Canonical correlation analysis for irregularly and sparsely observed functional data

Abstract

Several approaches for functional canonical correlation analysis have been developed to measure the association between paired functional data. However, the existing methods in the literature have been developed for dense and balanced functional data, and they cannot be directly applicable to the situations where the observed curves are recorded in the irregular and sparse fashion. In this paper, we model the associations between paired functional data into a linear mixed-effects model framework by relating two sets of curves using canonical correlation analysis. The proposed approach automatically deals with irregularly or sparsely observed functional data, and brings a new insight into the interpretation of canonical correlation analysis. Numerical studies are carried out to demonstrate finite sample behavior. Two real data applications are provided to illustrate the methodology.