Relational duals of cluster-validity functions for the c-means family

Authors:
Isaac J. Sledge;Timothy C. Havens;James C. Bezdek;James M. Keller
Affiliations:
Electrical and Computer Engineering Department, University of Missouri, Columbia, MO;Electrical and Computer Engineering Department, University of Missouri, Columbia, MO;Electrical and Computer Engineering Department, University of Missouri, Columbia, MO;Electrical and Computer Engineering Department, University of Missouri, Columbia, MO
Venue:
IEEE Transactions on Fuzzy Systems
Year:
2010

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Abstract

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 c-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.