A hierarchical Bayesian approach for learning sparse spatio-temporal decompositions of multichannel EEG

Multichannel electroencephalography (EEG) offers a non-invasive tool to explore spatio-temporal dynamics of brain activity. With EEG recordings consisting of multiple trials, traditional signal processing approaches that ignore inter-trial variability in the data may fail to accurately estimate the underlying spatio-temporal brain patterns. Moreover, precise characterization of such inter-trial variability per se can be of high scientific value in establishing the relationship between brain activity and behavior. In this paper, a statistical modeling framework is introduced for learning spatio-temporal decompositions of multiple-trial EEG data recorded under two contrasting experimental conditions. By modeling the variance of source signals as random variables varying across trials, the proposed two-stage hierarchical Bayesian model is able to capture inter-trial amplitude variability in the data in a sparse way where a parsimonious representation of the data can be obtained. A variational Bayesian (VB) algorithm is developed for statistical inference of the hierarchical model. The efficacy of the proposed modeling framework is validated with the analysis of both synthetic and real EEG data. In the simulation study we show that even at low signal-to-noise ratios our approach is able to recover with high precision the underlying spatio-temporal patterns and the dynamics of source amplitude across trials; on two brain-computer interface (BCI) data sets we show that our VB algorithm can extract physiologically meaningful spatio-temporal patterns and make more accurate predictions than other two widely used algorithms: the common spatial patterns (CSP) algorithm and the Infomax algorithm for independent component analysis (ICA). The results demonstrate that our statistical modeling framework can serve as a powerful tool for extracting brain patterns, characterizing trial-to-trial brain dynamics, and decoding brain states by exploiting useful structures in the data.

[1]  Justin L. Vincent,et al.  Intrinsic Fluctuations within Cortical Systems Account for Intertrial Variability in Human Behavior , 2007, Neuron.

[2]  K.-R. Muller,et al.  Optimizing Spatial filters for Robust EEG Single-Trial Analysis , 2008, IEEE Signal Processing Magazine.

[3]  J L Kenemans,et al.  Habituation: an event-related potential and dipole source analysis study. , 2000, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[4]  Hans Knutsson,et al.  Adaptive analysis of fMRI data , 2003, NeuroImage.

[5]  Ulrich Hoffmann,et al.  Bayesian machine learning applied in a brain-computer interface for disabled users , 2007 .

[6]  Arnaud Delorme,et al.  EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis , 2004, Journal of Neuroscience Methods.

[7]  H. Hotelling.  Relations Between Two Sets of Variates , 1936 .

[8]  A. Rukhin.  Bayes and Empirical Bayes Methods for Data Analysis , 1997 .

[9]  D. F. Andrews,et al.  Scale Mixtures of Normal Distributions , 1974 .

[10]  A. Cichocki,et al.  EEG filtering based on blind source separation (BSS) for early detection of Alzheimer's disease , 2005, Clinical Neurophysiology.

[11]  Klaus-Robert Müller,et al.  A regularized discriminative framework for EEG analysis with application to brain–computer interface , 2010, NeuroImage.

[12]  T. W. Anderson.  An Introduction to Multivariate Statistical Analysis , 1959 .

[13]  Andrzej Cichocki,et al.  Adaptive blind signal and image processing , 2002 .

[14]  Sotirios Chatzis,et al.  Signal Modeling and Classification Using a Robust Latent Space Model Based on $t$ Distributions , 2008, IEEE Transactions on Signal Processing.

[15]  Christian P. Robert,et al.  The Bayesian choice : from decision-theoretic foundations to computational implementation , 2007 .

[16]  Lucas C. Parra,et al.  Recipes for the linear analysis of EEG , 2005, NeuroImage.

[17]  R N Vigário,et al.  Extraction of ocular artefacts from EEG using independent component analysis. , 1997, Electroencephalography and clinical neurophysiology.

[18]  S Makeig,et al.  Blind separation of auditory event-related brain responses into independent components. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[19]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[20]  G. Pfurtscheller,et al.  Brain-Computer Interfaces for Communication and Control. , 2011, Communications of the ACM.

[21]  Martin J. Wainwright,et al.  Scale Mixtures of Gaussians and the Statistics of Natural Images , 1999, NIPS.

[22]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[23]  T. W. Anderson.  An Introduction to Multivariate Statistical Analysis, 2nd Edition. , 1985 .

[24]  Aapo Hyvärinen,et al.  Independent component analysis of short-time Fourier transforms for spontaneous EEG/MEG analysis , 2010, NeuroImage.

[25]  David J. C. MacKay,et al.  Bayesian Interpolation , 1992, Neural Computation.

[26]  Robert Tibshirani,et al.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd Edition , 2001, Springer Series in Statistics.

[27]  Emery N. Brown,et al.  A probabilistic framework for learning robust common spatial patterns , 2009, 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[28]  A. Walker.  Electroencephalography, Basic Principles, Clinical Applications and Related Fields , 1982 .

[29]  P. Comon,et al.  Ica: a potential tool for bci systems , 2008, IEEE Signal Processing Magazine.

[30]  Bernhard Schölkopf,et al.  Classifying Event-Related Desynchronization in EEG, ECoG and MEG Signals , 2006, DAGM-Symposium.

[31]  Keinosuke Fukunaga,et al.  Application of the Karhunen-Loève Expansion to Feature Selection and Ordering , 1970, IEEE Trans. Computers.

[32]  T. Lagerlund,et al.  Spatial filtering of multichannel electroencephalographic recordings through principal component analysis by singular value decomposition. , 1997, Journal of clinical neurophysiology : official publication of the American Electroencephalographic Society.

[33]  José del R. Millán,et al.  Towards Brain-Computer Interfacing , 2007 .

