Bayesian Clustering of Functional Data Using Local Features

Abstract

The use of exploratory methods is an important step in the understanding of data. When clustering functional data, most methods use traditional clustering techniques on a vector of estimated basis coefficients, assuming that the underlying signal functions live in the $L_2$-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 propose differs in this respect: we employ a model that does not assume that any of the signal functions are truly identical, but possibly share many of their local features, represented by coefficients in a multiresolution wavelet basis expansion. We cluster each wavelet coefficient of the signal functions using conditionally independent Dirichlet process priors, thus focusing on exact matching of local features. We then demonstrate the method using two datasets from different fields to show broad application potential.