  We consider model-based clustering methods for continuous, correlated data
that account for external information available in the presence of mixed-type
fixed covariates by proposing the MoEClust suite of models. These models allow
different subsets of covariates to influence the component weights and/or
component densities by modelling the parameters of the mixture as functions of
the covariates. A familiar range of constrained eigen-decomposition
parameterisations of the component covariance matrices are also accommodated.
This paper thus addresses the equivalent aims of including covariates in
Gaussian parsimonious clustering models and incorporating parsimonious
covariance structures into all special cases of the Gaussian mixture of experts
framework. The MoEClust models demonstrate significant improvement from both
perspectives in applications to both univariate and multivariate data sets.
Novel extensions to include a uniform noise component for capturing outliers
and to address initialisation of the EM algorithm, model selection, and the
visualisation of results are also proposed.
