Adjusted Concordance Index: an Extensionl of the Adjusted Rand Index to Fuzzy Partitions

In comparing clustering partitions, the Rand index (RI) and the adjusted Rand index (ARI) are commonly used for measuring the agreement between partitions. Such external validation indexes can be used to quantify how close the clusters are to a reference partition (or to prior knowledge about the data) by counting classified pairs of elements. To evaluate the solution of a fuzzy clustering algorithm, several extensions of the Rand index and other similarity measures to fuzzy partitions have been proposed. An extension of the ARI for fuzzy partitions based on the normalized degree of concordance is proposed. The performance of the proposed index is evaluated through Monte Carlo simulation studies.