A self-organized recurrent neural network for estimating the effective connectivity and its application to EEG data

Objective: Effective connectivity is an important notion in neuroscience research, useful for detecting the interactions between regions of the brain. New method: Since we are dealing with a dynamic system, it seems that using a dynamic tool could effectively achieve better results. In this paper, a novel approach, called Recurrent Neural Network - Neuron Growth Using Error Whiteness - Granger Causality (RNN-NGUEW-GC) is proposed to estimate the effective connectivity. An RNN is used for predicting and modeling time series and multivariate signals. NGUEW is used to determine the optimum time lag with the help of an error whiteness criterion. When this criterion is not satisfied, the number of neurons in the network input is increased, producing an increase in the time lag. Accordingly, the network achieves a self-organized structure. Finally, causal effects are determined for linear and nonlinear models using the concept of Granger causality. Also, an indicator of the intensity of causality is defined to approximate the strength of the linear interactions based on the structure of the network and the weights of the connections. Conclusions: RNN-NGUEW-GC had a major outcome in terms of both method accuracy on simulation data and prediction of epileptic seizures on the EEG dataset. The main advantages of this method in comparison with other methods of determining the effective connectivity are: 1) there is no need for physiological information; 2) it yields a self-organized network structure. In addition, the calculation of the appropriate time lag using NGUEW is another superiority of this method in comparison with multivariate auto-regressive models.