AMAtt: Manifold Attention Network with Adaptive Log-Euclidean Metrics for Brain Signals

In this paper, we discuss the recognition of electroencephalographic (EEG) signals, which is crucial in order to improve the performance of non-invasive brain-computer interfaces (BCIs). Although deep learning (DL) has achieved considerable advancements in the decoding of EEG signals, it frequently encounters difficulties related to noisy data and non-stationarity challenges. We discuss geometric learning which offers a more robust way to handle EEG signals by leveraging the mathematical structure of the data. We extended the existing Manifold Attention Network (MAtt), a novel deep learning model that applies a manifold attention mechanism to better capture the spatiotemporal patterns of EEG signals. Instead of using traditional Euclidean space, we mapped the data onto a Riemannian symmetric positive definite (SPD) manifold, which allows for more effective feature extraction. One major issue with existing SPD-based deep learning approaches is that they rely on fixed Riemannian metrics, which can be suboptimal. To solve this, we integrate Adaptive Log-Euclidean Metrics (ALEMs)---a learnable metric framework into the MAtt network that adapts to the specific structure of EEG data, improving model performance with minimal extra computation. AMAtt achieves 63.19% accuracy on BCIC-IV-2a and 46.00% on MAMEM-SSVEP-II, outperforming the MAtt baseline by 5.55% and 4.60% respectively. This adaptive geometric approach opens new possibilities for robust, subject-independent EEG decoding, paving the way towards practical BCI systems.