Gradient Synchronization for Multivariate Functional Data: Application to Brain Connectivity

• Activity Number: 521 - Statistical Methods for Functional Data
• Type: Contributed
• Date/Time: Thursday, August 11, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yaqing Chen* and Shu-Chin Lin and Yang Zhou and Owen Carmichael and Hans-Georg Müller and Jane-Ling Wang
• Companies: University of California, Davis and University of California, Davis and University of California, Davis and Louisiana State University and University of California, Davis and University of California, Davis
• Keywords: Alzheimer's disease; Concordance; fMRI; Functional data analysis; Functional connectivity; Pearson correlation

Abstract

Quantifying the association between components of multivariate random curves is of general interest. An important application is assessing functional connectivity based on functional magnetic resonance imaging (fMRI), where one aims to determine the similarity of fMRI signals recorded on anatomically separated brain regions. In the literature, the static temporal Pearson correlation has been the prevailing measure for functional connectivity. However, recent research has revealed temporally changing patterns of functional connectivity, leading to the study of dynamic functional connectivity. This motivates new similarity measures for pairs of random curves that reflect dynamic features of functional similarity. Specifically, we introduce gradient synchronization measures in a general setting that are based on the concordance and discordance of the gradients between paired smooth random functions. We obtain asymptotic normality of the proposed estimates and illustrate the proposed synchronization measures via an application to fMRI data from the Alzheimer's Disease Neuroimaging Initiative and they are found to improve discrimination between subjects with different disease status.