Alexandre Barachant

Gijsbrecht Van Veen, Alexandre Barachant, Anton Andreev et al.

We describe the experimental procedures for a dataset that we have made publicly available at https://doi.org/10.5281/zenodo.2649006 in mat and csv formats. This dataset contains electroencephalographic (EEG) recordings of 25 subjects testing the Brain Invaders (Congedo, 2011), a visual P300 Brain-Computer Interface inspired by the famous vintage video game Space Invaders (Taito, Tokyo, Japan). The visual P300 is an event-related potential elicited by a visual stimulation, peaking 240-600 ms after stimulus onset. EEG data were recorded by 16 electrodes in an experiment that took place in the GIPSA-lab, Grenoble, France, in 2012 (Van Veen, 2013 and Congedo, 2013). Python code for manipulating the data is available at https://github.com/plcrodrigues/py.BI.EEG.2012-GIPSA. The ID of this dataset is BI.EEG.2012-GIPSA.

Erwan Vaineau, Alexandre Barachant, Anton Andreev et al.

We describe the experimental procedures for a dataset that we have made publicly available at https://doi.org/10.5281/zenodo.1494163 in mat and csv formats. This dataset contains electroencephalographic (EEG) recordings of 24 subjects doing a visual P300 Brain-Computer Interface experiment on PC. The visual P300 is an event-related potential elicited by visual stimulation, peaking 240-600 ms after stimulus onset. The experiment was designed in order to compare the use of a P300-based brain-computer interface on a PC with and without adaptive calibration using Riemannian geometry. The brain-computer interface is based on electroencephalography (EEG). EEG data were recorded thanks to 16 electrodes. Data were recorded during an experiment taking place in the GIPSA-lab, Grenoble, France, in 2013 (Congedo, 2013). Python code for manipulating the data is available at https://github.com/plcrodrigues/py.BI.EEG.2013-GIPSA. The ID of this dataset is BI.EEG.2013-GIPSA.

Marco Congedo, Bijan Afsari, Alexandre Barachant et al.

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 in the manifold of SPD matrices endowed with the Fisher information metric. The resulting mean has several important invariance properties and has proven very useful in diverse engineering applications such as biomedical and image data processing. While for two SPD matrices the mean has an algebraic closed form solution, for a set of more than two SPD matrices it can only be estimated by iterative algorithms. However, none of the existing iterative algorithms feature at the same time fast convergence, low computational complexity per iteration and guarantee of convergence. For this reason, recently other definitions of geometric mean based on symmetric divergence measures, such as the Bhattacharyya divergence, have been considered. The resulting means, although possibly useful in practice, do not satisfy all desirable invariance properties. In this paper we consider geometric means of co-variance matrices estimated on high-dimensional time-series, assuming that the data is generated according to an instantaneous mixing model, which is very common in signal processing. We show that in these circumstances we can approximate the Fisher information geometric mean by employing an efficient AJD algorithm. Our approximation is in general much closer to the Fisher information geometric mean as compared to its competitors and verifies many invariance properties. Furthermore, convergence is guaranteed, the computational complexity is low and the convergence rate is quadratic. The accuracy of this new geometric mean approximation is demonstrated by means of simulations.

Alexandre Barachant, Marco Congedo

This paper presents a new classification methods for Event Related Potentials (ERP) based on an Information geometry framework. Through a new estimation of covariance matrices, this work extend the use of Riemannian geometry, which was previously limited to SMR-based BCI, to the problem of classification of ERPs. As compared to the state-of-the-art, this new method increases performance, reduces the number of data needed for the calibration and features good generalisation across sessions and subjects. This method is illustrated on data recorded with the P300-based game brain invaders. Finally, an online and adaptive implementation is described, where the BCI is initialized with generic parameters derived from a database and continuously adapt to the individual, allowing the user to play the game without any calibration while keeping a high accuracy.

Marco Congedo, Alexandre Barachant, Anton Andreev

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, robust and will maintain good performances within and across sessions. A general classification framework based on recent advances in Riemannian geometry and possessing these characteristics is presented. It applies equally well to BCI based on event-related potentials (ERP), sensorimotor (mu) rhythms and steady-state evoked potential (SSEP). The framework is very simple, both algorithmically and computationally. Due to its simplicity, its ability to learn rapidly (with little training data) and its good across-subject and across-session generalization, this strategy a very good candidate for building a new generation of BCIs, thus we hereby propose it as a benchmark method for the field.