Two-way standardization and preprocessing of a three-way data set

Abstract

In this paper a transformation of a three-way array is considered, which minimizes a measure of three-way variability. The proposed transformation makes matrices be more comparable with respect to multivariate measures of variability (Rizzi and Vichi, 1995), but it is more general, since both variables and occasions are not constrained to a constant measure of total variability. Furthermore, it reduces the three-way variability of the weighted array, which can influence the application of three-way methods. Hence, a preprocessing of the data set can be carried out, in order to standardize and possibly the data, before performing further analyses.