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ABSTRACT: 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%.
IEEE transactions on bio-medical engineering 10/2011; 59(4):920-8. · 2.15 Impact Factor
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ABSTRACT: This article describes a new algorithm to select a subset of electrodes in BCI experiments. It is illustrated on a two-class motor imagery paradigm. The proposed approach is based on the Riemannian distance between spatial covariance matrices which allows to indirectly assess the discriminability between classes. Sensor selection is automatically done using a backward elimination principle. The method is tested on the dataset IVa from BCI competition III. The identified subsets are both consistent with neurophysiological principles and effective, achieving optimal performances with a reduced number of channels.
Neural Engineering (NER), 2011 5th International IEEE/EMBS Conference on; 06/2011
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ABSTRACT: This paper presents a link between the well known Common Spatial Pattern (CSP) algorithm and Riemannian geometry in the context of Brain Computer Interface (BCI). It will be shown that CSP spatial filtering and Log variance features extraction can be resumed as a computation of a Riemann distance in the space of covariances matrices. This fact yields to highlight several approximations with respect to the space topology. According to these conclusions, we propose an improvement of classical CSP method.
Multimedia Signal Processing (MMSP), 2010 IEEE International Workshop on; 11/2010
