  In cluster analysis, it can be useful to interpret the partition built from
the data in the light of external categorical variables which were not directly
involved to cluster the data. An approach is proposed in the model-based
clustering context to select a model and a number of clusters which both fit
the data well and take advantage of the potential illustrative ability of the
external variables. This approach makes use of the integrated joint likelihood
of the data and the partitions at hand, namely the model-based partition and
the partitions associated to the external variables. It is noteworthy that each
mixture model is fitted by the maximum likelihood methodology to the data,
excluding the external variables which are used to select a relevant mixture
model only. Numerical experiments illustrate the promising behaviour of the
derived criterion.
