Clustering with Repulsive Prototypes

Abstract

Although there is no exact definition for the term cluster, in the 2D case, it is fairly easy for human beings to decide which objects belong together. For machines on the other hand, it is hard to determine which objects form a cluster. Depending on the problem, the success of a clustering algorithm depends on the idea of their creators about what a cluster should be. Likewise, each clustering algorithm comprises a characteristic idea of the term cluster. For example the fuzzy c-means algorithm (Kruse et al., Advances in Fuzzy Clustering and Its Applications, Wiley, New York, 2007, pp. 3–30; Höppner et al., Fuzzy Clustering, Wiley, Chichester, 1999) tends to find spherical clusters with equal numbers of objects. Noise clustering (Rehm et al., Soft Computing – A Fusion of Foundations, Methodologies and Applications 11(5):489–494) focuses on finding spherical clusters of user-defined diameter. In this paper, we present an extension to noise clustering that tries to maximize the distances between prototypes. For that purpose, the prototypes behave like repulsive magnets that have an inertia depending on their sum of membership values. Using this repulsive extension, it is possible to prevent that groups of objects are divided into more than one cluster. Due to the repulsion and inertia, we show that it is possible to determine the number and approximate position of clusters in a data set.