What’s in a distance? Exploring the interplay between distance measures and internal cluster validity in multi-objective clustering

摘要

The problem of cluster analysis eludes a unique mathematical definition. Instead, a variety of different instantiations of theproblem can be defined using specific measures of internal cluster validity. In turn, such internal cluster validity measuresrely on quantifying dissimilarity between entities. This article explores the interaction between dissimilarity measures andinternal cluster validity techniques in the context of multi-objective clustering. It does so by contrasting two conceptuallydifferent approaches to multi-objective clustering: the multi-criterion clustering algorithm D-MOCK, designed to optimisedifferent measures of internal cluster validity over a single dissimilarity space, and the multi-view clustering algorithmMVMC, designed to optimise a single measure of internal cluster validity over distinct dissimilarity spaces. Our comparisonhighlights the interchangeable roles of distance functions and measures of internal cluster validity, which paves theway for the future design of a flexible, dual-purpose approach to multi-objective clustering.