On the non-existence of optimal solutions and the occurrence of ``degeneracy in the CANDECOMP/PARAFAC model
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Publication:477955
DOI10.1007/s11336-008-9056-1zbMath1301.62121OpenAlexW2076603483WikidataQ41835334 ScholiaQ41835334MaRDI QIDQ477955
Alwin Stegeman, Wim P. Krijnen, Theo K. Dijkstra
Publication date: 10 December 2014
Published in: Psychometrika (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11336-008-9056-1
Factor analysis and principal components; correspondence analysis (62H25) Factorization of matrices (15A23) Multilinear algebra, tensor calculus (15A69) Applications of statistics to psychology (62P15)
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Uses Software
Cites Work
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- The commutation matrix: Some properties and applications
- On Kruskal's uniqueness condition for the Candecomp/Parafac decomposition
- A comparison of algorithms for fitting the PARAFAC model
- Convergence of the sequence of parameters generated by alternating least squares algorithms
- Three-way metric unfolding via alternating weighted least squares
- Simple structure in component analysis techniques for mixtures of qualitative and quantitative variables
- More factors than subjects, tests and treatments: An indeterminacy theorem for canonical decomposition and individual differences scaling
- Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics
- Multilinear models: applications in spectroscopy. With comments by Jan de Leeuw, Pieter M. Kroonenberg and Donald S. Burdick and a rejoinder by the authors
- Computational solutions for the problem of negative saliences and nonsymmetry in INDSCAL
- Degeneracy in Candecomp/Parafac explained for \(p\times p\times 2\) arrays of rank \(p+1\) or higher
- Degeneracy in Candecomp/Parafac and Indscal explained for several three-sliced arrays with a two-valued typical rank
- Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young decomposition
- Hadamard products and multivariate statistical analysis
- Explicit Candecomp/Parafac solutions for a contrived 2\(\times 2\times 2\) array of rank three
- Low-Rank Approximation of Generic $p \timesq \times2$ Arrays and Diverging Components in the Candecomp/Parafac Model
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