Lp (p ≤ 1) Norm Partial Directed Coherence for Directed Network Analysis of Scalp EEGs

Partial directed coherence (PDC), which is capable of estimating directed brain networks in the frequency domain, has been widely used in various physiological recordings such as electroencephalograms (EEGs) and functional magnetic resonance imaging. However, clinical data from EEGs are inevitably contaminated with unexpected outlier artifacts. This will result in biased networks, which are different from the original physiological mechanism because of the L2 norm structure utilized in PDC to estimate the directed links. In this work, we define a new PDC model in the Lp norm (p ≤ 1) space to restrict outlier influence and use a feasible iteration procedure to solve this model for directed network construction. The quantitative evaluation using a predefined simulation network demonstrates that Lp-PDC is more consistent with the predefined networks than LS-PDC and Lasso-PDC under various simulated outlier conditions. Applying the Lp-PDC model to resting-state EEGs with ocular artifacts also show that the proposed PDC can effectively restrict the ocular artifacts to recover the networks, which is also more consistent with the physiological basis. Both simulation and real-life EEG applications demonstrate the efficiency of the proposed PDC in suppressing the influence of outliers in EEG signals, and the proposed Lp-PDC may be helpful to capture reliable causal relationships for related studies contaminated with outlier artifacts.