  Model-based clustering of moderate or large dimensional data is notoriously
difficult. We propose a model for simultaneous dimensionality reduction and
clustering by assuming a mixture model for a set of latent scores, which are
then linked to the observations via a Gaussian latent factor model. This
approach was recently investigated by Chandra et al. (2023). The authors use a
factor-analytic representation and assume a mixture model for the latent
factors. However, performance can deteriorate in the presence of model
misspecification. Assuming a repulsive point process prior for the
component-specific means of the mixture for the latent scores is shown to yield
a more robust model that outperforms the standard mixture model for the latent
factors in several simulated scenarios. The repulsive point process must be
anisotropic to favor well-separated clusters of data, and its density should be
tractable for efficient posterior inference. We address these issues by
proposing a general construction for anisotropic determinantal point processes.
We illustrate our model in simulations as well as a plant species co-occurrence
dataset.
