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

Abstract

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. 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. 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. odenRiSC/mcRiSC are anticipated to contribute to making real-life BCIs outside labs and neuroergonomics applications more robust. RiSC can work as a robust EEG outlier detector and multimodal classifier.