Brain-Computer Interfaces (BCIs) are a groundbreaking technology for interacting with external devices using brain signals. Despite advancements, electroencephalogram (EEG)-based Motor Imagery (MI) tasks face challenges like amplitude and phase variability, and complex spatial correlations, with a need for smaller model size and faster inference. This study introduces the LGL-BCI framework, employing a Geometric Deep Learning Framework for EEG processing in non-Euclidean metric spaces, particularly the Symmetric Positive Definite (SPD) Manifold space. LGL-BCI offers robust EEG data representation and captures spatial correlations. We propose an EEG channel selection solution via a feature decomposition algorithm to reduce SPD matrix dimensionality, with a lossless transformation boosting inference speed. Extensive experiments show LGL-BCI's superior accuracy and efficiency compared to current solutions, highlighting geometric deep learning's potential in MI-BCI applications. The efficiency, assessed on two public EEG datasets and two real-world EEG devices, significantly outperforms the state-of-the-art solution in accuracy ($82.54\%$ versus $62.22\%$) with fewer parameters (64.9M compared to 183.7M).

翻译：脑机接口是一种利用大脑信号与外部设备交互的突破性技术。尽管取得了进展，基于脑电图（EEG）的运动想象任务仍面临幅度与相位变异性、复杂空间相关性等挑战，且需要更小的模型尺寸与更快的推理速度。本研究提出LGL-BCI框架，采用几何深度学习框架在非欧几里得度量空间（特别是对称正定流形空间）中进行EEG处理。LGL-BCI提供了稳健的EEG数据表示，并能够捕获空间相关性。我们提出了一种基于特征分解算法的EEG通道选择方案，以降低SPD矩阵的维度，并采用无损变换提升推理速度。大量实验表明，与现有方案相比，LGL-BCI在准确率和效率上具有显著优势，凸显了几何深度学习在MI-BCI应用中的潜力。基于两个公开EEG数据集与两个真实世界EEG设备的效率评估显示，其在准确率（$82.54\%$ 对比 $62.22\%$）和参数数量（64.9M 对比 183.7M）上均显著优于当前最优方案。