  There is an increasingly rich literature about Bayesian nonparametric models
for clustering functional observations. However, most of the recent proposals
rely on infinite-dimensional characterizations that might lead to overly
complex cluster solutions. In addition, while prior knowledge about the
functional shapes is typically available, its practical exploitation might be a
difficult modeling task. Motivated by an application in e-commerce, we propose
a novel enriched Dirichlet mixture model for functional data. Our proposal
accommodates the incorporation of functional constraints while bounding the
model complexity. To clarify the underlying partition mechanism, we
characterize the prior process through a P\'olya urn scheme. These features
lead to a very interpretable clustering method compared to available
techniques. To overcome computational bottlenecks, we employ a variational
Bayes approximation for tractable posterior inference.
