Effective Connectivity Estimation by a Hybrid Neural Network, Empirical Wavelet Transform, and Bayesian Optimization

Accurately measuring nonlinear effective connectivity is a crucial step in investigating brain functions. Brain signals like EEG is nonstationary. Many effective connectivity methods have been proposed but they have drawbacks in their models such as a weakness in proposing a way for hyperparameter and time lag selection as well as dealing with non-stationarity of the time series. This paper proposes an effective connectivity model based on a hybrid neural network model which uses Empirical Wavelet Transform (EWT) and a long short-term memory network (LSTM). The best hyperparameters and time lag are selected using Bayesian Optimization (BO). Due to the importance of generalizability in neural networks and calculating GC, an algorithm was proposed to choose the best generalizable weights. The model was evaluated using simulated and real EEG data consisting of attention deficit hyperactivity disorder (ADHD) and healthy subjects. The proposed model's performance on simulated data was evaluated by comparing it with other neural networks, including LSTM, CNN-LSTM, GRU, RNN, and MLP, using a Blocked cross-validation approach. GC of the simulated data was compared with GRU, linear Granger causality (LGC), Kernel Granger Causality (KGC), Partial Directed Coherence (PDC), and Directed Transfer Function (DTF). Our results demonstrated that the proposed model was superior to the mentioned models. Another advantage of our model is robustness against noise. The results showed that the proposed model can identify the connections in noisy conditions. The comparison of the effective connectivity of ADHD and the healthy group showed that the results are in accordance with previous studies.