Multiclass Brain-Computer Interface Classification by Riemannian Geometry

• Published in: IEEE transactions on biomedical engineering Vol. 59; no. 4; pp. 920 - 928
• Main Authors: Barachant, Alexandre, Bonnet, Stéphane, Congedo, Marco, Jutten, Christian
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2012; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Biological and medical sciences; Brain computer interfaces; Classification; classification algorithms; Computer Science; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Computerized, statistical medical data processing and models in biomedicine; Covariance matrix; Discriminant analysis; Electrodiagnosis. Electric activity recording; Electroencephalography; Electroencephalography - methods; Engineering Sciences; Evoked Potentials, Motor - physiology; Exact sciences and technology; Geometry; Humans; Imagination; information geometry; Investigative techniques, diagnostic techniques (general aspects); Manifolds; Matrix decomposition; Medical management aid. Diagnosis aid; Medical sciences; Motor Cortex - physiology; Movement - physiology; Nervous system; Pattern Recognition, Automated - methods; Reproducibility of Results; Sensitivity and Specificity; Signal and Image Processing; Silicon; Software; Studies; Symmetric matrices; Topology; User-Computer Interface; classification algorithms; Electrophysiology; Man machine dialogue; Electroencephalography; Covariance matrix; Algorithm; Geometry; Brain-computer interface; Electrodiagnosis; information geometry; User interface; Biomedical engineering; Brain computer interfaces; electroencephalography; covariance matrix
• ISSN: 0018-9294; 1558-2531; 1558-2531
• DOI: 10.1109/TBME.2011.2172210

This paper presents a new classification framework for brain-computer interface (BCI) based on motor imagery. This framework involves the concept of Riemannian geometry in the manifold of covariance matrices. The main idea is to use spatial covariance matrices as EEG signal descriptors and to rely on Riemannian geometry to directly classify these matrices using the topology of the manifold of symmetric and positive definite (SPD) matrices. This framework allows to extract the spatial information contained in EEG signals without using spatial filtering. Two methods are proposed and compared with a reference method [multiclass Common Spatial Pattern (CSP) and Linear Discriminant Analysis (LDA)] on the multiclass dataset IIa from the BCI Competition IV. The first method, named minimum distance to Riemannian mean (MDRM), is an implementation of the minimum distance to mean (MDM) classification algorithm using Riemannian distance and Riemannian mean. This simple method shows comparable results with the reference method. The second method, named tangent space LDA (TSLDA), maps the covariance matrices onto the Riemannian tangent space where matrices can be vectorized and treated as Euclidean objects. Then, a variable selection procedure is applied in order to decrease dimensionality and a classification by LDA is performed. This latter method outperforms the reference method increasing the mean classification accuracy from 65.1% to 70.2%.