Geometry-aware Common Spatial Patterns for Motor Imagery-based Brian-Computer Interfaces.

Background: The common spatial patterns (CSP) is a widely used EEG feature extractor for motor imagerybased brain-computer interfaces, with the optimal spatial filter formulated as a generalized Rayleigh quotient. However, the traditional CSP uses Euclidean metric, which ignores the specific geometric structure of symmetry positive definite (SPD) matrices, resulting in issues such as swelling effect, noncomplete space, and indefinite matrices. Methods: To address these limitations, this paper introduces three alternative approaches with considering the geometric properties of SPD matrices. The geometry-aware CSP with diagonalization (gaCSPd) replaces the Euclidean means in the joint diagonalization principle of CSP with Riemannian means. The geometry-aware CSP with maximum discriminative information between classes (gaCSPb) aims to find an optimal projection matrix on a Riemannian manifold while maximizing the Riemannian distance between classes. The geometry-aware CSP with maximum within-class variance (gaCSPw) seeks a low-dimensional submanifold with the maximum intra-class variance in the projected data. Results: Experiment results on two BCI competition datasets demonstrate the competitiveness against state-of-the-art methods and confirm the effectiveness of geometry-aware CSP as a feature extractor for motor imagery-based brain-computer interfaces. [ABSTRACT FROM AUTHOR]