A Riemannian Geometry Approach to Reduced and Discriminative Covariance Estimation in Brain Computer Interfaces.

Abstract

Spatial covariance matrices are extensively employed as brain activity descriptors in brain computer interface (BCI) research that, typically, involve the whole array of sensors. Here, we introduce a methodological framework for delineating the subset of sensors, the covariance structure of which offers a reduced, but more powerful, representation of brain's coordination patterns that ultimately leads to reliable mind reading. Adopting a Riemannian geometry approach, we turn the problem of sensor selection as a maximization of a functional that is computed over the manifold of symmetric positive definite (SPD) matrices and encapsulates class separability in a way that facilitates the search among subsets of different size. The introduced optimization task, namely discriminative covariance reduction (DCR), lacks an analytical solution and is tackled via the cross-entropy optimization technique. Based on two different EEG datasets and three distinct classification schemes, we demonstrate that the DCR approach provides a noteworthy gain in terms of accuracy (in some cases exceeding 20%) and a remarkable reduction in classification time (on average 82%). Additionally, results include the intriguing empirical finding that the pattern of selected sensors in the case of disabled persons depends on the type of disability. The proposed DCR framework can speed up the classification time in BCI-systems operating on the SPD manifolds by simultaneously enhancing their reliability. This is achieved without sacrificing the neuroscientific interpretability endowed in the topographical arrangement of the selected sensors. Riemannian geometry is exploited for DCR in BCI systems, in a dimensionality-agnostic manner, guaranteeing improved performance.