Abstract
A number of methods for the analysis of three-way data are described and shown to be variants of principal components analysis (PCA) of the two-way supermatrix in which each two-way slice is “strung out” into a column vector. The methods are shown to form a hierarchy such that each method is a constrained variant of its predecessor. A strategy is suggested to determine which of the methods yields the most useful description of a given three-way data set.
Keywords
SupermatrixHierarchySet (abstract data type)Principal component analysisMathematicsData setCorrespondence analysisColumn (typography)Hierarchical clusteringComputer scienceData miningAlgorithmAlgebra over a fieldStatisticsCluster analysisPure mathematics
Related Publications
Principal component analysis
Abstract Principal component analysis (PCA) is a multivariate technique that analyzes a data table in which observations are described by several inter‐correlated quantitative d...
Cross-Validatory Choice of the Number of Components From a Principal Component Analysis
A method is described for choosing the number of components to retain in a principal component analysis when the aim is dimensionality reduction. The correspondence between prin...
Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition
An individual differences model for multidimensional scaling is outlined in which individuals are assumed differentially to weight the several dimensions of a common “psychologi...
Tensor Decompositions and Applications
This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or N-way array. Decompositions...
Candelinc: A General Approach to Multidimensional Analysis of Many-Way Arrays with Linear Constraints on Parameters
Very general multilinear models, called CANDELINC, and a practical least-squares fitting procedure, also called CANDELINC, are described for data consisting of a many-way array....
Publication Info
- Year
- 1991
- Type
- article
- Volume
- 56
- Issue
- 3
- Pages
- 449-470
- Citations
- 132
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
132
OpenAlex
Cite This
Henk A. L. Kiers
(1991).
Hierarchical Relations Among Three-Way Methods.
Psychometrika
, 56
(3)
, 449-470.
https://doi.org/10.1007/bf02294485
Identifiers
- DOI
- 10.1007/bf02294485