By overlapping clustering I mean clustering where an object may belong to several clusters. By extrinsic evaluation I mean that I have the ground truth (a list of correct clusters) and I want to compare the output of my cluster algorithm against the ground truth. The clustering algorithm needs to determine the number of clusters, so the metrics should be robust against the number of clusters.
Entropy and Purity are likely the most popular. See Zhao and Karypis, 2001 (http://glaros.dtc.umn.edu/gkhome/fetch/papers/vsclusterTR01.pdf). Several pair counting metrics have also been popular, especially in the Information Retrieval community, including Precision, Recall, F1, and Rand Index. Amigo et al, 2009 (http://nlp.uned.es/docs/amigo2007a.pdf), discuss and compare a number of metrics and propose that BCubed metrics better capture clustering quality in diverse scenarios. However, BCubed metrics are less efficient to compute -- O(n^2), where n is the number of items -- as compared to the rest.
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