Modeling spatially dependent functional data via regression with differential regularization

We propose a method for modeling spatially dependent functional data, based on regression with differential regularization. The regularizing term enables to include problem-specific information about the spatio-temporal variation of the phenomenon under study, formalized in terms of a time-dependent...

Full description

Saved in:
Bibliographic Details
Published in:Journal of multivariate analysis 2019-03, Vol.170, p.275-295
Main Authors: Arnone, Eleonora, Azzimonti, Laura, Nobile, Fabio, Sangalli, Laura M.
Format: Article
Language:English
Subjects:
Finite elements
Partial differential equation
Penalized regression
Smoothing
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We propose a method for modeling spatially dependent functional data, based on regression with differential regularization. The regularizing term enables to include problem-specific information about the spatio-temporal variation of the phenomenon under study, formalized in terms of a time-dependent partial differential equation. The method is implemented using a discretization based on finite elements in space and finite differences in time. This non-tensor product basis allows to handle efficiently data distributed over complex domains and where the shape of the domain influences the phenomenon’s behavior. Moreover, the method can comply with specific conditions at the boundary of the domain of interest. Simulation studies compare the proposed model to available techniques for spatio-temporal data. The method is also illustrated via an application to the study of blood-flow velocity field in a carotid artery affected by atherosclerosis, starting from echo-color doppler and magnetic resonance imaging data.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2018.09.006