Functional principal component model for high-dimensional brain imaging

Abstract

We explore a connection between the singular value decomposition (SVD) and functional principal component analysis (FPCA) models in high-dimensional brain imaging applications. We formally link right singular vectors to principal scores of FPCA. This, combined with the fact that left singular vectors estimate principal components, allows us to deploy the numerical efficiency of SVD to fully estimate the components of FPCA, even for extremely high-dimensional functional objects, such as brain images. As an example, a FPCA model is fit to high-resolution morphometric (RAVENS) images. The main directions of morphometric variation in brain volumes are identified and discussed.