We establish a fundamental equivalence between singular value decomposition (SVD) and functional principal components analysis (FPCA) models. The constructive relationship allows 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 functional mixed effect model is fitted to high-resolution morphometric (RAVENS) images. The main directions of morphometric variation in brain volumes are identified and discussed.
Statistical Methodology | Statistical Theory
Zipunnikov, Vadim; Caffo, Brian S.; Yousem, David M.; Davatzikos, Christos; Schwartz, Brian S.; and Crainiceanu, Ciprian, "FUNCTIONAL PRINCIPAL COMPONENTS MODEL FOR HIGH-DIMENSIONAL BRAIN IMAGING" (January 2011). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 223.