Discriminant Analysis of Distributional Data viaFractional Programming

TL;DR

This paper introduces a novel linear discriminant analysis method for classifying distributional data, such as histograms or intervals, using quantile functions and Mallows distance, demonstrated on airline delay data.

Contribution

It proposes a new discriminant analysis approach for distributional data based on quantile functions and fractional programming, extending classification techniques to complex data types.

Findings

Effective classification of airline delay distributions.

Applicable to various distributional data in different domains.

Demonstrated on real-world airline delay data.

Abstract

We address classification of distributional data, where units are described by histogram or interval-valued variables. The proposed approach uses a linear discriminant function where distributions or intervals are represented by quantile functions, under specific assumptions. This discriminant function allows defining a score for each unit, in the form of a quantile function, which is used to classify the units in two a priori groups, using the Mallows distance. There is a diversity of application areas for the proposed linear discriminant method. In this work we classify the airline companies operating in NY airports based on air time and arrival/departure delays, using a full year fights.