Simulation experiments for an overall similarity index between two hierarchical clusterings

In Morlini and Zani (2011) we have proposed a new dissimilarity index for comparingtwo hierarchical clusterings, on the basis of the whole dendrograms. We havepresented and discussed its basic properties and we have shown that the index canbe decomposed into contributions pertaining to each stage of the hierarchies. Wehave shown the relation of each component of the index with the currently usedcriteria for comparing two partitions, namely the Rand index and the simple matchingcoefficient. We have obtained a similarity index S as the complement to oneof a suggested distance measure and we have shown that its single components Skobtained at each stage k of the hierarchies can be related to the measure Bk suggestedby Fowlkes & Mallows (1983). Finally, we have dealt with the adjustment ofthe similarity index Sk for agreement due to chance. In this paper we report resultsof a series of Monte Carlo experiments aimed at comparing the behavior of S, Skand other similarity measures over different experimental conditions. The first setof simulations is aimed at determining the behavior of the indexes when the clusteringsbeing compared are unrelated. The second set of simulations tries to investigatethe robustness of the indexes with respect to different level of noise.