Comparing Partitions by Subset Similarities

Abstract

Comparing partitions is an important issue in classification and clustering when comparing results from different methods, parameters, or initializations. A well–established method for comparing partitions is the Rand index but this index is suitable for crisp partitions only. Recently, the Hüllermeier–Rifqi index was introduced which is a generalization of the Rand index to fuzzy partitions. In this paper we introduce a new approach to comparing partitions based on the similarities of their clusters in the sense of set similarity. All three indices, Rand, Hüllermeier–Rifqi, and subset similarity, are reflexive, invariant against row permutations, and invariant against additional empty subsets. The subset similarity index is not a generalization of the Rand index, but produces similar values. Subset similarity yields more intuitive similarities than Hüllermeier–Rifqi when comparing crisp and fuzzy partitions, and yields smoother nonlinear transitions. Finally, the subset similarity index has a lower computational complexity than the Hüllermeier–Rifqi index for large numbers of objects.