Spatio Temporal EEG Source Imaging with the Hierarchical Bayesian Elastic Net and Elitist Lasso Models
The estimation of EEG generating sources constitutes an Inverse Problem (IP) in Neuroscience. This is an ill-posed problem due to the non-uniqueness of the solution and regularization or prior information is needed to undertake Electrophysiology Source Imaging. Structured Sparsity priors can be atta...
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doaj-3b9e19cdbd5f4e96ad92ae77805e9de12020-11-25T01:06:12ZengFrontiers Media S.A.Frontiers in Neuroscience1662-453X2017-11-011110.3389/fnins.2017.00635246056Spatio Temporal EEG Source Imaging with the Hierarchical Bayesian Elastic Net and Elitist Lasso ModelsDeirel Paz-Linares0Deirel Paz-Linares1Mayrim Vega-Hernández2Pedro A. Rojas-López3Pedro A. Rojas-López4Pedro A. Valdés-Hernández5Pedro A. Valdés-Hernández6Eduardo Martínez-Montes7Eduardo Martínez-Montes8Pedro A. Valdés-Sosa9Pedro A. Valdés-Sosa10The Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu, ChinaNeuroinformatics Department, Cuban Neuroscience Center, Havana, CubaNeuroinformatics Department, Cuban Neuroscience Center, Havana, CubaThe Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu, ChinaNeuroinformatics Department, Cuban Neuroscience Center, Havana, CubaNeuroinformatics Department, Cuban Neuroscience Center, Havana, CubaDepartment of Biomedical Engineering, Florida International University, Miami, FL, United StatesNeuroinformatics Department, Cuban Neuroscience Center, Havana, CubaPolitecnico di Torino, Turin, ItalyThe Clinical Hospital of Chengdu Brain Science Institute, MOE Key Lab for Neuroinformation, University of Electronic Science and Technology of China, Chengdu, ChinaNeuroinformatics Department, Cuban Neuroscience Center, Havana, CubaThe estimation of EEG generating sources constitutes an Inverse Problem (IP) in Neuroscience. This is an ill-posed problem due to the non-uniqueness of the solution and regularization or prior information is needed to undertake Electrophysiology Source Imaging. Structured Sparsity priors can be attained through combinations of (L1 norm-based) and (L2 norm-based) constraints such as the Elastic Net (ENET) and Elitist Lasso (ELASSO) models. The former model is used to find solutions with a small number of smooth nonzero patches, while the latter imposes different degrees of sparsity simultaneously along different dimensions of the spatio-temporal matrix solutions. Both models have been addressed within the penalized regression approach, where the regularization parameters are selected heuristically, leading usually to non-optimal and computationally expensive solutions. The existing Bayesian formulation of ENET allows hyperparameter learning, but using the computationally intensive Monte Carlo/Expectation Maximization methods, which makes impractical its application to the EEG IP. While the ELASSO have not been considered before into the Bayesian context. In this work, we attempt to solve the EEG IP using a Bayesian framework for ENET and ELASSO models. We propose a Structured Sparse Bayesian Learning algorithm based on combining the Empirical Bayes and the iterative coordinate descent procedures to estimate both the parameters and hyperparameters. Using realistic simulations and avoiding the inverse crime we illustrate that our methods are able to recover complicated source setups more accurately and with a more robust estimation of the hyperparameters and behavior under different sparsity scenarios than classical LORETA, ENET and LASSO Fusion solutions. We also solve the EEG IP using data from a visual attention experiment, finding more interpretable neurophysiological patterns with our methods. The Matlab codes used in this work, including Simulations, Methods, Quality Measures and Visualization Routines are freely available in a public website.http://journal.frontiersin.org/article/10.3389/fnins.2017.00635/fullEEG source imaginginverse problemsparsity regularizationsparse Bayesian learningempirical Bayeselastic net |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Deirel Paz-Linares Deirel Paz-Linares Mayrim Vega-Hernández Pedro A. Rojas-López Pedro A. Rojas-López Pedro A. Valdés-Hernández Pedro A. Valdés-Hernández Eduardo Martínez-Montes Eduardo Martínez-Montes Pedro A. Valdés-Sosa Pedro A. Valdés-Sosa |
