Uniqueness proof for a family of models sharing features of Tucker's three-mode factor analysis and PARAFAC/CANDECOMP

DOI10.1007/BF02296963zbMath0866.62032OpenAlexW2101815756MaRDI QIDQ676536

Richard A. Harshman, Margaret E. Lundy

Publication date: 24 July 1997

Published in: Psychometrika (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02296963

zbMATH Keywords

principal componentsmultidimensional scalingaxis orientationfactor rotation probleminteracting dimensionsintrinsic axesoblique confactorPARAFAC2parallel profiles modelparallel proportional profilesquadrilinear modelsthree-way DEDICOMtrilinear models

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Applications of statistics to psychology (62P15)

Related Items

Estimating latent trends in multivariate longitudinal data via Parafac2 with functional and structural constraints, Space-time spreading-multiplexing for MIMO wireless communication systems using the PARATUCK-2 tensor model, The special sign indeterminacy of the direct-fitting Parafac2 model: some implications, cautions, and recommendations for simultaneous component analysis, Some uniqueness results for PARAFAC2, Unfoldings and the rank-one approximation of the tensor, An alternating least squares algorithm for PARAFAC2 and three-way DEDICOM, An AO-ADMM Approach to Constraining PARAFAC2 on All Modes

Uses Software

• PARAFAC

Cites Work

• Unnamed Item
• PARAFAC: Parallel factor analysis
• Some uniqueness results for PARAFAC2
• Principal component analysis of three-mode data by means of alternating least squares algorithms
• 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
• A new computational method to fit the weighted Euclidean distance model
• Notes on factorial invariance
• Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young decomposition
• Relations between multidimensional scaling and three-mode factor analysis
• A Decomposition for Three-Way Arrays
• Annotated bibliography of three-mode factor analysis