Distance-based linear discriminant analysis for interval-valued data

Przemysław Grzegorzewski , Ana Ramos-Guajardo

Abstract

Interval-valued observations arise in many real-life situations as either the precise representation of the objective entity or the representation of incomplete knowledge. Thus given p features observed over a sample of objects belonging to one of two possible classes, each observation can be perceived as a non-empty closed and bounded hyperrectangle on R^p . The aim of the paper is to suggest a p-dimensional classification method for random inter- vals when two or more classes are considered, by the generalization of Fisher’s procedure for linear discriminant analysis. The idea consists of finding a directional vector which maximizes the ratio of the dispersion between the classes and within the classes of the observed hyperrectangles. A classification rule for new observations is also provided and some simulations are carried out to compare the behavior of the proposed classification procedure with respect to other methods known from the literature. Finally, the suggested methodology are applied on a real-life situation example.