Fuzzy Variant of Affinity Propagation in Comparison to Median Fuzzy c-Means

Authors:
T. Geweniger;D. Zühlke;B. Hammer;Thomas Villmann
Affiliations:
University of Leipzig - Med. Dep., Computational Intelligence Group, Leipzig, Germany 04103;Fraunhofer Institute for Applied Information Technology, Schloss Birlinghoven, Sankt Augustin, Germany 53229;Institute of Computer Science, Clausthal University of Technology, Clausthal-Zellerfeld, Germany;Department of Mathematics/Physics/Informatics, Computational Intelligence Group, University of Applied Sciences Mittweida, Mittweida, Germany 09648
Venue:
WSOM '09 Proceedings of the 7th International Workshop on Advances in Self-Organizing Maps
Year:
2009

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Abstract

In this paper we extend the crisp Affinity Propagation (AP) cluster algorithm to a fuzzy variant. AP is a message passing algorithm based on the max-sum-algorithm optimization for factor graphs. Thus it is applicable also for data sets with only dissimilarities known, which may be asymmetric. The proposed Fuzzy Affinity Propagation algorithm (FAP) returns fuzzy assignments to the cluster prototypes based on a probabilistic interpretation of the usual AP. To evaluate the performance of FAP we compare the clustering results of FAP for different experimental and real world problems with solutions obtained by employing Median Fuzzy c-Means (M-FCM) and Fuzzy c-Means (FCM). As measure for cluster agreements we use a fuzzy extension of Cohen's *** based on t-norms.