  The parsimonious Gaussian mixture models, which exploit an eigenvalue
decomposition of the group covariance matrices of the Gaussian mixture, have
shown their success in particular in cluster analysis. Their estimation is in
general performed by maximum likelihood estimation and has also been considered
from a parametric Bayesian prospective. We propose new Dirichlet Process
Parsimonious mixtures (DPPM) which represent a Bayesian nonparametric
formulation of these parsimonious Gaussian mixture models. The proposed DPPM
models are Bayesian nonparametric parsimonious mixture models that allow to
simultaneously infer the model parameters, the optimal number of mixture
components and the optimal parsimonious mixture structure from the data. We
develop a Gibbs sampling technique for maximum a posteriori (MAP) estimation of
the developed DPMM models and provide a Bayesian model selection framework by
using Bayes factors. We apply them to cluster simulated data and real data
sets, and compare them to the standard parsimonious mixture models. The
obtained results highlight the effectiveness of the proposed nonparametric
parsimonious mixture models as a good nonparametric alternative for the
parametric parsimonious models.
