Multi-Feature Riemannian Hypergraph for Online Test-Time Adaptation of Motor Imagery Brain-Computer Interface

Clinical motor imagery brain-computer interfaces (MI-BCIs) require robust decoding of neural signals without requiring frequent, time-consuming recalibration sessions before every use. However, real-world deployment faces severe performance degradation due to non-stationarity and distribution shifts in EEG and ECoG signals across different days. While hypergraph learning can capture complex, higher-order relationships among samples to improve generalization, existing methods for online transfer learning rely on Euclidean metrics and cosine similarity, completely ignoring the manifold properties of neural covariance matrices. This paper asks how to integrate Riemannian geometry into a hypergraph learning framework to enable effective online test-time adaptation for MI-BCI decoding under cross-day distribution shifts.

The authors propose the Multi-feature Riemannian Hypergraph (MRieHy) framework to bridge the gap between manifold-based transfer learning and higher-order hypergraph modeling. During offline training, MRieHy computes Riemannian means of symmetric positive-definite covariance matrices to align multi-day source distributions. It then extracts two complementary feature representations: deep neural features and covariance matrices.

From these representations, MRieHy constructs two distinct hypergraphs. The covariance hypergraph uses Riemannian distance-based metrics (such as tangent space cosine similarity or Gaussian kernel similarity on the Riemannian manifold) to capture geometry-aware relationships. The deep feature hypergraph relies on standard cosine similarity. These two hypergraphs are fused using adaptively learned combination weights optimized jointly with label projection matrices. During online testing, incoming unlabeled trials are stored in a first-in-first-out buffer, dynamically aligned using Riemannian alignment against the source distribution, and decoded using the pre-learned multi-feature hypergraph classifier.

MRieHy is evaluated on three diverse motor imagery datasets: a private 128-channel ECoG dataset and two public EEG datasets (BCI Competition IV 2a and Stieger2021). The method is compared against ten baseline techniques, including standard deep neural decoders, Riemannian minimum distance to mean classifiers, state-of-the-art online test-time adaptation algorithms (such as Tent, CoTTA, and T-TIME), and Euclidean hypergraph variants.

Experimental results show that MRieHy consistently outperforms all baselines across datasets. On the ECoG dataset, MRieHy achieves an average accuracy of 64.1%, surpassing the second-best ensemble baseline by 1.4% and standard adaptation methods by up to 6.1%. Ablation studies and comparisons with Euclidean hypergraph variants (EuHy and MEuHy) confirm that incorporating Riemannian geometry and multi-feature fusion is essential for handling cross-day distribution shifts in neural signal decoding.