  Count data is becoming more and more ubiquitous in a wide range of
applications, with datasets growing both in size and in dimension. In this
context, an increasing amount of work is dedicated to the construction of
statistical models directly accounting for the discrete nature of the data.
Moreover, it has been shown that integrating dimension reduction to clustering
can drastically improve performance and stability. In this paper, we rely on
the mixture of multinomial PCA, a mixture model for the clustering of count
data, also known as the probabilistic clustering-projection model in the
literature. Related to the latent Dirichlet allocation model, it offers the
flexibility of topic modeling while being able to assign each observation to a
unique cluster. We introduce a greedy clustering algorithm, where inference and
clustering are jointly done by mixing a classification variational expectation
maximization algorithm, with a branch & bound like strategy on a variational
lower bound. An integrated classification likelihood criterion is derived for
model selection, and a thorough study with numerical experiments is proposed to
assess both the performance and robustness of the method. Finally, we
illustrate the qualitative interest of the latter in a real-world application,
for the clustering of anatomopathological medical reports, in partnership with
expert practitioners from the Institut Curie hospital.
