On External Measures for Validation of Fuzzy Partitions

摘要

The procedure of evaluating the results of a clustering algorithm is know under the term cluster validity. In general terms, cluster validity criteria can be classified in three categories: internal, external and relative. In this work we focus on the external criteria, which evaluate the results of a clustering algorithm based on a pre-specified structure S, that pertains to the data but which is independent of it. Usually S is a crisp partition (i.e. the data labels), and the most common approach for external validation of fuzzy partitions is to apply measures defined for crisp partitions to fuzzy partitions, using crisp partitions derived (hardened) from them. In this paper we discuss fuzzy generalizations of two well known crisp external measures, which are able to assess the quality of a partition U without the hardening of U. We also define a new external validity measure, that we call DNC index, useful for comparing a fuzzy U to a crisp S. Numerical examples based on four real world data sets are given, demonstrating the higher reliability of the DNC index.