EEG feature descriptors and discriminant analysis under Riemannian Manifold perspective

Abstract

Abstract This paper presents a framework to classify motor imagery in the context of multi-class Brain Computer Interface based on electroencephalography (EEG). Covariance matrices are extracted as the EEG signal descriptors, and different dissimilarity metrics on the manifold of Symmetric Positive Definite (SPD) matrices are investigated to classify these covariance descriptors. Specifically, we compare the performance of the Log Euclidean distance, Stein divergence, Kullback–Leibler divergence and Von Neumann divergence. Furthermore, inspired from the conventional Common Spatial Pattern, discriminant analysis performed directly on the SPD manifold using different mentioned metrics are proposed to improve the classification accuracy. We also propose a new feature, namely Heterogeneous Orders Relevance Composition (HORC), by combining different relevance matrices, such as Covariance, Mutual Information or Kernel Matrix under the Tensor Framework and Multiple Kernel fusion. Multi-Class Multi-Kernel Relevance Vector Machine is adopted to provide a sparse classifier and Bayesian confidence prediction. Finally, we compare the performance of total 16 methods on the dataset IIa of the BCI Competition IV. The results shows that the mentioned dissimilarity metrics perform quite equally on the original manifold, whereas the proposed discrimination methods can improve the accuracy by 3–5% on the reduced dimension manifold.