Simplicity and typical rank results for three-way arrays
From MaRDI portal
Publication:629174
DOI10.1007/s11336-010-9193-1zbMath1208.62181OpenAlexW2114372649MaRDI QIDQ629174
Publication date: 8 March 2011
Published in: Psychometrika (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11336-010-9193-1
Factor analysis and principal components; correspondence analysis (62H25) Multilinear algebra, tensor calculus (15A69) Basic linear algebra (15A99)
Related Items
A contribution to the visualisation of three-way arrays ⋮ Typical ranks of certain 3-tensors and absolutely full column rank tensors
Cites Work
- Tensor Decompositions and Applications
- Transforming three-way arrays to maximal simplicity
- On uniqueness in CANDECOMP/PARAFAC
- Symmetry transformations for square sliced three-way arrays, with applications to their typical rank
- On Kruskal's uniqueness condition for the Candecomp/Parafac decomposition
- Kruskal's condition for uniqueness in Candecomp/Parafac when ranks and \(k\)-ranks coincide
- The Carroll and Chang conjecture of equal Indscal components when Candecomp/Parafac gives perfect fit
- Simplicity transformations for three-way arrays with symmetric slices, and applications to Tucker-3 models with sparse core arrays
- On uniqueness conditions for Candecomp/Parafac and Indscal with full column rank in one mode
- Generic and typical ranks of multi-way arrays
- 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
- Kruskal's polynomial for \(2 \times{}2 \times{}2\) arrays and a generalization to \(2 \times{}n \times{}n\) arrays
- 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.
- Uniqueness of three-mode factor models with sparse cores: The \(3\times 3\times 3\) case
- Typical rank and indscal dimensionality for symmetric three-way arrays of order \(I\times 2\times 2\) or \(I\times 3\times 3\)
- Typical ranks for \(m\times n\times (m-1)n\) tensors with \(m \leq n\)
- A case of extreme simplicity of the core matrix in three-mode principal components analysis
- The typical rank of tall three-way arrays
- Sufficient conditions for uniqueness in Candecomp/Parafac and Indscal with random component matrices
- 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
- Some Numerical Results on the Rank of Generic Three-Way Arrays over $\mathbb{R}$
- A Link between the Canonical Decomposition in Multilinear Algebra and Simultaneous Matrix Diagonalization
- Kruskal's Permutation Lemma and the Identification of CANDECOMP/PARAFAC and Bilinear Models with Constant Modulus Constraints
