SPDAlign: Interpretable Riemannian Alignment for EEG Forward Modeling Shifts

2026-10-05

AI Summary

This study addresses the cross-domain distribution shift caused by the non-stationarity of EEG signals by proposing an unsupervised domain adaptation framework grounded in Riemannian geometry. We theoretically prove that forward modeling shifts can be fully recovered via linear transformations on the symmetric positive definite (SPD) manifold, thereby establishing a globally linear and intrinsically interpretable alignment mechanism. Furthermore, Wasserstein Procrustes optimal transport is introduced to jointly align means and correct rotational discrepancies. Experimental evaluations on both simulated and public EEG datasets demonstrate that the proposed method achieves superior performance, accurately identifies critical frequency bands and spatial patterns, and effectively overcomes inter-subject variability.

Abstract

Electroencephalography (EEG) based brain-computer interfaces enable direct brain-to-device communication for applications such as rehabilitation and communication. However, their practical utility is often limited as the non-stationary nature of the EEG data introduces distribution shifts across domains (e.g., sessions and subjects). Adapting machine learning models to be invariant to these shifts in an unsupervised way, without using costly labeled calibration data, would drastically improve the utility of EEG data. In this work, we use a classic generative model of EEG to study distribution shifts introduced by the domain-specific forward process, which is associated with factors such as head geometry. We theoretically show that such distribution shifts can be recovered solely through linear transformations on the Symmetric Positive Definite manifold. Building on this insight, we propose SPDAlign, an interpretable framework for promoting domain-invariant EEG learning. SPDAlign first aligns the domain-specific means and corrects global rotations across domains using a recent optimal transport technique called Wasserstein Procrustes. We systematically study the proposed approach through simulations and demonstrate its competitive performance on extensive public EEG datasets. Additionally, SPDAlign is a globally linear framework and is intrinsically interpretable, so that the framework can identify frequency ranges of interest, determine the spatial patterns reflecting source-sensor relationships, and address cross-subject variability.

Problem

• EEG
• distribution shift
• domain adaptation
• brain-computer interface
• forward modeling

Innovation

• Symmetric Positive Definite manifold
• Optimal transport
• Wasserstein Procrustes
• Domain adaptation
• Interpretable EEG modeling