L1-norm based time-varying brain neural network and its application to dynamic analysis for motor imagery

Objective.Electroencephalogram (EEG)-based motor imagery (MI) brain-computer interface offers a promising way to improve the efficiency of motor rehabilitation and motor skill learning. In recent years, the power of dynamic network analysis for MI classification has been proved. In fact, its usability mainly depends on the accurate estimation of brain connection. However, traditional dynamic network estimation strategies such as adaptive directed transfer function (ADTF) are designed in the L2-norm. Usually, they estimate a series of pseudo connections caused by outliers, which results in biased features and further limits its online application. Thus, how to accurately infer dynamic causal relationship under outlier influence is urgent.Approach.In this work, we proposed a novel ADTF, which solves the dynamic system in the L1-norm space (L1-ADTF), so as to restrict the outlier influence. To enhance its convergence, we designed an iteration strategy with the alternating direction method of multipliers, which could be used for the solution of the dynamic state-space model restricted in the L1-norm space. Furthermore, we compared L1-ADTF to traditional ADTF and its dual extension across both simulation and real EEG experiments.Main results.A quantitative comparison between L1-ADTF and other ADTFs in simulation studies demonstrates that fewer bias errors and more desirable dynamic state transformation patterns can be captured by the L1-ADTF. Application to real MI EEG datasets seriously noised by ocular artifacts also reveals the efficiency of the proposed L1-ADTF approach to extract the time-varying brain neural network patterns, even when more complex noises are involved.Significance.The L1-ADTF may not only be capable of tracking time-varying brain network state drifts robustly but may also be useful in solving a wide range of dynamic systems such as trajectory tracking problems and dynamic neural networks.