Simulation experiments for similarity indexes between two hierarchical clusterings

Morlini and Zani (2012) have proposed a new dissimilarity indexfor comparing two hierarchical clusterings on the basis of thewhole dendrograms. They have presented and discussed its basicproperties and have shown that the index can be decomposed intocontributions pertaining to each stage of the hierarchies. Then,they have obtained a similarity index $S$ as the complement to oneof the suggested distance and have shown that its singlecomponents $S_k$ obtained at each stage $k$ of the hierarchies canbe related to the measure $B_k$ suggested by Fowlkes \& Mallows(1983) and to the Rand index $R_k$. In this paper, we reportresults of a series of simulation experiments aimed at comparingthe behavior of these new indexes with other well-establishedsimilarity measures, over different experimental conditions. Thefirst set of simulations is aimed at determining the behavior ofthe indexes when the clusterings being compared are unrelated. Thesecond set tries to investigate the robustness to different levelsof noise