  Deep learning (DL) has been widely investigated in a vast majority of
applications in electroencephalography (EEG)-based brain-computer interfaces
(BCIs), especially for motor imagery (MI) classification in the past five
years. The mainstream DL methodology for the MI-EEG classification exploits the
temporospatial patterns of EEG signals using convolutional neural networks
(CNNs), which have remarkably succeeded in visual images. However, since the
statistical characteristics of visual images depart radically from EEG signals,
a natural question arises whether an alternative network architecture exists
apart from CNNs. To address this question, we propose a novel geometric deep
learning (GDL) framework called Tensor-CSPNet, which characterizes spatial
covariance matrices derived from EEG signals on symmetric positive definite
(SPD) manifolds and fully captures the temporospatiofrequency patterns using
existing deep neural networks on SPD manifolds, integrating with experiences
from many successful MI-EEG classifiers to optimize the framework. In the
experiments, Tensor-CSPNet attains or slightly outperforms the current
state-of-the-art performance on the cross-validation and holdout scenarios in
two commonly-used MI-EEG datasets. Moreover, the visualization and
interpretability analyses also exhibit the validity of Tensor-CSPNet for the
MI-EEG classification. To conclude, in this study, we provide a feasible answer
to the question by generalizing the DL methodologies on SPD manifolds, which
indicates the start of a specific GDL methodology for the MI-EEG
classification.
