An Introduction to EEG Source Analysis with an Illustration of a Study on Error-Related Potentials

Congedo, Marco; Rousseau, Sandra; Jutten, Christian

doi:10.1007/978-1-4471-6584-2_8

Cited by 6 publications

(10 citation statements)

References 53 publications

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“…[15] for an overview. In this work, we construct the set of matrices following the method proposed in [20], which is adapted to the analysis of EEG signals containing event-related potentials. We take the two covariance matrices of the means of the signals of the two classes along with the 20 Fourier cospectra between 1-20Hz with 1Hz resolution.…”

Section: Real Electroencephalographic Datamentioning

confidence: 99%

Approximate Joint Diagonalization with Riemannian Optimization on the General Linear Group

Bouchard¹,

Afsari²,

Malick³

et al. 2020

SIAM J. Matrix Anal. Appl.

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We consider the classical problem of approximate joint diagonalization of matrices, which can be cast as an optimization problem on the general linear group. We propose a versatile Riemannian optimization framework for solving this problem -unifiying existing methods and creating new ones. We use two standard Riemannian metrics (left-and right-invariant metrics) having opposite features regarding the structure of solutions and the model. We introduce the Riemannian optimization tools (gradient, retraction, vector transport) in this context, for the two standard nondegeneracy constraints (oblique and non-holonomic constraints). We also develop tools beyond the classical Riemannian optimization framework to handle the non-Riemannian quotient manifold induced by the non-holonomic constraint with the right-invariant metric. We illustrate our theoretical developments with numerical experiments on both simulated data and a real electroencephalographic recording.

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Section: Real Electroencephalographic Datamentioning

confidence: 99%

Approximate Joint Diagonalization with Riemannian Optimization on the General Linear Group

Bouchard¹,

Afsari²,

Malick³

et al. 2020

SIAM J. Matrix Anal. Appl.

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“…2) Preprocessing: From the recorded signals, we selected 16 representative electrodes from the first subject (N=16): Fp1-Fp2-F5-AFz-F6-T7-Cz-T8-P7-P3-Pz-P4-P8-O1-Oz-O2. The signals were filtered by a fourth order forwardbackward Butterworth band pass filter [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] Hz and downsampled at Fs=128Hz. The signals were segmented into trials X k of 1s (T=128) starting at each visual stimulation.…”

Section: B Proceduresmentioning

confidence: 99%

“…AJD has been successfully used in source separation of continuous electroencephalographic (EEG) sources [3] using co-spectral as target matrices. More recently, [4] proposed to add the covariance matrices of the estimated evoked activity for the separation of Event Error Related Potential (ErrP) sources. In ERPs, the evoked sources have both a spatial and a temporal (bilinear) fixed structure such as…”

Section: Introductionmentioning

confidence: 99%

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Mining the bilinear structure of data with approximate joint diagonalization

Korczowski

Bouchard

Jutten

et al. 2016

2016 24th European Signal Processing Conference (EUSIPCO)

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Approximate Joint Diagonalization of a matrix set can solve the linear Blind Source Separation problem. If the data possesses a bilinear structure, for example a spatio-temporal structure, transformations such as tensor decomposition can be applied. In this paper we show how the linear and bilinear joint diagonalization can be applied for extracting sources according to a composite model where some of the sources have a linear structure and other a bilinear structure. This is the case of Event Related Potentials (ERPs). The proposed model achieves higher performance in term of shape and robustness for the estimation of ERP sources in a Brain Computer Interface experiment.

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“…One of the main research topics on the application of ICA to EEG signals is the dynamic modeling of brain oscillations in humans [230,189,109,61] and lab rats [232,10]. This research attempts to combine the advantages of independent component analysis with the capabilities of certain dynamic models to deal with the temporal variability of the EEG.…”

Section: Application On Electroencephalographic Signalsmentioning

confidence: 99%

New Insights in Prediction and Dynamic Modeling from Non-Gaussian Mixture Processing Methods

Armero¹

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This thesis considers new applications of non-Gaussian mixtures in the framework of statistical signal processing and pattern recognition. The non-Gaussian mixtures were implemented by mixtures of independent component analyzers (ICA). The fundamental hypothesis of ICA is that the observed signals can be expressed as a linear transformation of a set of hidden variables, usually referred to as sources, which are statistically independent. This independence allows factoring the original M-dimensional probability density function (PDF) of the data as a product of one-dimensional probability densities, greatly simplifying the modeling of the data. ICA mixture models (ICAMM) provide further flexibility by alleviating the independency requirement of ICA, thus allowing the model to obtain local projections of the data without compromising its generalization capabilities. Here are explored new possibilities of ICAMM for the purposes of estimation and classification of signals.The thesis makes several contributions to the research in non-Gaussian mixtures: (i) a method for maximum-likelihood estimation of missing data, based on the maximization of the PDF of the data given the ICAMM; (ii) a method for Bayesian estimation of missing data that minimizes the mean squared error and can obtain the confidence interval of the prediction; (iii) a generalization of the sequential dependence model for ICAMM to semi-supervised or supervised learning and multiple chains of dependence, thus allowing the use of multimodal data; and (iv) introduction of ICAMM in diverse novel applications, both for estimation and for classification.The developed methods were validated via an extensive number of simulations that covered multiple scenarios. These tested the sensitivity of the proposed methods with respect to the following parameters: number of values to estimate; kinds of source distributions; correspondence of the data with respect to the assumptions of the model; number of classes in the mixture model; and unsupervised, semi-supervised, and supervised learning. The performance of the proposed methods was evaluated using several figures of merit, and compared with the performance of multiple classical and state-of-the-art techniques for estimation and classification.Aside from the simulations, the methods were also tested on several sets of real data from different types: data from seismic exploration studies; ground penetrating radar surveys; and biomedical data. These data correspond to the following applications: reconstruction of damaged or missing data from ground-penetrating radar surveys of historical walls; reconstruction of damaged or missing data from a seismic exploration survey; reconstruction of artifacted or missing electroencephalographic (EEG) data; diagnosis of sleep disorders; modeling of the brain response during memory tasks; and exploration of EEG data from subjects performing a battery of neuropsychological tests. The obtained results demonstrate the capability of the proposed methods to work on problems wi...

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An Introduction to EEG Source Analysis with an Illustration of a Study on Error-Related Potentials

Cited by 6 publications

References 53 publications

Approximate Joint Diagonalization with Riemannian Optimization on the General Linear Group

Approximate Joint Diagonalization with Riemannian Optimization on the General Linear Group

Mining the bilinear structure of data with approximate joint diagonalization

New Insights in Prediction and Dynamic Modeling from Non-Gaussian Mixture Processing Methods

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