Clustering Quality Measures

Aiming towards the development of a general clustering theory, addressing issues that are common to the different clustering paradigms, we wish to initiate a systematic study of measures for the quality of a given data clustering. A clustering quality measure is a function that, given a data set and its partition into clusters, returns a non-negative real number representing the quality of that clustering. We analyze what clustering quality measures should look like by introducing a set of requirements (‘axioms’) of clustering quality measures. We propose quality measures for wide families of common clustering approaches, like loss-based clustering, centerbased clustering, and linkage-based clustering. We show that our proposed measures satisfy the axioms and analyze their computational complexity.