CGNet: A Complex-valued Graph Network for jointly learning amplitude-phase information in EEG-based brain-computer interfaces.

The synergy between amplitude and phase in electroencephalogram (EEG)-based brain-computer interfaces (BCIs) provides comprehensive and essential insights into neural oscillatory processes. However, constrained by real-valued computation paradigms, most deep learning methods have to process amplitude and phase independently, neglecting their crucial interaction mechanisms. To address this issue, we construct a Complex-valued Graph Network (CGNet) to capture comprehensive information from EEG signals, where both amplitude and phase information are encoded into the complex-valued representation. Specifically, we design a two-scale complex-valued convolutional network to learn local spatio-temporal information, develop a spatial attention module to enhance spatial information learning, and formulate a dynamic graph convolution to capture global temporal dependencies. Furthermore, we extend CGNet to Filter-Band CGNet (FBCGNet), enhancing the model's adaptability to broadband EEG data. Applied to motor imagery and execution BCI tasks, CGNet achieves state-of-the-art classification performance while maintaining computational efficiency comparable to other advanced algorithms. Notably, FBCGNet further improves CGNet's performance. Visualization results show that CGNet can identify the key spatio-temporal information consistent with paradigm principles. In addition, compared with using amplitude or phase alone, CGNet can capture more comprehensive task-related neural activities, thereby showing higher classification performance. CGNet is a promising tool for mining amplitude-phase information and offering more comprehensive neural decoding in EEG-based BCIs.