Generalized hard cluster analysis

Wim de Mulder (1)

1 UGENT - Universiteit Gent = Ghent University

In this paper we generalize the hard clustering paradigm. While in this paradigm a data set is subdivided in disjoint clusters, we allow different clusters to have a nonempty intersection. The concept of hard clustering is then analyzed in this general setting, and we show which specific properties hard clusterings possess in comparison to more general clusterings. We also introduce the concept of equivalent clusterings and show that in case of hard clusterings equivalence and equality coincide. However, if more general clusterings are considered, these two concepts differ and this implies the undesired fact that equivalent clusterings can have different representations in the traditional view on clustering. We show how a matrix representation can solve this representation problem.

Keywords: Physical Sciences

Domains: Computer Science [cs]

Wim de Mulder. Generalized hard cluster analysis. International Journal of Computer Mathematics, 2011, pp.1. ⟨10.1080/00207160.2011.560667⟩. ⟨hal-00710046⟩