Hierarchical Relations Among Three-Way Methods

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.