Manifold transfer learning

Manifold transfer learning aims to reuse a decoder across sessions, subjects, or even devices by exploiting the SPD manifold's structure to reduce distribution shift, cutting or eliminating per-session calibration. The workhorse is affine-invariance-based recentering (align each domain's geometric mean to the identity), optionally followed by dispersion scaling and rotation (Riemannian Procrustes Analysis); parallel transport moves tangent-space models between reference points, and pooling recentered data enables subject-independent or zero-calibration decoders.

Empirically these methods are among the most reliable transfer techniques for oscillatory and ERP BCI and were central to several BCI-competition-winning pipelines. Limits remain: label shift, strongly non-stationary neurophysiology, and paradigm or electrode changes beyond an affine map are not fixed by geometry alone, and unsupervised alignment can still fail when the target has too few trials or when classes are imbalanced across domains.