In the companion paper [C. Maugis and B. Michel,
A non asymptotic penalized criterion for Gaussian mixture model selection. ESAIM: P&S15 (2011) 41–68] , a penalized likelihood
criterion is proposed to select a Gaussian mixture model among a
specific model collection. This criterion depends on unknown
constants which have to be calibrated in practical situations. A
“slope heuristics” method is described and experimented to deal
with this practical problem. In a model-based clustering context,
the specific form of the considered Gaussian mixtures allows us to
detect the noisy variables in order to improve the data clustering
and its interpretation. The behavior of our data-driven criterion
is highlighted on simulated datasets, a curve clustering example
and a genomics application.