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Curve registration and clustering are fundamental tools in the analysis offunctional data. While several methods have been developed and explored foreither task individually, limited work has been done to infer functionalclusters and register curves simultaneously. We propose a hierarchical modelfor joint curve clustering and registration. Our proposal combines a Dirichletprocess mixture model for clustering of common shapes, with a reproducingkernel representation of phase variability for registration. We show howinference can be carried out applying standard posterior simulation algorithmsand compare our method to several alternatives in both engineered data and abenchmark analysis of the Berkeley growth data. We conclude our investigationwith an application to time course gene expression.

Joint Clustering and Registration of Functional Data