Bayesian Clustering of Functional Data Using Local Features

The use of exploratory methods is an important step in the understand- ing of data. When clustering functional data, most methods have used traditional clustering techniques on a vector of estimated basis coecients, assuming that the underlying signal functions live in the L2-space. Bayesian methods use models which imply the belief that some observations are realizations from some signal plus noise models with identical underlying signal functions. The method we pro- pose diers in this respect: we employ a model that does not assume that any of the signal functions are truly identical. We cluster each signal coecient using conditionally independent Dirichlet process priors, which leads to exact match- ing of local features, represented by coecients in a multiresolution wavelet basis. We then demonstrate the method using two datasets from dierent elds to show broad application potential.