Functional connectivity measures, such as partial correlation (PC) and Granger causality, play a key role in identifying interactions among brain regions from functional magnetic resonance imaging (fMRI) time series. Motivated by the generally nonlinear mechanisms generating the blood-oxygen-level dependent signal, the present thesis introduces kernel- based nonlinear counterparts of partial correlation and partial Granger causality (PGC). The form of kernel-induced nonlinearity that “best” models the data is learned through a data-driven approach that optimally combines multiple kernels. Synthetically generated data based on a dynamic causal model are used to validate the proposed approaches in resting-state (RS) fMRI scenarios, highlighting the gains in edge presence and directionality detection performance when compared with the linear PC and existing PGC methods, respectively. Tests on real RS-fMRI data demonstrate that connectivity patterns revealed by linear and nonlinear models exhibit noticeable differences. In particular, the networks estimated by the proposed kernel-based PC approach capture known features of RS networks, while at the same time being more reflective of the underlying structural connectivity, as compared to linear PC networks.
University of Minnesota M.S.E.E. thesis. December 2016. Major: Electrical Engineering. Advisor: Georgios Giannakis. 1 computer file (PDF); v, 35 pages.
Karanikolas, Vasileios Georgios.
Multi-kernel based nonlinear functional connectivity models.
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