Nonparametric Registration to Low-Dimensional Functionspaces

Registration aims to decompose amplitude and phase variation of samples of curves. Phase variation is captured by warping functions which monotonically transform the domains of sample curves. Resulting registered curves should then only exhibit amplitude variation. Most existing registration method rely on aligning typical shape features like peaks or valleys to be found in each sample function. It is shown that this is not necessarily an optimal strategy for subsequent statistical data exploration and inference. In this context a major goal is to identify low dimensional linear subspaces of functions that are able to provide accurate approximations of the observed functional data. In this paper we present a registration method where warping functions are defined in such a way that the resulting registered curves span a low dimensional linear function space. Problems of identifiability are discussed in detail, and connections to established registration procedures are analyzed. The method is applied to real and simulated data. contact: laura.sangalli@polimi.it