Visualising three-way arrays

Abstract

This paper considers the use of the Tensor Singular Value decomposition approximation as a basis for visualising three-way data, particularly in the spirit of the PCA biplot, and proposes a plot based on the orthogonal rank decomposition of a three-way array. It is shown how the decomposition can be used to partition terms as a product of one mode and a combination of the remaining two modes. This allows for a two dimensional representation with triplot axes, similar to PCA biplots.