  In model-based-clustering mixture models are used to group data points into
clusters. A useful concept introduced for Gaussian mixtures by Malsiner Walli
et al (2016) are sparse finite mixtures, where the prior distribution on the
weight distribution of a mixture with $K$ components is chosen in such a way
that a priori the number of clusters in the data is random and is allowed to be
smaller than $K$ with high probability. The number of cluster is then inferred
a posteriori from the data.
  The present paper makes the following contributions in the context of sparse
finite mixture modelling. First, it is illustrated that the concept of sparse
finite mixture is very generic and easily extended to cluster various types of
non-Gaussian data, in particular discrete data and continuous multivariate data
arising from non-Gaussian clusters. Second, sparse finite mixtures are compared
to Dirichlet process mixtures with respect to their ability to identify the
number of clusters. For both model classes, a random hyper prior is considered
for the parameters determining the weight distribution. By suitable matching of
these priors, it is shown that the choice of this hyper prior is far more
influential on the cluster solution than whether a sparse finite mixture or a
Dirichlet process mixture is taken into consideration.
