Suboptimal Comparison of Partitions

The distinction between classification and clustering is often based on a priori knowledge of classification labels. However, in the purely theoretical situation where a data-generating model is known, the optimal solutions for clustering do not necessarily correspond to optimal solutions for classification. Exploring this divergence leads us to conclude that no standard measures of either internal or external validation can guarantee a correspondence with optimal clustering performance. We provide recommendations for the suboptimal evaluation of clustering performance. Such suboptimal approaches can provide valuable insight to researchers hoping to add a post hoc interpretation to their clusters. Indices based on pairwise linkage provide the clearest probabilistic interpretation, while a triplet-based index yields information on higher level structures in the data. Finally, a graphical examination of receiver operating characteristics generated from hierarchical clustering dendrograms can convey information that would be lost in any one number summary.