  Model-based clustering is a technique widely used to group a collection of
units into mutually exclusive groups. There are, however, situations in which
an observation could in principle belong to more than one cluster. In the
context of Next-Generation Sequencing (NGS) experiments, for example, the
signal observed in the data might be produced by two (or more) different
biological processes operating together and a gene could participate in both
(or all) of them. We propose a novel approach to cluster NGS discrete data,
coming from a ChIP-Seq experiment, with a mixture model, allowing each unit to
belong potentially to more than one group: these multiple allocation clusters
can be flexibly defined via a function combining the features of the original
groups without introducing new parameters. The formulation naturally gives rise
to a `zero-inflation group' in which values close to zero can be allocated,
acting as a correction for the abundance of zeros that manifest in this type of
data. We take into account the spatial dependency between observations, which
is described through a latent Conditional Auto-Regressive process that can
reflect different dependency patterns. We assess the performance of our model
within a simulation environment and then we apply it to ChIP-seq real data.
