Stiefel-SPD Manifold Graph Convolution for End-to-End EEG Learning.

Area of Science:

• Neuroscience
• Machine Learning
• Signal Processing

Background:

• Electroencephalographic (EEG) decoding utilizes second-order covariance structure on the manifold of symmetric positive-definite (SPD) matrices.
• Conventional Euclidean deep networks distort SPD geometry, while Riemannian methods have limitations in adaptivity and computational cost.

Purpose of the Study:

• To propose a fully geometry-consistent deep learning architecture for EEG decoding that preserves manifold structure end-to-end.
• To improve task adaptivity and computational efficiency compared to existing methods.

Main Methods:

• A depthwise-separable convolutional neural network (CNN) generates features with regularized SPD covariances.
• A learnable orthonormal projection on the Stiefel manifold optimizes dimensionality reduction using Riemannian SGD with QR retraction.
• Tangent space graph-SPD aggregation and log-Euclidean mapping are employed for classification.

Main Results:

• The proposed model achieves high accuracy (83.2%/81.5%/79.7%) and improved macro-F1 scores on three public EEG datasets.
• Demonstrates strong separability (macro-AUROC ≈ 0.90) and well-calibrated probabilities (ECE ≤ 0.04).
• Outperforms Euclidean CNNs and Riemannian baselines while maintaining computational pragmatism.

Conclusions:

• Full geometric consistency is crucial for effective EEG decoding, avoiding Euclidean shortcuts and maintaining SPD properties.
• The proposed architecture offers a computationally pragmatic and highly accurate approach for EEG signal analysis.
• This method advances the field of brain-computer interfaces and neural decoding.