Journal
APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY
Volume 39, Issue 2, Pages 232-250Publisher
WILEY
DOI: 10.1002/asmb.2736
Keywords
Bayesian clustering; Bayesian nonparametrics; functional data analysis
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This paper introduces a novel enriched Dirichlet mixture model for clustering functional data, incorporating functional constraints and bounding the model complexity. The prior process is characterized through a urn scheme, enhancing the interpretability of clustering. Variational Bayes approximation is employed for tractable posterior inference, overcoming computational bottlenecks.
There 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.
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