  Methods based on Riemannian geometry have proven themselves to be good models
for decoding in brain-computer interfacing (BCI). However, one major drawback
of these methods is that it is not possible to determine what aspect of the
signal the classifier is built on, leaving open the possibility that artifacts
drive classification performance. In areas where artifactual control is
problematic, specifically neurofeedback and BCIs in patient populations, this
has led people to continue to rely on spatial filters as a way of generating
features that are provably brain-related. Furthermore, these methods also
suffer from the curse of dimensionality and are almost infeasible in
high-density online BCI systems. To tackle these drawbacks, we introduce here a
method for computing spatial filters from any linear function in the Riemannian
tangent space, which allows for more efficient classification as well as the
removal of artifact sources from classifiers built on Riemannian methods. We
first prove a fundamental relationship between certain tangent spaces and
spatial filtering methods, including an explanation of common spatial patterns
within this framework, and then validate our proposed approach using an
open-access BCI analysis framework.
