Mixture of segmentation for heterogeneous functional data

In this paper, we consider functional data with heterogeneity in time and population. We propose a mixture model with segmentation of time to represent this heterogeneity while keeping the functional struc-ture. The maximum likelihood estimator is considered and proved to be identifiable and consistent. In practice, an EM algorithm is used, combined with dynamic programming for the maximization step, to approximate the maximum likelihood estimator. The method is illustrated on a simulated dataset and used on a real dataset of electricity consumption.