RepSPD: Enhancing SPD Manifold Representation in EEGs via Dynamic Graphs

2026-02-26

AI Summary

This work addresses the limitations of existing symmetric positive definite (SPD) methods in EEG analysis, which often overlook segment-specific synchronization and local topological structures of brain regions, thereby failing to accurately characterize functional connectivity. To overcome this, the authors propose RepSPD, a novel model that uniquely integrates dynamic graph-driven functional connectivity with SPD manifold representations. The approach leverages a cross-attention mechanism on the Riemannian manifold to modulate the geometric properties of SPD matrices and introduces a global bidirectional alignment strategy to refine tangent space embeddings, effectively mitigating geometric distortions caused by manifold curvature. Extensive experiments demonstrate that RepSPD significantly outperforms state-of-the-art methods across multiple EEG tasks, exhibiting superior robustness and generalization capability.

Technology Category

• Machine Learning: Learning with Manifolds
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Computer Vision: Representation Learning for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• SPD manifold
• EEG
• functional connectivity
• geometric representation
• brain topology

Innovation

• SPD manifold
• geometric deep learning
• dynamic graph
• Riemannian attention
• tangent-space alignment