Alexandre Barachant

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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(More)
In brain computer interface based on motor imagery, covari-ances matrices are widely used through spatial filters computation and other signal processing methods. Covariances matrices lie in the space of Semi-definite Positives (SPD) matrices and therefore, fall within the Riemannian geometry domain. Using a differential geometry frameworks, we propose(More)
The use of spatial covariance matrix as feature is investigated for motor imagery EEG-based classification. A new kernel is derived by establishing a connection with the Riemannian geometry of symmetric positive definite matrices. Different kernels are tested, in combination with support vector machines, on a past BCI competition dataset. We demonstrate(More)
—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(More)
Based on the cumulated experience over the past 25 years in the field of Brain-Computer Interface (BCI) we can now envision a new generation of BCI. Such BCIs will not require training; instead they will be smartly initialized using remote massive databases and will adapt to the user fast and effectively in the first minute of use. They will be reliable,(More)
We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate joint diagonalization (AJD). Today there is a considerable interest in estimating the geometric mean of a SPD matrix set(More)
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