Abstract (EN)

During the last decade, stability-based measures became popular in order to validate the results of partitioning methods. Among these measures, those are the simplest and most commonly used estimate the stability of a partition by performing a large number of comparisons between two partitions achieved on distinct perturbed sets. The Rand index provides a simple and easily interpretable way to achieve such comparisons. In this paper, we first propose an additive decomposition of a partitioning stability measure derived from the Rand index. Then, we derive a bi-criterion, which is based both on the isolation and on the cohesion of each individual cluster, in order to assess the optimal number of clusters of a partition. Based on simulated data sets, we compare our approach with the most successful methods for predicting the number of clusters.