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Relational Duals of Cluster-Validity Functions for the c -Means Family

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4 Author(s)
Isaac J. Sledge ; Electrical and Computer Engineering Department, University of Missouri, Columbia, USA ; Timothy C. Havens ; James C. Bezdek ; James M. Keller

Clustering aims to identify groups of similar objects. To evaluate the results of cluster algorithms, an investigator uses cluster-validity indices. While the theory of cluster validity is well established for vector object data, little effort has been made to extend it to relationship-based data. As such, this paper proposes a theory of reformulation for object-data validity indices so that they can be used to rank the results produced by the relational -means clustering algorithms. More specifically, we create a class of relational validity indices, which is called dual-relational indices, that are guaranteed under certain, but easily met, constraints to produce the same results and, hence, the same cluster counts, as their object-data counterparts.

Published in:

IEEE Transactions on Fuzzy Systems  (Volume:18 ,  Issue: 6 )