Low-rank matrix completion techniques applied to functional fragments

Functional data analysis is a branch of statistics concerned with complex data objects, such as curves, that can be seen as realizations of a random function. When each curve of a dataset is only observed on a random subinterval of the whole domain of definition, the data are called functional fragments and their analysis is quite challenging. In this talk we will explore how Low-Rank Matrix Completion (LRMC) techniques can be used to analyse this kind of data. In a first time we present a nonparametric covariance function estimator based on LRMC and we give assumptions on the smoothness and rank of the unknown covariance function such that nonparametric estimation is feasible. In a second time we consider the problem of registration for functional fragments, i.e. we assume that the dataset contains both amplitude and phase variations and we want to separate the two types of variations. We propose a registration method using LRMC where the « aligned » fragments, i.e. the data containing amplitude variation only, belong to a low-dimensional space. Both methods are illustrated with simulated and real data.