ARImp: A Generalized Adjusted Rand Index for Cluster Ensembles

Adjusted Rand Index (ARI) is one of the most popular measure to evaluate the consistency between two partitions of data sets in the areas of pattern recognition. In this paper, ARI is generalized to a new measure, Adjusted Rand Index between a similarity matrix and a cluster partition (ARImp), to evaluate the consistency between a set of clustering solutions (or cluster partitions) and their associated consensus matrix in a cluster ensemble. The generalization property of ARImp from ARI is proved and its preservation of desirable properties of ARI is illustrated with simulated experiments. Also, we show with application experiments on several real data sets that ARImp can serve as a filter to identify the less effective cluster ensemble methods.