[34]  M. Yuan,et al.  Model selection and estimation in regression with grouped variables , 2006 .

[35]  B L McNaughton,et al.  Dynamics of the hippocampal ensemble code for space. , 1993, Science.

[36]  Radford M. Neal.  Pattern Recognition and Machine Learning , 2007, Technometrics.

[37]  Hagai Attias,et al.  A graphical model for estimating stimulus-evoked brain responses from magnetoencephalography data with large background brain activity , 2006, NeuroImage.

[38]  Wei Wu,et al.  Frequency Recognition Based on Canonical Correlation Analysis for SSVEP-Based BCIs , 2006, IEEE Transactions on Biomedical Engineering.

[39]  Clemens Brunner,et al.  Nonstationary Brain Source Separation for Multiclass Motor Imagery , 2010, IEEE Transactions on Biomedical Engineering.

[40]  Karl J. Friston,et al.  Bayesian estimation of evoked and induced responses , 2006, Human brain mapping.

[41]  Z J Koles,et al.  Spatio-temporal decomposition of the EEG: a general approach to the isolation and localization of sources. , 1995, Electroencephalography and clinical neurophysiology.

[42]  Samuel M. McClure,et al.  Neural Correlates of Behavioral Preference for Culturally Familiar Drinks , 2004, Neuron.

[43]  Bhaskar D. Rao,et al.  Sparse solutions to linear inverse problems with multiple measurement vectors , 2005, IEEE Transactions on Signal Processing.

[44]  Clemens Brunner,et al.  Nonstationary Brain Source Separation for Multiclass Motor Imagery , 2010, IEEE Transactions on Biomedical Engineering.

[45]  T. Louis,et al.  Bayes and Empirical Bayes Methods for Data Analysis. , 1997 .

[46]  Hagai Attias,et al.  A Spatiotemporal Framework for Estimating Trial-to-Trial Amplitude Variation in Event-Related MEG/EEG , 2009, IEEE Transactions on Biomedical Engineering.

[47]  W. Ray,et al.  EEG alpha activity reflects attentional demands, and beta activity reflects emotional and cognitive processes. , 1985, Science.

[48]  Richard M. Leahy,et al.  Electromagnetic brain mapping , 2001, IEEE Signal Process. Mag..

[49]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[50]  G. Casella,et al.  Statistical Inference , 2003, Encyclopedia of Social Network Analysis and Mining.

[51]  Klaus-Robert Müller,et al.  Spatio-spectral filters for improving the classification of single trial EEG , 2005, IEEE Transactions on Biomedical Engineering.

[52]  Xiaojin Zhu,et al.  --1 CONTENTS , 2006 .

[53]  Andrzej Cichocki,et al.  A New Learning Algorithm for Blind Signal Separation , 1995, NIPS.

[54]  G. Pfurtscheller,et al.  Event-related cortical desynchronization detected by power measurements of scalp EEG. , 1977, Electroencephalography and clinical neurophysiology.

[55]  I. Rampil.  A Primer for EEG Signal Processing in Anesthesia , 1998, Anesthesiology.

[56]  Klaus-Robert Müller,et al.  Combined Optimization of Spatial and Temporal Filters for Improving Brain-Computer Interfacing , 2006, IEEE Transactions on Biomedical Engineering.

[57]  Karl J. Friston.  The free-energy principle: a unified brain theory? , 2010, Nature Reviews Neuroscience.

[58]  Lucas C. Parra,et al.  Blind Source Separation via Generalized Eigenvalue Decomposition , 2003, J. Mach. Learn. Res..

[59]  Erkki Oja,et al.  Independent Component Analysis , 2001 .

[60]  Jean-Baptiste Poline,et al.  A group model for stable multi-subject ICA on fMRI datasets , 2010, NeuroImage.

[61]  Michael I. Jordan,et al.  A Probabilistic Interpretation of Canonical Correlation Analysis , 2005 .

[62]  Matthew J. Beal.  Variational algorithms for approximate Bayesian inference , 2003 .

[63]  E. Oja,et al.  BSS and ICA in Neuroinformatics: From Current Practices to Open Challenges , 2008, IEEE Reviews in Biomedical Engineering.

[64]  David P. Wipf,et al.  A unified Bayesian framework for MEG/EEG source imaging , 2009, NeuroImage.

[65]  Christoph Braun,et al.  Coherence of gamma-band EEG activity as a basis for associative learning , 1999, Nature.

[66]  G. Pfurtscheller,et al.  The BCI competition III: validating alternative approaches to actual BCI problems , 2006, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[67]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[68]  Bhaskar D. Rao,et al.  An Empirical Bayesian Strategy for Solving the Simultaneous Sparse Approximation Problem , 2007, IEEE Transactions on Signal Processing.

[69]  Wei Wu,et al.  Classifying Single-Trial EEG During Motor Imagery by Iterative Spatio-Spectral Patterns Learning (ISSPL) , 2008, IEEE Transactions on Biomedical Engineering.

[70]  Eric Moulines,et al.  A blind source separation technique using second-order statistics , 1997, IEEE Trans. Signal Process..

[71]  Richard A. Davis,et al.  Introduction to time series and forecasting , 1998 .

[72]  T. Ergenoğlu,et al.  Alpha rhythm of the EEG modulates visual detection performance in humans. , 2004, Brain research. Cognitive brain research.

[73]  Dinh-Tuan Pham,et al.  Blind separation of instantaneous mixtures of nonstationary sources , 2001, IEEE Trans. Signal Process..

[74]  W. Klimesch.  EEG alpha and theta oscillations reflect cognitive and memory performance: a review and analysis , 1999, Brain Research Reviews.