774
Jorge N. Tendeiro, Henk A. L. Kiers, Jos M. F. ten Berge
Publication date: 10 February 2009
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://pure.rug.nl/ws/files/111692695/1_s2.0_S0024379508004229_main.pdf
sparse arraysCandecompParafacthree-mode component analysistypical tensorial rankmaximal simplicityTucker transformations
Factor analysis and principal components; correspondence analysis (62H25) Linear transformations, semilinear transformations (15A04) Multilinear algebra, tensor calculus (15A69)
Related Items (3)
Cites Work
- Transforming three-way arrays to maximal simplicity
- Simplicity of core arrays in three-way principal component analysis and the typical rank of \(p\times q\times 2\) arrays
- Principal component analysis of three-mode data by means of alternating least squares algorithms
- A canonical form for a pair of real symmetric matrices that generate a nonsingular pencil
- Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics
- Three-way SIMPLIMAX for oblique rotation of the three-mode factor analysis core to simple structure.
- Typical rank and indscal dimensionality for symmetric three-way arrays of order \(I\times 2\times 2\) or \(I\times 3\times 3\)
- A case of extreme simplicity of the core matrix in three-mode principal components analysis
- The typical rank of tall three-way arrays
- Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young decomposition
- Restrictions on the Reduced Form and the Rank and Order Conditions
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