Riemannian recentering and alignment

The workhorse family for cross-session and cross-subject robustness in EEG-based BCI, where trials are represented by their spatial covariance matrices, which live on a curved (Riemannian) manifold of symmetric positive-definite matrices. Much of the session-to-session shift is a bulk change in this covariance — a change in overall scale and orientation of the signal statistics — and it can be removed by recentering: whiten each session by its own mean covariance so that, after transport, every session shares a common reference point. Euclidean alignment does the same idea with a simpler, cheaper whitening in the ambient space.

This is powerful because it is unsupervised (the session mean needs no labels), it directly targets the dominant, benign part of the shift, and after recentering a single classifier trained across many subjects can transfer to a new one with little or no calibration. Its limits mirror the covariate-shift picture: recentering corrects a global covariance change but not a task-specific relabeling, and it assumes the shift is well-approximated by that bulk geometric move, which artifact-heavy or strongly non-stationary real-world data can violate.