Multiclass Classification Framework of Motor Imagery EEG by Riemannian Geometry Networks

In motor imagery (MI) tasks for brain computer interfaces (BCIs), the spatial covariance matrix (SCM) of electroencephalogram (EEG) signals plays a critical role in accurate classification. Given that SCMs are symmetric positive definite (SPD), Riemannian geometry is widely utilized to extract classification features. However, calculating distances between SCMs is computationally intensive due to operations like eigenvalue decomposition, and classical optimization techniques, such as gradient descent, cannot be directly applied to Riemannian manifolds, making the computation of the Riemannian mean more complex and reliant on iterative methods or approximations. In this paper, we propose a novel multiclass classification framework that integrates Riemannian geometry and neural networks to mitigate these challenges. The framework comprises two modules: a Riemannian module with multiple branches and a classification module. During training, a fusion loss function is introduced to update the branch corresponding to the true label, while other branches are updated using different loss functions along with the classification module. Comprehensive experiments on four sets of MI EEG data demonstrate the efficiency and effectiveness of the proposed model.