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We propose a novel framework for sparse functional clustering that alsoembeds an alignment step. Sparse functional clustering means finding a groupingstructure while jointly detecting the parts of the curves' domains where theirgrouping structure shows the most. Misalignment is a well-known issue infunctional data analysis, that can heavily affect functional clustering resultsif not properly handled. Therefore, we develop a sparse functional clusteringprocedure that accounts for the possible curve misalignment: the coherence ofthe functional measure used in the clustering step to the class where thewarping functions are chosen is ensured, and the well-posedness of the sparseclustering problem is proved. A possible implementing algorithm is alsoproposed, that jointly performs all these tasks: clustering, alignment, anddomain selection. The method is tested on simulated data in various realisticsituations, and its application to the Berkeley Growth Study data and to theAneuRisk65 data set is discussed.

A novel framework for joint sparse clustering and alignment of functional data