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.

Riemannian Channel Selection for BCI With Between-Session Non-Stationarity Reduction Capabilities.

OBJECTIVE: Between-session non-stationarity is a major challenge of current Brain-Computer Interfaces (BCIs) that affects system performance. In this paper, we investigate the use of channel selection for reducing between-session non-stationarity with Riemannian BCI classifiers. We use the Riemannian geometry framework of covariance matrices due to its robustness and promising performances. Current Riemannian channel selection methods do not consider between-session non-stationarity and are usually tested on a single session. Here, we propose a new channel selection approach that specifically considers non-stationarity effects and is assessed on multi-session BCI data sets. METHODS: We remove the least significant channels using a sequential floating backward selection search strategy. Our contributions include: 1) quantifying the non-stationarity effects on brain activity in multi-class problems by different criteria in a Riemannian framework and 2) a method to predict whether BCI performance can improve using channel selection. RESULTS: We evaluate the proposed approaches on three multi-session and multi-class mental tasks (MT)-based BCI datasets. They could lead to significant improvements in performance as compared to using all channels for datasets affected by between-session non-stationarity and to significant superiority to the state-of-the-art Riemannian channel selection methods over all datasets, notably when selecting small channel set sizes. CONCLUSION: Reducing non-stationarity by channel selection could significantly improve Riemannian BCI classification accuracy. SIGNIFICANCE: Our proposed channel selection approach contributes to make Riemannian BCI classifiers more robust to between-session non-stationarities.

Long-Term BCI Training of a Tetraplegic User: Adaptive Riemannian Classifiers and User Training.

While often presented as promising assistive technologies for motor-impaired users, electroencephalography (EEG)-based Brain-Computer Interfaces (BCIs) remain barely used outside laboratories due to low reliability in real-life conditions. There is thus a need to design long-term reliable BCIs that can be used outside-of-the-lab by end-users, e.g., severely motor-impaired ones. Therefore, we propose and evaluate the design of a multi-class Mental Task (MT)-based BCI for longitudinal training (20 sessions over 3 months) of a tetraplegic user for the CYBATHLON BCI series 2019. In this BCI championship, tetraplegic pilots are mentally driving a virtual car in a racing video game. We aimed at combining a progressive user MT-BCI training with a newly designed machine learning pipeline based on adaptive Riemannian classifiers shown to be promising for real-life applications. We followed a two step training process: the first 11 sessions served to train the user to control a 2-class MT-BCI by performing either two cognitive tasks (REST and MENTAL SUBTRACTION) or two motor-imagery tasks (LEFT-HAND and RIGHT-HAND). The second training step (9 remaining sessions) applied an adaptive, session-independent Riemannian classifier that combined all 4 MT classes used before. Moreover, as our Riemannian classifier was incrementally updated in an unsupervised way it would capture both within and between-session non-stationarity. Experimental evidences confirm the effectiveness of this approach. Namely, the classification accuracy improved by about 30% at the end of the training compared to initial sessions. We also studied the neural correlates of this performance improvement. Using a newly proposed BCI user learning metric, we could show our user learned to improve his BCI control by producing EEG signals matching increasingly more the BCI classifier training data distribution, rather than by improving his EEG class discrimination. However, the resulting improvement was effective only on synchronous (cue-based) BCI and it did not translate into improved CYBATHLON BCI game performances. For the sake of overcoming this in the future, we unveil possible reasons for these limited gaming performances and identify a number of promising future research directions. Importantly, we also report on the evolution of the user's neurophysiological patterns and user experience throughout the BCI training and competition.

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.

EEG representation using multi-instance framework on the manifold of symmetric positive definite matrices.

OBJECTIVE: The generalization and robustness of an electroencephalogram (EEG)-based system are crucial requirements in actual practices. APPROACH: To reach these goals, we propose a new EEG representation that provides a more realistic view of brain functionality by applying multi-instance (MI) framework to consider the non-stationarity of the EEG signal. In this representation, the non-stationarity of EEG is considered by describing the signal as a bag of relevant and irrelevant concepts. The concepts are provided by a robust representation of homogeneous segments of EEG signal using spatial covariance matrices. Due to the nonlinear geometry of the space of covariance matrices, we determine the boundaries of the homogeneous segments based on adaptive segmentation of the signal in a Riemannian framework. Each subject is described as a bag of covariance matrices of homogeneous segments and the bag-level discriminative information is used for classification. MAIN RESULTS: To evaluate the performance of the proposed approach, we examine it in a cultural neuroscience application for classification Iranian versus Swiss normal subjects to discover if strongly differing cultures can result in distinguishing patterns in brain electrical activity of the subjects. To confirm the effectiveness of the proposed representation, we also evaluate the proposed representation in EEG-based mental disorder diagnosis application for attention deficit hyperactivity disorder (ADHD)/bipolar mood disorder (BMD), Schizophrenia/ normal, and Major Depression Disorder/normal diagnosis applications. SIGNIFICANCE: Experimental results confirm the superiority of the proposed approach, which is gained due to the robustness of covariance descriptor, the effectiveness of Riemannian geometry, the benefits of considering the inherent non-stationary nature of the brain by applying bag-level discriminative information, and automatic handling the artifacts.

Dimensionality reduction based on distance preservation to local mean for symmetric positive definite matrices and its application in brain-computer interfaces.

OBJECTIVE: In this paper, we propose a nonlinear dimensionality reduction algorithm for the manifold of symmetric positive definite (SPD) matrices that considers the geometry of SPD matrices and provides a low-dimensional representation of the manifold with high class discrimination in a supervised or unsupervised manner. APPROACH: The proposed algorithm tries to preserve the local structure of the data by preserving distances to local means (DPLM) and also provides an implicit projection matrix. DPLM is linear in terms of the number of training samples. MAIN RESULTS: We performed several experiments on the multi-class dataset IIa from BCI competition IV and two other datasets from BCI competition III including datasets IIIa and IVa. The results show that our approach as dimensionality reduction technique-leads to superior results in comparison with other competitors in the related literature because of its robustness against outliers and the way it preserves the local geometry of the data. SIGNIFICANCE: The experiments confirm that the combination of DPLM with filter geodesic minimum distance to mean as the classifier leads to superior performance compared with the state of the art on brain-computer interface competition IV dataset IIa. Also the statistical analysis shows that our dimensionality reduction method performs significantly better than its competitors.