Sparse Multi-task Inverse Covariance Estimation for Connectivity Analysis in EEG Source Space

Understanding how different brain areas interact to generate complex behavior is a primary goal of neuroscience research. One approach, functional connectivity analysis, aims to characterize the connectivity patterns within brain networks. In this paper, we address the problem of discriminative connectivity, i.e. determining the differences in network structure under different experimental conditions. We introduce a novel model called Sparse Multi-task Inverse Covariance Estimation (SMICE) which is capable of estimating a common connectivity network as well as discriminative networks across different tasks. We apply the method to EEG signals after solving the inverse problem of source localization, yielding networks defined on the cortical surface. We propose an efficient algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve SMICE. We apply our newly developed framework to find common and discriminative connectivity patterns for α-oscillations during the Sleep Onset Process (SOP) and during Rapid Eye Movement (REM) sleep. Even though both stages exhibit a similar α-oscillations, we show that the underlying networks are distinct.