Quality assessment in clustering is a long-standing problem. In this contribution we describe some indexes to measure properties of clusterings, taking advantage of the added flexibility provided by fuzzy paradigms. We first present an approach to evaluate some indicators of quality of an individual clustering, by analyzing the co-association matrix. Then we describe a technique to evaluate the similarity of pairs of clusterings by comparing their respective co-association matrices by means of generalizations of well-known indexes of partition comparisons. Finally, we illustrate how some indexes borrowed from spectral graph theory can be used to evaluate clustering stability and diversity in ensembles of several clusterings.
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