Rectifying Geometric Misalignment: Online Source-Free Adaptation for Class-Imbalanced EEG

Electroencephalography (EEG) based Brain-Computer Interfaces (BCIs) often require unsupervised domain adaptation (UDA) to generalize across subjects and sessions. While Riemannian alignment methods like the Riemannian Centering Transformation (RCT) are effective for handling covariate shifts, they implicitly assume balanced class priors. However, in realistic online BCI scenarios, the label distributions vary dynamically (label shift), causing standard alignment techniques to geometrically misalign the target data distributions. In this work, we propose OSPDIM (Online SPD manifold information maximization), a source-free online UDA framework designed to address label shifts on the Riemannian manifold. OSPDIM introduces a manifold-constrained bias parameter into the tangent space mapping, which is optimized via information maximization to correct the geometric skew caused by imbalanced data streams. Unlike offline methods relying on global batch statistics, OSPDIM estimates and corrects geometric bias on-the-fly. Simulations on 2D SPD matrices visually demonstrate that OSPDIM successfully rectifies the misalignment where standard centering fails. Extensive experiments on multiple motor imagery datasets show that OSPDIM significantly outperforms standard Riemannian baselines, particularly in challenging online adaptation scenarios with severe class imbalance, offering a robust solution for practical, plug-and-play BCI systems.

HEEGNet: Hyperbolic Embeddings for EEG

Electroencephalography (EEG)-based brain-computer interfaces facilitate direct communication with a computer, enabling promising applications in human-computer interactions. However, their utility is currently limited because EEG decoding often suffers from poor generalization due to distribution shifts across domains (e.g., subjects). Learning robust representations that capture underlying task-relevant information would mitigate these shifts and improve generalization. One promising approach is to exploit the underlying hierarchical structure in EEG, as recent studies suggest that hierarchical cognitive processes, such as visual processing, can be encoded in EEG. While many decoding methods still rely on Euclidean embeddings, recent work has begun exploring hyperbolic geometry for EEG. Hyperbolic spaces, regarded as the continuous analogue of tree structures, provide a natural geometry for representing hierarchical data. In this study, we first empirically demonstrate that EEG data exhibit hyperbolicity and show that hyperbolic embeddings improve generalization. Motivated by these findings, we propose HEEGNet, a hybrid hyperbolic network architecture to capture the hierarchical structure in EEG and learn domain-invariant hyperbolic embeddings. To this end, HEEGNet combines both Euclidean and hyperbolic encoders and employs a novel coarse-to-fine domain adaptation strategy. Extensive experiments on multiple public EEG datasets, covering visual evoked potentials, emotion recognition, and intracranial EEG, demonstrate that HEEGNet achieves state-of-the-art performance.