Channel Selection Procedure using Riemannian distance for BCI applications

International audienceThis 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

Filtrage spatial robuste à partir d'un sous-ensemble optimal d'électrodes en BCI EEG

La réalisation d'une interface cerveau machine EEG nécessite généralement l'utilisation d'un grand nombre d'électrodes, causant la gêne de l'utilisateur et augmentant considérablement le coût calculatoire des traitements. Cependant, un choix judicieux de l'emplacement des ces électrodes peut permettre une réduction importante de leur nombre sans perte significative en performance. Cet article présente une méthode de sélection automatique d'un sous-ensemble quasi optimal d'électrodes et de filtres spatiaux calculés par Common Spatial Pattern (CSP) . Cette méthode, basée sur un calcul de coefficient de détermination multiple et l'utilisation du critère d'Akaike, est traitée de manière à résister aux artefacts par l'utilisation d'estimateurs robustes de variance et de matrice de covariance . Il est ainsi montré qu'une réduction très importante du nombre d'électrode est possible sans perte d'information sur les caractéristiques spatiales et que cette méthode résiste parfaitement à un grand nombre d'artefacts lorsque les signaux sont corrompus par des artefacts

General wetting energy boundary condition in a fully explicit non-ideal fluids solver

We present an explicit finite difference method to simulate the non-ideal multi-phase fluid flow. The local density and the momentum transport are modeled by the Navier-Stokes (N-S) equations and the pressure is computed by the Van der Waals equation of the state (EOS). The static droplet and the dynamics of liquid-vapor separation simulations are performed as validations of this numerical scheme. In particular, to maintain the thermodynamic consistency, we propose a general wetting energy boundary condition at the contact line between fluids and the solid boundary. We conduct a series of comparisons between the current boundary condition and the constant contact angle boundary condition as well as the stress-balanced boundary condition. This boundary condition alleviates the instability induced by the constant contact angle boundary condition at $\theta \approx0$ and $\theta \approx \pi$. Using this boundary condition, the equilibrium contact angle is correctly recovered and the contact line dynamics are consistent with the simulation by applying a stress-balanced boundary condition. Nevertheless, unlike the stress-balanced boundary condition for which we need to further introduce the interface thickness parameter, the current boundary condition implicitly incorporates the interface thickness information into the wetting energy

Spatial filtering optimisation in motor imagery EEG-based BCI

ISBN : 978-2-9532965-0-1Common spatial pattern (CSP) is becoming a standard way to combine linearly multi-channel EEG data in order to increase discrimination between two motor imagery tasks. We demonstrate in this article that the use of robust estimates allow improving the quality of CSP decomposition and CSP-based BCI. Furthermore, an evolutionary algorithm (EA)-type for electrode subset selection is proposed. It is shown that CSP with the obtained subset electrode yield comparable results with the ones obtained with CSP over large multi-channel recordings

Curve Stabbing Depth: Data Depth for Plane Curves

Measures of data depth have been studied extensively for point data. Motivated by recent work on analysis, clustering, and identifying representative elements in sets of trajectories, we introduce {\em curve stabbing depth} to quantify how deeply a given curve $Q$ is located relative to a given set $\cal C$ of curves in $\mathbb{R}^2$. Curve stabbing depth evaluates the average number of elements of $\cal C$ stabbed by rays rooted along the length of $Q$. We describe an $O(n^3 + n^2 m\log^2m+nm^2\log^2 m)$-time algorithm for computing curve stabbing depth when $Q$ is an $m$-vertex polyline and $\cal C$ is a set of $n$ polylines, each with $O(m)$ vertices.Comment: Preprin

Few-shot Quality-Diversity Optimization

In the past few years, a considerable amount of research has been dedicated to the exploitation of previous learning experiences and the design of Few-shot and Meta Learning approaches, in problem domains ranging from Computer Vision to Reinforcement Learning based control. A notable exception, where to the best of our knowledge, little to no effort has been made in this direction is Quality-Diversity (QD) optimization. QD methods have been shown to be effective tools in dealing with deceptive minima and sparse rewards in Reinforcement Learning. However, they remain costly due to their reliance on inherently sample inefficient evolutionary processes. We show that, given examples from a task distribution, information about the paths taken by optimization in parameter space can be leveraged to build a prior population, which when used to initialize QD methods in unseen environments, allows for few-shot adaptation. Our proposed method does not require backpropagation. It is simple to implement and scale, and furthermore, it is agnostic to the underlying models that are being trained. Experiments carried in both sparse and dense reward settings using robotic manipulation and navigation benchmarks show that it considerably reduces the number of generations that are required for QD optimization in these environments.Comment: Accepted for publication in the IEEE Robotics and Automation Letters (RA-L) journa

An impedance boundary condition EFIE that is low-frequency and refinement stable

A discretization of the impedance boundary condition electric field integral equation (IBC-EFIE) is introduced that: 1) yields the correct solution at arbitrarily small frequencies and 2) requires for its solution a number of matrix vector products bounded as the frequency tends to zero and as the mesh density increases. The low frequency stabilization is based on a projector-based discrete Helmholtz splitting, rescaling, and recombination that depends on the low frequency behavior of both the EFIE operator and the surface impedance condition. The dense mesh stabilization is a modification of the perfect electric conductor operator preconditioning approach taking into account the effect on the singular value spectrum of the IBC term

Riemannian geometry applied to BCI classification

ISBN 978-3-642-15994-7, SoftcoverInternational audienceIn brain-computer interfaces based on motor imagery, covariance matrices are widely used through spatial filters computation and other signal processing methods. Covariance matrices lie in the space of Symmetric Positives-Definite (SPD) matrices and therefore, fall within the Riemannian geometry domain. Using a differential geometry framework, we propose different algorithms in order to classify covariance matrices in their native space