  Transfer learning makes use of data or knowledge in one problem to help solve
a different, yet related, problem. It is particularly useful in brain-computer
interfaces (BCIs), for coping with variations among different subjects and/or
tasks. This paper considers offline unsupervised cross-subject
electroencephalogram (EEG) classification, i.e., we have labeled EEG trials
from one or more source subjects, but only unlabeled EEG trials from the target
subject. We propose a novel manifold embedded knowledge transfer (MEKT)
approach, which first aligns the covariance matrices of the EEG trials in the
Riemannian manifold, extracts features in the tangent space, and then performs
domain adaptation by minimizing the joint probability distribution shift
between the source and the target domains, while preserving their geometric
structures. MEKT can cope with one or multiple source domains, and can be
computed efficiently. We also propose a domain transferability estimation (DTE)
approach to identify the most beneficial source domains, in case there are a
large number of source domains. Experiments on four EEG datasets from two
different BCI paradigms demonstrated that MEKT outperformed several
state-of-the-art transfer learning approaches, and DTE can reduce more than
half of the computational cost when the number of source subjects is large,
with little sacrifice of classification accuracy.
