Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains
By Clara Happ, Sonja Greven. 2015
389 citations recorded by the source corpus.
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, such as functions and images. The theoretical basis for multivariate functional principal component analysis is given in terms of a Karhunen–Loève Theorem. For the practically relevant case of a finite Karhunen–Loève 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.
Subfields: Cognitive Neuroscience, Radiology, Nuclear Medicine and Imaging, Signal Processing
View Paper: https://www.semanticscholar.org/paper/6089d97a06616fda78f735da4736d536f9e4930b
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Citations in the corpus
- Partial Separability and Functional Graphical Models for Multivariate Gaussian Processes (2019, background): “…behavioral tracking (Chiou & M¨uller 2014), blood protein levels (Dubin & M¨uller 2005), traffic measurements (Chiou et al. 2014, 2016), and neuroimaging data (Petersen & M¨uller 2016, Happ & Greven 2018), for which dimensionality reduction and regression have been the primary methods investigated.”