Linear discriminant analysis for interval data

This paper compares different approaches to the multivariate analysis of interval data, focusing on discriminant analysis. Three fundamental approaches are considered. The first approach assumes an uniform distribution in each observed interval, derives the corresponding measures of dispersion and association, and appropriately defines linear combinations of interval variables that maximize the usual discriminant criterion. The second approach expands the original data set into the set of all interval description vertices, and proceeds with a classical analysis of the expanded set. Finally, a third approach replaces each interval by a midpoint and range representation. Resulting representations, using intervals or single points, are discussed and distance based allocation rules are proposed. The three approaches are illustrated on a real data set.