Covariance based low-dimensional registration for function-on-function regression
Monday 24th December 2018
Boschi, T.; Chiaromonte, F.; Secchi, P.; Li, B.
We propose a new low-dimensional registration procedure that exploits the relationship between response and predictor in a function-on-function regression. In this context, Functional Covariance Components (FCC) provide a flexible and powerful tool to represent the data in a low-dimensional space, capturing the most meaningful modes of dependency between the two set of curves. Based on this reduced representation, our procedure aligns simultaneously the two sets of curves, in a way that optimizes the subsequent regression analysis. To implement our procedure, we use both the Continuous Registration algorithm (CR) and a novel parallel algorithm coded in R. We then compare it to other common registration approaches via simulations and an application to the AneuRisk data.