2019/06/04 by David Sabbagh, Sabbagh, David, Pierre Ablin +7
Neuroscience · #Functional Brain Connectivity Studies #Neural dynamics and brain function #EEG and Brain-Computer Interfaces
paper · pdf · doi:10.48550/arxiv.1906.02687
Magnetoencephalography and electroencephalography (M/EEG) can reveal neuronal\ndynamics non-invasively in real-time and are therefore appreciated methods in\nmedicine and neuroscience. Recent advances in modeling brain-behavior\nrelationships have highlighted the effectiveness of Riemannian geometry for\nsummarizing the spatially correlated time-series from M/EEG in terms of their\ncovariance. However, after artefact-suppression, M/EEG data is often rank\ndeficient which limits the application of Riemannian concepts. In this article,\nwe focus on the task of regression with rank-reduced covariance matrices. We\nstudy two Riemannian approaches that vectorize the M/EEG covariance\nbetween-sensors through projection into a tangent space. The Wasserstein\ndistance readily applies to rank-reduced data but lacks affine-invariance. This\ncan be overcome by finding a common subspace in which the covariance matrices\nare full rank, enabling the affine-invariant geometric distance. We\ninvestigated the implications of these two approaches in synthetic generative\nmodels, which allowed us to control estimation bias of a linear model for\nprediction. We show that Wasserstein and geometric distances allow perfect\nout-of-sample prediction on the generative models. We then evaluated the\nmethods on real data with regard to their effectiveness in predicting age from\nM/EEG covariance matrices. The findings suggest that the data-driven Riemannian\nmethods outperform different sensor-space estimators and that they get close to\nthe performance of biophysics-driven source-localization model that requires\nMRI acquisitions and tedious data processing. Our study suggests that the\nproposed Riemannian methods can serve as fundamental building-blocks for\nautomated large-scale analysis of M/EEG.\n