A study of divisive clustering with Hausdorff distances for interval data

Abstract

Clustering methods are becoming key as analysts try to understand what knowledge is buried inside contemporary large data sets. This article analyzes the impact of six different Hausdorff distances on sets of multivariate interval data (where, for each dimension, an interval is defined as an observation [a, b] with a ≤ b and with a and b taking values on the real line R1), used as the basis for Chavent’s [15, 16] divisive clustering algorithm. Advantages and disadvantages are summarized for each distance. Comparisons with two other distances for interval data, the Gowda–Diday and Ichino–Yaguchi measures are included. All have specific strengths depending on the type of data present. Global normalization of a distance is not recommended; and care needs to be made when using local normalizations to ensure the features of the underlying data sets are revealed. The study is based on sets of simulated data, and on a real data set.