Modeling Complex EEG Data Distribution on the Riemannian Manifold Toward Outlier Detection and Multimodal Classification

Objective: The usage of Riemannian geometry for Brain-computer interfaces (BCIs) has gained momentum in recent years. Most of the machine learning techniques proposed for Riemannian BCIs consider the data distribution on a manifold to be unimodal. However, the distribution is likely to be multimodal rather than unimodal since high-data variability is a crucial limitation of electroencephalography (EEG). In this paper, we propose a novel data modeling method for considering complex data distributions on a Riemannian manifold of EEG covariance matrices, aiming to improve BCI reliability. Methods: Our method, Riemannian spectral clustering (RiSC), represents EEG covariance matrix distribution on a manifold using a graph with proposed similarity measurement based on geodesic distances, then clusters the graph nodes through spectral clustering. This allows flexibility to model both a unimodal and a multimodal distribution on a manifold. RiSC can be used as a basis to design an outlier detector named outlier detection Riemannian spectral clustering (odenRiSC) and a multimodal classifier named multimodal classifier Riemannian spectral clustering (mcRiSC). All required parameters of odenRiSC/mcRiSC are selected in data-driven manner. Moreover, there is no need to pre-set a threshold for outlier detection and the number of modes for multimodal classification. Results: The experimental evaluation revealed odenRiSC can detect EEG outliers more accurately than existing methods and mcRiSC outperformed the standard unimodal classifier, especially on high-variability datasets. Conclusion: odenRiSC/mcRiSC are anticipated to contribute to making real-life BCIs outside labs and neuroergonomics applications more robust. Significance: RiSC can work as a robust EEG outlier detector and multimodal classifier.