Orthogonal basis transformation layers for EEG-BCI: Geometry-preserving mid-level information fusion on SPD manifolds

In electroencephalogram (EEG)-based brain-computer interfaces (BCIs), robust decoding of non-stationary signals remains a fundamental challenge. Although recent deep learning models have improved performance, they often overlook the intrinsic geometric constraints of covariance-based EEG representations. Motivated by advances in geometric learning, we introduce a deep architecture that integrates an orthogonal transformation on the Stiefel manifold with a log-Euclidean mapping on the symmetric positive definite (SPD) manifold. Specifically, a learnable orthogonal matrix W transforms SPD-structured EEG covariance features via a congruence mapping X ↦ W ⊤ XW without leaving the SPD manifold, and the log-Euclidean step then maps the transformed matrices to a tangent space for subsequent Euclidean operations. Our distinctive contribution is a learnable, Stiefel-constrained congruence alignment applied directly to multiple within-trial SPD covariance views prior to log-Euclidean projection, enabling geometry-preserving mid-level fusion across complementary views (e.g., temporal windows and frequency bands) and explicitly addressing view misalignment under non-stationarity. We evaluate the method on both time-synchronous and time-asynchronous EEG datasets, showing consistent improvements over state-of-the-art baselines in accuracy, robustness, and interpretability. We further analyze the learned manifold-aware components to illustrate how the proposed alignment-and-projection mechanism captures subtle spatiotemporal EEG dynamics and mitigates non-stationarity.