Comparing high-dimensional partitions with the Co-clustering Adjusted Rand Index

Valérie Robert (1, 2) , Yann Vasseur (3) , Vincent Brault (4)

1 LIM - Laboratoire d'Informatique et de Mathématiques
2 Université Paris-Saclay
3 LMO - Laboratoire de Mathématiques d'Orsay
4 SVH - Statistique pour le Vivant et l’Homme

We consider the simultaneous clustering of rows and columns of a matrix and more particularly the ability to measure the agreement between two co-clustering partitions. The new criterion we developed is based on the Adjusted Rand Index and is called the Co-clustering Adjusted Rand Index named CARI. We also suggest new improvements to existing criteria such as the Classification Error which counts the proportion of misclassified cells and the Extended Normalized Mutual Information criterion which is a generalization of the criterion based on mutual information in the case of classic classifications. We study these criteria with regard to some desired properties deriving from the co-clustering context. Experiments on simulated and real observed data are proposed to compare the behavior of these criteria.

Mots clés: Classification error; Adjusted Rand Index; Partition; Coclustering; Agreement; Co-clustering; Mutual information

Domaines: Applications [stat.AP]; Statistiques [stat]; Méthodologie [stat.ME]

Valérie Robert, Yann Vasseur, Vincent Brault. Comparing high-dimensional partitions with the Co-clustering Adjusted Rand Index. Journal of Classification, 2021, 38, pp.158-186. ⟨10.1007/s00357-020-09379-w⟩. ⟨hal-01524832v5⟩