A Sliced-Wasserstein Framework on Correlation Matrices for EEG Decoding

2026-06-04

AI Summary

This work addresses the sensitivity of covariance descriptors to channel-wise scaling in EEG decoding, which leads to degraded generalization under distribution shifts. To overcome this limitation, the authors propose a Pullback Euclidean Metric-based Sliced Wasserstein framework (PEMSW), which introduces the sliced Wasserstein distance to the manifold of full-rank correlation matrices for the first time. By integrating two novel geometric structures—Off-Log and Log-Scaled—the method achieves scale-invariant domain generalization without incurring additional inference overhead. Experimental results on three EEG datasets demonstrate that the proposed approach significantly improves decoding performance under distribution shifts while maintaining low training costs and zero inference overhead.

Abstract

Electroencephalography (EEG) offers noninvasive, millisecond resolution recordings of neuronal activity and is widely used in neuroscience and healthcare. Many EEG decoding pipelines rely on covariance descriptors for their robustness to noise, but such representations are sensitive to channel-wise scaling. Recent studies have therefore advocated full-rank correlation matrices as a scale-invariant alternative for EEG decoding. In this paper, we propose a general framework for Sliced Wasserstein (SW) discrepancies on manifolds endowed with Pullback Euclidean Metrics (PEMs), termed Pullback Euclidean Metric Sliced Wasserstein (PEMSW). Within this framework, we instantiate two Correlation Sliced-Wasserstein (CorSW) discrepancies on the manifold of full-rank correlation matrices under two recently introduced correlation geometries, \textit{i.e.}, the Off-Log Metric (OLM) and Log-Scaled Metric (LSM). Building on CorSW, we further develop a domain generalization (DG) framework for EEG decoding. Experiments on three EEG datasets demonstrate improved generalization under distribution shifts, with low training overhead and no additional inference cost. The source code is available at https://github.com/ChenHu-ML/CorSW.

Problem

• EEG decoding
• correlation matrices
• domain generalization
• distribution shift
• scale invariance

Innovation

• Sliced-Wasserstein
• Correlation Matrices
• Pullback Euclidean Metric
• Domain Generalization
• EEG Decoding