Detecting single-trial EEG evoked potential using a wavelet domain linear mixed model: application to error potentials classification

Objective. The main goal of this work is to develop a model for multi-sensor signals such as MEG or EEG signals, that accounts for the inter-trial variability, suitable for corresponding binary classification problems. An important constraint is that the model be simple enough to handle small size and unbalanced datasets, as often encountered in BCI type experiments. Approach. The method involves linear mixed effects statistical model, wavelet transform and spatial filtering, and aims at the characterization of localized discriminant features in multi-sensor signals. After discrete wavelet transform and spatial filtering, a projection onto the relevant wavelet and spatial channels subspaces is used for dimension reduction. The projected signals are then decomposed as the sum of a signal of interest (i.e. discriminant) and background noise, using a very simple Gaussian linear mixed model. Main results. Thanks to the simplicity of the model, the corresponding parameter estimation problem is simplified. Robust estimates of class-covariance matrices are obtained from small sample sizes and an effective Bayes plug-in classifier is derived. The approach is applied to the detection of error potentials in multichannel EEG data, in a very unbalanced situation (detection of rare events). Classification results prove the relevance of the proposed approach in such a context. Significance. The combination of linear mixed model, wavelet transform and spatial filtering for EEG classification is, to the best of our knowledge, an original approach, which is proven to be effective. This paper improves on earlier results on similar problems, and the three main ingredients all play an important role

High resolution in z-direction: The simulation of disc-bulge-halo galaxies using the particle-mesh code SUPERBOX

SUPERBOX is known as a very efficient particle-mesh code with highly-resolving sub-grids. Nevertheless, the height of a typical galactic disc is small compared to the size of the whole system. Consequently, the numerical resolution in z-direction, i.e. vertically with respect to the plane of the disc, remains poor. Here, we present a new version of SUPERBOX that allows for a considerably higher resolution along z. The improved code is applied to investigate disc heating by the infall of a galaxy satellite. We describe the improvement and communicate our results. As an important application we discuss the disruption of a dwarf galaxy within a disc-bulge-halo galaxy that consists of some 10^6 particles.Comment: Comments: 4 pages, 5 figures, pre-peer reviewed version. In: Galactic and stellar dynamics in the era of high-resolution surveys, Boily C., Combes F., Hensler G., eds., Strasbourg (France), March 2008, in press (Astronomische Nachrichten

Modeling Merging Galaxies using MINGA - Improving Restricted N-body by Dynamical Friction

Modeling interacting galaxies to reproduce observed systems is still a challenge due to the extended parameter space (among other problems). Orbit and basic galaxy parameters can be tackled by fast simulation techniques like the restricted N-body method, applied in the fundamental work by Toomre & Toomre (1972). This approach allows today for the study of millions of models in a short time. One difficulty for the classical restricted N-body method is the missing orbital decay, not allowing for galaxy mergers. Here we present an extension of the restricted N-body method including dynamical friction. This treatment has been developed by a quantitative comparison with a set of self-consistent merger simulations. By varying the dynamical friction (formalism, strength and direction), we selected the best-fitting parameters for a set of more than 250000 simulations. We show that our treatment reliably reproduces the orbital decay and tidal features of merging disk galaxies for mass ratios up to q=1/3 between host and satellite. We implemented this technique into our genetic algorithm based modeling code MINGA and present first results.Comment: To be published in the proceedings of the "Galactic and Stellar Dynamics 2008" conference. 4 pages, 4 figures, 2 table

FINDING EEG SPACE-TIME-SCALE LOCALIZED FEATURES USING MATRIX-BASED PENALIZED DISCRIMINANT ANALYSIS

International audienceThis paper proposes a new method for constructing and selecting of discriminant space-time-scale features for electroencephalogram (EEG) signal classification, suitable for Error Related Potentials (ErrP)detection in brain-computer interface (BCI). The method rests on a new variant of matrix-variate Linear Discriminant Analysis (LDA), and differs from previously proposed approaches in mainly three ways. First, a discrete wavelet expansion is introduced for mapping time-courses to time-scale coefficients, yielding time-scale localized features. Second, the matrix-variate LDA is modified in such a way that it yields an interesting duality property, that makes interpretation easier. Third, a space penalization is introduced using a surface Laplacian, so as to enforce spatial smoothness. The proposed approaches, termed D-MLDA and D-MPDA are tested on EEG signals, with the goal of detecting ErrP. Numerical results show that D-MPDA outperforms D-MLDA and other matrix-variate LDA techniques. In addition this method produces relevant features for interpretation in ErrP signals

Une approche modèle mixte pour la classification supervisée de signaux électrophysiologiques

