The domain adaptation (DA) problem on symmetric positive definite (SPD)
manifolds has raised interest in the machine learning community because of the
growing potential for the SPD-matrix representations across many cross-domain
applicable scenarios. However, due to the different underlying space, the
previous experience and solution to the DA problem cannot benefit this new
scenario directly. This study addresses a specific DA problem: the marginal and
conditional distributions differ in the source and target domains on SPD
manifolds. We then formalize this problem from an optimal transport perspective
and derive an optimal transport framework on SPD manifolds for supervised
learning. In addition, we propose a computational scheme under the optimal
transport framework, Deep Optimal Transport (DOT), for general computation,
using the generalized joint distribution adaptation approach and the existing
Riemannian-based network architectures on SPD manifolds. DOT is applied to the
real-world scenario and becomes a specific EEG-BCI classifier against the
cross-session motor-imagery classification from the calibration phase to the
feedback phase. In the experiments, DOT exhibits a marked improvement in the
average accuracy in two highly non-stationary cross-session scenarios in the
EEG-BCI classification, respectively, indicating the proposed methodology's
validity.

该研究提出了一种基于对称正定流形上的最优传输框架的迁移学习方法，并应用于 EEG-BCI 领域的跨会话运动想象分类问题，有效提升了分类的准确率。