Robust Granger Analysis in Lp Norm Space for Directed EEG Network Analysis

Granger analysis (GA) is widely used to construct directed brain networks based on various physiological recordings, such as functional magnetic resonance imaging, and electroencephalogram (EEG). However, in real applications, EEGs are inevitably contaminated by unexpected artifacts that may distort the networks because of the L2 norm structure utilized in GAs when estimating directed links. Compared with the L2 norm, the Lp ( ) norm can compress outlier effects. In this paper, an extended GA is constructed by applying the Lp ( ) norm strategy to estimate robust causalities under outlier conditions, and a feasible iteration procedure is utilized to solve the new GA model. A quantitative evaluation using a predefined simulation network demonstrates smaller bias errors and higher linkage consistence for the Lp ( , 0.8, 0.6, 0.4, 0.2) -GAs compared with both the Lasso- and L2-GAs under various simulated outlier conditions. Applications in resting-state EEGs that contain ocular artifacts also show that the proposed GA can effectively compress the ocular outlier influence and recover the reliable networks. The proposed Lp-GA may be helpful in capturing the reliable network structure when EEGs are contaminated with artifacts in related studies.