1.3 Simultaneous Gaussian Model-Based Clustering for Samples of Multiple Origins

Mixture model-based clustering usually assumes that the data arise from a mixture population in order to estimate some hypothetical underlying partition of the dataset. In this work, we are interested in the case where several samples have to be clustered at the same time, that is when the data arise not only from one but possibly from several mixtures. In the multinormal context, we establish a linear stochastic link between the components of the mixtures wich allows to estimate jointly their parameter – estimations are performed here by Maximum of Likelihood – and to classsify simultaneously the diverse samples. We propose several useful models of constraint on this stochastic link, and we give their parameter estimators. The interest of those models is highlighted in a biological context where some birds belonging to several species have to be classified according to their sex. We show firstly that our simultaneous clustering method does improve the partition obtained by clustering independently each sample. We show then that this method is also efficient in order to assess the cluster number when assuming it is ignored. Some additional experiments are finally performed for showing the robustness of our simultaneous clustering method to one of its main assumption relaxing.