An enriched mixture model for functional clustering

Abstract

AbstractThere is an increasingly rich literature about Bayesian nonparametric models for clustering functional observations. Most 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. We characterize the prior process through a urn scheme to clarify the underlying partition mechanism. These features lead to a very interpretable clustering method compared to available techniques. Moreover, we employ a variational Bayes approximation for tractable posterior inference to overcome computational bottlenecks.