Relationships between higher‐order data array configurations and problem formulations in multivariate data analysis

Abstract

A scaffold for detailed understanding of the concept ‘dimensionality’ in data analysis is furnished by a systematic classification of higher‐order data array configurations. Three major types of problem formulation in multivariate data analysis can be characterized for relevant data classes: data description (intra‐class data structure modelling of inter‐object and inter‐variable relationships) classification (inter‐class discrimination) correlation, regression (inter‐variable relationships). The relationship between these three categories of data analytical problem formulation and the fundamental data array classification is exposed. These relations are augmented to include the general case of data arrays of order R, and R‐way data analysis with the use of bilinear projections is presented. Based upon this, some possible directions for the future development of data analysis may be imagined.