spellingShingle |
Deirel Paz-Linares Deirel Paz-Linares Mayrim Vega-Hernández Pedro A. Rojas-López Pedro A. Rojas-López Pedro A. Valdés-Hernández Pedro A. Valdés-Hernández Eduardo Martínez-Montes Eduardo Martínez-Montes Pedro A. Valdés-Sosa Pedro A. Valdés-Sosa Spatio Temporal EEG Source Imaging with the Hierarchical Bayesian Elastic Net and Elitist Lasso Models Frontiers in Neuroscience EEG source imaging inverse problem sparsity regularization sparse Bayesian learning empirical Bayes elastic net |
author_facet |
Deirel Paz-Linares Deirel Paz-Linares Mayrim Vega-Hernández Pedro A. Rojas-López Pedro A. Rojas-López Pedro A. Valdés-Hernández Pedro A. Valdés-Hernández Eduardo Martínez-Montes Eduardo Martínez-Montes Pedro A. Valdés-Sosa Pedro A. Valdés-Sosa |
author_sort |
Deirel Paz-Linares |
title |
Spatio Temporal EEG Source Imaging with the Hierarchical Bayesian Elastic Net and Elitist Lasso Models |
title_short |
Spatio Temporal EEG Source Imaging with the Hierarchical Bayesian Elastic Net and Elitist Lasso Models |
title_full |
Spatio Temporal EEG Source Imaging with the Hierarchical Bayesian Elastic Net and Elitist Lasso Models |
title_fullStr |
Spatio Temporal EEG Source Imaging with the Hierarchical Bayesian Elastic Net and Elitist Lasso Models |
title_full_unstemmed |
Spatio Temporal EEG Source Imaging with the Hierarchical Bayesian Elastic Net and Elitist Lasso Models |
title_sort |
spatio temporal eeg source imaging with the hierarchical bayesian elastic net and elitist lasso models |
publisher |
Frontiers Media S.A. |
series |
Frontiers in Neuroscience |
issn |
1662-453X |
publishDate |
2017-11-01 |
description |
The estimation of EEG generating sources constitutes an Inverse Problem (IP) in Neuroscience. This is an ill-posed problem due to the non-uniqueness of the solution and regularization or prior information is needed to undertake Electrophysiology Source Imaging. Structured Sparsity priors can be attained through combinations of (L1 norm-based) and (L2 norm-based) constraints such as the Elastic Net (ENET) and Elitist Lasso (ELASSO) models. The former model is used to find solutions with a small number of smooth nonzero patches, while the latter imposes different degrees of sparsity simultaneously along different dimensions of the spatio-temporal matrix solutions. Both models have been addressed within the penalized regression approach, where the regularization parameters are selected heuristically, leading usually to non-optimal and computationally expensive solutions. The existing Bayesian formulation of ENET allows hyperparameter learning, but using the computationally intensive Monte Carlo/Expectation Maximization methods, which makes impractical its application to the EEG IP. While the ELASSO have not been considered before into the Bayesian context. In this work, we attempt to solve the EEG IP using a Bayesian framework for ENET and ELASSO models. We propose a Structured Sparse Bayesian Learning algorithm based on combining the Empirical Bayes and the iterative coordinate descent procedures to estimate both the parameters and hyperparameters. Using realistic simulations and avoiding the inverse crime we illustrate that our methods are able to recover complicated source setups more accurately and with a more robust estimation of the hyperparameters and behavior under different sparsity scenarios than classical LORETA, ENET and LASSO Fusion solutions. We also solve the EEG IP using data from a visual attention experiment, finding more interpretable neurophysiological patterns with our methods. The Matlab codes used in this work, including Simulations, Methods, Quality Measures and Visualization Routines are freely available in a public website. |
topic |
EEG source imaging inverse problem sparsity regularization sparse Bayesian learning empirical Bayes elastic net |
url |
http://journal.frontiersin.org/article/10.3389/fnins.2017.00635/full |
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