Decomposition of the Rand index in order to assess both the stability and the number of clusters of a partition
El Moubarki, Lassad; Bertrand, Patrice; Bel Mufti, Ghazi (2012), Decomposition of the Rand index in order to assess both the stability and the number of clusters of a partition. https://basepub.dauphine.fr/handle/123456789/9693
TypeDocument de travail / Working paper
External document linkhttp://hal.archives-ouvertes.fr/hal-00707357
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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.
Subjects / Keywordsrandom noise; resampling; cluster cohesion; cluster isolation; Partition stability
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