Weighted Supervised Functional Principal Components Analysis

In functional linear regression, a supervised version of functional principal components analysis (FPCA) can automatically estimate the leading functional principal components (FPCs), which not only represent the major source of variation of the functional predictor but also are simultaneously correlated with the response. However, the existing supervised FPCA (sFPCA) is only applicable to single modal functional data. In this paper, we propose a weighted version of supervised FPCA (w-sFPCA) by considering the adaptive weighting of multi-modal functional predictors. The new w-sFPCA not only assigns corresponding weights to each modal of functional predictors, but also automatically estimates the leading FPCs associated with response variables, representing the main sources of variation in functional predictors. The method is demonstrated to have a better prediction accuracy than the conventional sFPCA method by using one real application on meteorological data and two carefully designed simulation studies.