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.

Class-distinctiveness-based frequency band selection on the Riemannian manifold for oscillatory activity-based BCIs: preliminary results.

Considering user-specific settings is known to enhance Brain-Computer Interface (BCI) performances. In particular, the optimal frequency band for oscillatory activity classification is highly user-dependent and many frequency band selection methods have been developed in the past two decades. However, it is not well studied whether those conventional methods can be efficiently applied to the Riemannian BCIs, a recent family of BCI systems that utilize the non-Euclidean nature of the data unlike conventional BCI pipelines. In this paper, we proposed a novel frequency band selection method working on the Riemannian manifold. The frequency band is selected considering the class distinctiveness as quantified based on the inter-class distance and the intra-class variance on the manifold. An advantage of this method is that the frequency bandwidth can be adjusted for each individual without intensive optimization steps. In a comparative experiment using a public dataset of motor imagery-based BCI, our method showed a substantial improvement in average accuracy over both a fixed broad frequency band and a popular conventional frequency band selection method. In particular, our method substantially improved performances for subjects with initially low accuracies. This preliminary result suggests the importance of developing new user-specific setting algorithms considering the manifold properties, rather than directly applying methods developed prior to the rise of the Riemannian BCIs.

Detecting EEG outliers for BCI on the Riemannian manifold using spectral clustering.

Automatically detecting and removing Electroencephalogram (EEG) outliers is essential to design robust brain-computer interfaces (BCIs). In this paper, we propose a novel outlier detection method that works on the Riemannian manifold of sample covariance matrices (SCMs). Existing outlier detection methods run the risk of erroneously rejecting some samples as outliers, even if there is no outlier, due to the detection being based on a reference matrix and a threshold. To address this limitation, our method, Riemannian Spectral Clustering (RiSC), detects outliers by clustering SCMs into non-outliers and outliers, based on a proposed similarity measure. This considers the Riemannian geometry of the space and magnifies the similarity within the non-outlier cluster and weakens it between non-outlier and outlier clusters, instead of setting a threshold. To assess RiSC performance, we generated artificial EEG datasets contaminated by different outlier strengths and numbers. Comparing Hit-False (HF) difference between RiSC and existing outlier detection methods confirmed that RiSC could detect outliers significantly better (p < 0.001). In particular, RiSC improved HF difference the most for datasets with the most severe outlier contamination.