# [YS10a] Comparing partitions of two sets of units based on the same variables

**Revue Internationale avec comité de lecture : **
*Journal Advances in Data Analysis and Classification*,

vol. 4(1),

pp. 53-64,
2010

**Mots clés: ** partition, cluster analysis, classification

**Résumé: **
We propose a procedure based on a latent variable model for the comparison of two partitions of different units described by the same set of variables. The null hypothesis here is that the two partitions come from the same underlying mixture
model.We define a method of projecting partitions using a supervised classification method: once one partition is taken as a reference; the individuals of the second data set are allocated to the clusters of the reference partition; it gives two partitions of the
same units of the second data set: the original and the projected one and we evaluate their difference by usual measures of association. The empirical distributions of the
association measures are derived by simulation.