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Title: A study of the manifold hypothesis for functional data by using spectral clustering Authors:  Julien Ah-Pine - University of Lyon (France) [presenting]
Anne Francoise Yao - Universite Clermont Auvergne/LMBP (France)
Abstract: Most of functional data clustering methods assume that the observations belong to linear subspaces. This hypothesis may not be verified in practice. To investigate this point we use spectral clustering on functional data. This clustering method uses the eigen-decomposition of the (discrete) Laplacian of the affinity graph of the observations as a Euclidean embedding of the proximity relationships. In this framework, several affinity measures and neighborhood selection procedures can be used in order to approach the non-linear manifold underlying the data. Our experimental results include several real-world clustering tasks and support the manifold hypothesis for functional data.