Asymptotic and Finite Sample Characteristics of Four External Criterion Measures

Finite and asymptotic formulas are derived for the Rand, adjusted Rand, Fowlkes and Mallows, and Jaccard external criterion measures. The formulas were developed for ten clustering situations which have been used previously in the clustering literature. The results indicated that the Jaccard and Fowlkes and Mallows measures were fairly similar. The Rand and adjusted Rand indices formed another similar pair. Weaknesses involving the Rand and the Fowlkes and Mallows indices are noted. Based on these and previous simulation results, it is recommended that the adjusted Rand and Jaccard measures be used in validation studies of clustering algorithms.