Supervised Sparse and Functional Principal Component Analysis

Regularized PCA methods, such as sparse PCA and functional PCA, have been developed to incorporate special features in many real applications. Sometimes additional variables (referred to as supervision) are measured on the same set of samples, which can potentially drive low-rank structures of the primary data of interest.

Classical PCA methods cannot make use of such supervision data. In this paper, we propose a supervised sparse and functional principal component (SupSFPC) framework that can incorporate supervision information to recover underlying structures that are more interpretable. The framework unifies and generalizes several existing methods and flexibly adapts to the practical scenarios at hand.