Linear Manifold Modeling and Graph Estimation based on Multivariate Functional Data with Different Coarseness Scales

Abstract

We develop a high-dimensional graphical modeling approach for functional data where the number of functions exceeds the available sample size. This is accomplished by proposing a sparse estimator for a concentration matrix when identifying linear manifolds. As such, the procedure extends the ideas of the manifold representation for functional data to high-dimensional settings where the number of functions is larger than the sample size. By working in a penalized setting it enriches the functional data framework by estimating sparse undirected graphs that show how functional nodes connect to other functional nodes. The procedure allows multiple coarseness scales to be present in the data and proposes a simultaneous estimation of several related graphs. Its performance is illustrated using a real-life fMRI dataset and with simulated data.

Keywords:

• Graphical lasso
• Group penalty
• Joint estimation
• Multiscale functional data

Supplementary Materials

The supplementary material file contains the proofs, as well as additional figures. Software in the form of R code is available from the corresponding author.

Additional information

Funding

The authors gratefully acknowledge the computational resources provided by the supercomputing facilities of the UCLouvain (CISM/UCL) and the Consortium des Équipements de Calcul Intensif en Fédération Wallonie Bruxelles (CÉCI) funded by the Fond de la Recherche Scientifique de Belgique (F.R.S.-FNRS) under convention 2.5020.11 and by the Walloon Region. We acknowledge as well the support of the KU Leuven Research Fund C1-project C16/20/002.