Clustering with Repulsive Prototypes

Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

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.

Keywords

Air traffic management Fuzzy c-Means Noise clustering Repulsive prototypes 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bezdek, J. C. (1981). Pattern recognition with fuzzy objective function algorithms. New York: Plenum.MATHGoogle Scholar
  2. Dave, R. N., & Krishnapuram, R. (1997). Robust clustering methods: a unified view. IEEE Transactions on Fuzzy Systems, 5, 270–293.CrossRefGoogle Scholar
  3. Gath I., & Geva, A. B. (1989). Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 773–781.CrossRefGoogle Scholar
  4. Gustafson, D. E., & Kessel, W. C. (1979). Fuzzy clustering with a fuzzy covariance matrix. In Proceedings of the IEEE Conference on Decision and Control, San Diego, 761–766.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.German Aerospace CenterBerlinGermany

Personalised recommendations