RepSPD: Enhancing SPD Manifold Representation in EEGs via Dynamic Graphs

TL;DR

RepSPD implements a cross-attention mechanism on the Riemannian manifold to modulate the geometric attributes of SPD with graph-derived functional connectivity features, and introduces a global bidirectional alignment strategy to reshape tangent-space embeddings, mitigating geometric distortions caused by curvature and thereby enhancing geometric consistency.

Abstract

Decoding brain activity from electroencephalography (EEG) is crucial for neuroscience and clinical applications. Among recent advances in deep learning for EEG, geometric learning stands out as its theoretical underpinnings on symmetric positive definite (SPD) allows revealing structural connectivity analysis in a physics-grounded manner. However, current SPD-based methods focus predominantly on statistical aggregation of EEGs, with frequency-specific synchronization and local topological structures of brain regions neglected. Given this, we propose RepSPD, a novel geometric deep learning (GDL)-based model. RepSPD implements a cross-attention mechanism on the Riemannian manifold to modulate the geometric attributes of SPD with graph-derived functional connectivity features. On top of this, we introduce a global bidirectional alignment strategy to reshape tangent-space embeddings, mitigating geometric distortions caused by curvature and thereby enhancing geometric consistency. Extensive experiments demonstrate that our proposed framework significantly outperforms existing EEG representation methods, exhibiting superior robustness and generalization capabilities.

Figures (8)

• Figure 1: Concept of SPD point projections from the manifold to tangent space. Our goal is to modulate SPD representations to achieve effective tangent embeddings.
• Figure 2: Overview of the proposed RepSPD . Raw EEG signals and graph-constructed functional connectivity are separately encoded into SPD matrices. These SPD representations are processed via SPDNet to generate query, key, and value matrices for modulating the SPD with cross-attention. Our dynamic graph guided modulation operates on the Riemannian SPD manifold, computing attention weights based on Log-Euclidean distance and modulating the EEG representation with graph structures. A structure-aware loss function, combining task loss and a geometry-level alignment loss $\mathcal{L}_{GeoTop}$, ensures functional-structural consistency and robust discriminative representations in tangent space.
• Figure 3: Accuracy comparison on seizure detection and MI full classification. Bars show the mean accuracy and error bars indicate the standard deviation across 5-fold runs.
• Figure 4: Visualization of tangent-space with 2D PCA. (a) RepSPD produces well-structured clusters. (b) w/o $\mathcal{L}_{GeoTop}$ leads to increased overlap. (c) MAtt captures spatiotemporal patterns via manifold attention but yields looser clusters. (d) SPDNet exhibits the mixing clusters by the second-order statistics.
• Figure 5: Visualization of topological map of brain across different methods. Compared to SPDNet and RepSPD w/o proposed $\mathcal{L}_{GeoTop}$, our RepSPD more accurately restores the functional spatial pattern observed in the ground truth.