Direct lingam and visibility graphs for analyzing brain connectivity in BCI

The brain-computer interface (BCI) is a direct pathway of communication between the electrical activity of the brain and an external device. The present paper was aimed to investigate directed connectivity between different areas of the brain during motor imagery (MI)-based BCI. For this purpose, two methods were implemented including, Limited Penetrable Horizontal Visibility Graph (LPHVG) and Direct Lingam. The visibility graph (VG) is a robust algorithm for analyzing complex systems such as the brain. Direct Lingam uses a non-Gaussian model to extract causal links which is appropriate for analyzing large-scale connectivity. First, LPHVG map MI-EEG (electroencephalogram) signals into networks. After extracting the topological features of the networks, a support vector machine classifier was applied to categorize multi-classes MI. The network of all classes was found to be different from one another, and the kappa value of classification was 0.68. The degree sequence of LPHVG was calculated for each channel in order to obtain the direction of brain information flow. Transfer entropy (TE) is used to compute the relations of the channel degree sequence. Therefore, the directed graph between channels was formed. This method is called LPHVG_TE directed graph. The Bayesian network, also known as the Direct LiNGAM model, was implemented for the second method. Finally, images of the LPHVG and Direct Lingam were classified by convolutional neural network (CNN). In this study, Data sets 2a of BCI competition IV was used. The outcomes reveal that the brain network developed by LPHVG (92.7%) might be more effective to distinguish 4 classes of MI than the Direct Lingam (90.6%) and it was shown that graph theory has the potential to get better efficiency of BCI. Graphical abstract