International audienceAbstract. The classification of noisy-data with high variability is an important issue. Electrophysiological (EEG) signals correspond to this type of complex data. In a Reaction-Time task, brain activity has an important temporal variability accross repetitions and the signal of interest, which is of low amplitude, is embedded into a set of artifacts and noise. For a fixed subject, we propose a procedure in order to classify two types of brain signals using a parametric modeling based on the Gaussian Mixed-Effects model. The present work is based on the method presented by Huang et al. (2008). Our contribution is first a simplified formalization of the modeling and second the introduction of a wavelet transform which leads to a reduction of temporal dimension without loss of information. The procedure is applied to the detection of error-negativities during a cognitive task, and we study the performance of our method on six subjects by comparing the results with those obtained with a discriminant analysis.La classification de données fortement bruitées et présentant une importante variabilité constitue un enjeu important. Les signaux électrophysiologiques (EEG) correspondent à ce type de données complexes. Pour une tâche cognitive étudiée, l'activité cérébrale associée présente une importante variabilité temporelle d'une répétition à une autre et le signal d'intérêt, de faible amplitude, est noyé dans un ensemble d'artefacts et de bruit. Nous proposons une procédure permettant de classer, chez un même sujet, deux types de signaux cérébraux à partir d'une modélisation par le modèle linéaire mixte gaussien. Ce travail s'inspire de la méthode présentée par Huang et al. (2008). Notre contribution réside d'une part dans une formalisation simplifiée de la modélisation et d'autre part dans l'introduction d'une transformation en ondelettes permettant une réduction de la dimension temporelle sans perte d'information. La procédure présentée est appliquée à la détection d'ondes d'erreurs au cours d'une tâche cognitive, et nous étudions la performance de notre méthode sur six sujets en comparant les résultats obtenus aux résultats d'une analyse factorielle discriminante

Analyse discriminante matricielle descriptive. Application a l'étude de signaux EEG

National audienceWe focus on the descriptive approach to linear discriminant analysis for matrix-variate data in the binary case. Under a separability assumption on row and column variability, the most discriminant linear combinations of rows and columns are determined by the singular value decomposition of the difference of the class-averages with the Mahalanobis metric in the row and column spaces. This approach provides data representations of data in two-dimensional or three-dimensional plots and singles out discriminant components. An application to electroencephalographic multi-sensor signals illustrates the relevance of the method.Nous nous intéressons à l'approche descriptive de l'analyse discriminante linéaire de données matricielles dans le cas binaire. Sous l'hypothèse de séparabilité de la variabilité des lignes de celle des colonnes, les combinaisons linéaires des lignes et des colonnes les plus discriminantes sont déterminées par la décomposition en valeurs singulières de la différence des moyennes des deux classes en munissant les espaces des lignes et des colonnes de la métrique de Mahalanobis. Cette approche permet d'obtenir des représentations des données dans des plans factoriels et de dégager des composantes discriminantes. Une application a des signaux d'électroencéphalographie multi-capteurs illustre la pertinence de la méthode

Analyse discriminante matricielle descriptive. Application a l'\'etude de signaux EEG

We focus on the descriptive approach to linear discriminant analysis for matrix-variate data in the binary case. Under a separability assumption on row and column variability, the most discriminant linear combinations of rows and columns are determined by the singular value decomposition of the difference of the class-averages with the Mahalanobis metric in the row and column spaces. This approach provides data representations of data in two-dimensional or three-dimensional plots and singles out discriminant components. An application to electroencephalographic multi-sensor signals illustrates the relevance of the method.Comment: in French, Journ{\'e}es de statistique de la SFDS, Jun 2015, Lille, Franc

High resolution simulations of unstable modes in a collisionless disc

We present N-body simulations of unstable spiral modes in a dynamically cool collisionless disc. We show that spiral modes grow in a thin collisionless disk in accordance with the analytical perturbation theory. We use the particle-mesh code SUPERBOX with nested grids to follow the evolution of unstable spirals that emerge from an unstable equilibrium state. We use a large number of particles (up to 40 million particles) and high-resolution spatial grids in our simulations (128^3 cells). These allow us to trace the dynamics of the unstable spiral modes until their wave amplitudes are saturated due to nonlinear effects. In general, the results of our simulations are in agreement with the analytical predictions. The growth rate and the pattern speed of the most unstable bar-mode measured in N-body simulations agree with the linear analysis. However the parameters of secondary unstable modes are in lesser agreement because of the still limited resolution of our simulations.Comment: 11 pages, 8 figures in 22 files, A&A in print: Oct. 1st 200