OBJECTIVE: 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. METHODS: 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. RESULTS: 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. CONCLUSION: 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. SIGNIFICANCE: Riemannian geometry is exploited for DCR in BCI systems, in a dimensionality-agnostic manner, guaranteeing improved performance.
OBJECTIVE: 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. METHODS: 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. RESULTS: 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. CONCLUSION: 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. SIGNIFICANCE: Riemannian geometry is exploited for DCR in BCI systems, in a dimensionality-agnostic manner, guaranteeing improved performance.