title: Estimation of direct nonlinear effective connectivity using information theory and multilayer perceptron.
abstract: BACKGROUND
  Despite the variety of effective connectivity measures, few methods can quantify direct nonlinear causal couplings and most of them are not applicable to high-dimensional datasets.
  
  
  METHODS
  In this paper, a novel approach (called βmRMR-MLP-GC) is proposed to estimate direct nonlinear effective connectivity of high-dimensional datasets. βmRMR is used to select a suitable subset of candidate regressors for approximating each neural (here EEG) signal. The multilayer perceptron (MLP) is used for multivariate characterization of EEG signals while the optimum MLP structure is selected using an iterative cross-validation scheme. Finally a causality measure is defined based on Granger Causality (GC) concept to quantify the casual relations among EEG channels.
  
  
  RESULTS
  Applying βmRMR-MLP-GC to high-dimensional simulated datasets with different linear and nonlinear structures yields sensitivity and specificity values higher than 95%. Also, applying it to eyes-closed resting state EEG of six normal subjects in the alpha frequency band yields significant net activity propagations from the posterior to anterior brain regions. This is in accordance with the most previous studies in this field.
  
  
  CONCLUSIONS
  βmRMR-MLP-GC is compared with Granger Causality Index, Conditional Granger Causality Index, and Transfer Entropy. It outperforms these methods in terms of sensitivity and specificity in simulated datasets. Also, βmRMR-MLP-GC detects the most number of significant and reproducible Back-to-Front net information flows among the specified brain regions and highlights the posterior brain regions as dominant source of alpha activity propagation.
  
  
  CONCLUSIONS
  βmRMR-MLP-GC provides a novel tool to estimate the direct nonlinear causal networks of high-dimensional datasets.
authors.affiliation: Control and Intelligent Processing Center of Excellence, School of Electrical and Computer Engineering, University College of Engineering, University of Tehran, Tehran, Iran.
authors.forename: Ali
authors.initials: A
authors.lastname: Khadem
authors.affiliation: Control and Intelligent Processing Center of Excellence, School of Electrical and Computer Engineering, University College of Engineering, University of Tehran, Tehran, Iran; School of Cognitive Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran. Electronic address: ghzadeh@ut.ac.ir.
authors.forename: Gholam-Ali
authors.initials: GA
authors.lastname: Hossein-Zadeh
mesh_terms: D000328:Adult; D000465:Algorithms; D000513:Alpha Rhythm; D001921:Brain / Q000502:physiology; D003198:Computer Simulation; D004569:Electroencephalography / Q000379:methods*; D006801:Humans; D007257:Information Theory; D016014:Linear Models; D008297:Male; D015999:Multivariate Analysis; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D012044:Regression Analysis; D012146:Rest / Q000502:physiology; D012680:Sensitivity and Specificity; D055815:Young Adult
keywords: EEG; Granger Causality; Multilayer perceptron; Nonlinear effective connectivity; Regressor selection