Bioinformatics Seminar by Sonja Greven (LMU, Germany) -- Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains

Abstract: Existing approaches for multivariate functional principal component analysis
are restricted to data on the same one-dimensional interval.  The presented approach
focuses on multivariate functional data on different domains that may differ in
dimension, e.g.  functions and images.  The theoretical basis for multivariate
functional principal component analysis is given in terms of a Karhunen-Loeve Theorem.
For the practically relevant case of a finite Karhunen-Loeve representation, a
relationship between univariate and multivariate functional principal component analysis
is established.  This offers an estimation strategy to calculate multivariate functional
principal components and scores based on their univariate counterparts.  For the
resulting estimators, asymptotic results are derived.  The approach can be extended to
finite univariate expansions in general, not necessarily orthonormal bases.  It is also
applicable for sparse functional data or data with measurement error.  A flexible R
implementation is available on CRAN.  The new method is shown to be competitive to
existing approaches for data observed on a common one-dimensional domain.  The
motivating application is a neuroimaging study, where the goal is to explore how
longitudinal trajectories of a neuropsychological test score covary with FDG-PET brain
scans at baseline.  Supplementary material, including detailed proofs, additional
simulation results and software is available online.