Mixture of segmentation for heterogeneous functional data

This type of data is commonly encountered in many fields, including economy (Bugni et al. (2009)), computational biology (Giacofci et al. (2013)) or environmental sciences (Bouveyron et al. (2021a)), to name a few. For an in-depth review of techniques and applications, we refer the interested readers to the books of Ferraty and Vieu (2006) and Ramsay and Silverman (2002, 2005). In many of these applications, such as electricity load, used for illustration here, we observe multiple curves corresponding to several individuals over a given time interval. As a result, one can expect a high heterogeneity of the data, both at the level of the studied individuals, that may correspond to different behavior or consumer profiles, but also on the time dimension where changes of power consumption regimes are likely to occur over the course of one year for instance. To consider a parametric model, homogeneous data is required, both at population and time levels.