  Model-based clustering imposes a finite mixture modelling structure on data
for clustering. Finite mixture models assume that the population is a convex
combination of a finite number of densities, the distribution within each
population is a basic assumption of each particular model. Among all
distributions that have been tried, the generalized hyperbolic distribution has
the advantage that is a generalization of several other methods, such as the
Gaussian distribution, the skew t-distribution, etc. With specific parameters,
it can represent either a symmetric or a skewed distribution. While its
inherent flexibility is an advantage in many ways, it means the estimation of
more parameters than its special and limiting cases. The aim of this work is to
propose a mixture of generalized hyperbolic factor analyzers to introduce
parsimony and extend the method to high dimensional data. This work can be seen
as an extension of the mixture of factor analyzers model to generalized
hyperbolic mixtures. The performance of our generalized hyperbolic factor
analyzers is illustrated on real data, where it performs favourably compared to
its Gaussian analogue.
