Bayesian cluster analysis for registration and clustering homogeneous subgroups in multidimensional functional data

We introduce a new statistical model for clustering populations of functions and multidimensional curves where the domain is a real interval I. We consider that we are given a finite set of observations from a population of curves or functions with values in Rd, for a fixed d≥1 and arguments in I. We are interested in the population background where the clustering is the process of grouping curves into homogeneous sub-populations. In particular, we define a distribution function for each sub-population and use the statistical geometry of the the space of smooth densities to explore a Bayesian model with a spherical Gaussian process prior. We also give the expression of the log-posterior distribution on coefficients resulting from the expansion. Finally, the practical interest of the proposed method is illustrated on simulated and real datasets of multidimensional curves.