Network Community Structure Detection for Directional Neural Networks Inferred From Multichannel Multisubject EEG Data

In many neuroscience applications, one is interested in identifying the functional brain modules from multichannel, multiple subject neuroimaging data. However, most of the existing network community structure detection algorithms are limited to single undirected networks and cannot reveal the common community structure for a collection of directed networks. In this paper, we propose a community detection algorithm for weighted asymmetric (directed) networks representing the effective connectivity in the brain. Moreover, the issue of finding a common community structure across subjects is addressed by maximizing the total modularity of the group. Finally, the proposed community detection algorithm is applied to multichannel multisubject electroencephalogram data.

[1]  Sergio Gómez,et al.  Size reduction of complex networks preserving modularity , 2007, ArXiv.

[2]  W. Press,et al.  Numerical Recipes: The Art of Scientific Computing , 1987 .

[3]  E A Leicht,et al.  Community structure in directed networks. , 2007, Physical review letters.

[4]  Olaf Sporns,et al.  Complex network measures of brain connectivity: Uses and interpretations , 2010, NeuroImage.

[5]  Karl J. Friston.  Modalities, Modes, and Models in Functional Neuroimaging , 2009, Science.

[6]  Schreiber,et al.  Measuring information transfer , 2000, Physical review letters.

[7]  A. Arenas,et al.  Community detection in complex networks using extremal optimization. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Greg Hajcak,et al.  The stability of error-related brain activity with increasing trials. , 2009, Psychophysiology.

[9]  Jacob Cohen,et al.  Weighted kappa: Nominal scale agreement provision for scaled disagreement or partial credit. , 1968 .

[10]  Olaf Sporns,et al.  The small world of the cerebral cortex , 2007, Neuroinformatics.

[11]  J Martinerie,et al.  Functional modularity of background activities in normal and epileptic brain networks. , 2008, Physical review letters.

[12]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..

[13]  S. Mori,et al.  White matter atlases based on diffusion tensor imaging , 2009, Current opinion in neurology.

[14]  Joseph P. Romano,et al.  The stationary bootstrap , 1994 .

[15]  Jürgen Kayser,et al.  Principal components analysis of Laplacian waveforms as a generic method for identifying ERP generator patterns: I. Evaluation with auditory oddball tasks , 2006, Clinical Neurophysiology.

[16]  Alfred O. Hero,et al.  Using Directed Information to Build Biologically Relevant Influence Networks , 2007, J. Bioinform. Comput. Biol..

[17]  J. E. Glynn,et al.  Numerical Recipes: The Art of Scientific Computing , 1989 .

[18]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[19]  E A Leicht,et al.  Mixture models and exploratory analysis in networks , 2006, Proceedings of the National Academy of Sciences.

[20]  Jean-Loup Guillaume,et al.  Fast unfolding of communities in large networks , 2008, 0803.0476.

[21]  Mark Newman,et al.  Detecting community structure in networks , 2004 .

[22]  C. Granger.  Testing for causality: a personal viewpoint , 1980 .

[23]  Luiz A. Baccalá,et al.  Partial directed coherence: a new concept in neural structure determination , 2001, Biological Cybernetics.

[24]  Ying Liu,et al.  Time-lagged Directed Information , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[25]  Laura Astolfi,et al.  Cluster Structure of Functional Networks Estimated from High-Resolution EEG Data , 2008, Int. J. Bifurc. Chaos.

[26]  O. Sporns,et al.  Complex brain networks: graph theoretical analysis of structural and functional systems , 2009, Nature Reviews Neuroscience.

[27]  M E J Newman,et al.  Modularity and community structure in networks. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[28]  Roger Guimerà,et al.  Module identification in bipartite and directed networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Olivier J. J. Michel,et al.  On directed information theory and Granger causality graphs , 2010, Journal of Computational Neuroscience.

[30]  Todd P. Coleman,et al.  Estimating the directed information to infer causal relationships in ensemble neural spike train recordings , 2010, Journal of Computational Neuroscience.

[31]  S. Rombouts,et al.  Hierarchical functional modularity in the resting‐state human brain , 2009, Human brain mapping.

[32]  Thomas E. Nichols,et al.  Thresholding of Statistical Maps in Functional Neuroimaging Using the False Discovery Rate , 2002, NeuroImage.

[33]  Danielle Smith Bassett,et al.  Small-World Brain Networks , 2006, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

[34]  Adjustments Mind Your Errors : Evidence for a Neural Mechanism Linking Growth Mind-Set to Adaptive Posterror , 2011 .

[35]  C. Eriksen,et al.  Effects of noise letters upon the identification of a target letter in a nonsearch task , 1974 .

[36]  J. Massey.  CAUSALITY, FEEDBACK AND DIRECTED INFORMATION , 1990 .

[37]  Bin He,et al.  fMRI–EEG integrated cortical source imaging by use of time-variant spatial constraints , 2008, NeuroImage.

[38]  E. Bullmore,et al.  A Resilient, Low-Frequency, Small-World Human Brain Functional Network with Highly Connected Association Cortical Hubs , 2006, The Journal of Neuroscience.

[39]  Edward T. Bullmore,et al.  Efficiency and Cost of Economical Brain Functional Networks , 2007, PLoS Comput. Biol..

[40]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[41]  A. D. Medus,et al.  Community Detection in Networks , 2010, Int. J. Bifurc. Chaos.

[42]  Jonathan D. Power,et al.  Functional Brain Networks Develop from a “Local to Distributed” Organization , 2009, PLoS Comput. Biol..

[43]  G. Kramer,et al.  Capacity results for the discrete memoryless network , 1999, Proceedings of the 1999 IEEE Information Theory and Communications Workshop (Cat. No. 99EX253).

[44]  Aapo Hyvärinen,et al.  A Linear Non-Gaussian Acyclic Model for Causal Discovery , 2006, J. Mach. Learn. Res..

[45]  Karl J. Friston,et al.  Effective Connectivity and Intersubject Variability: Using a Multisubject Network to Test Differences and Commonalities , 2002, NeuroImage.

[46]  J. B. Garner,et al.  The standard error of Cohen's Kappa. , 1991, Statistics in medicine.

[47]  M E J Newman,et al.  Fast algorithm for detecting community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  Karl J. Friston,et al.  Evaluation of different measures of functional connectivity using a neural mass model , 2004, NeuroImage.

[49]  Edward T. Bullmore,et al.  Age-related changes in modular organization of human brain functional networks , 2009, NeuroImage.

[50]  O. Sporns,et al.  Identification and Classification of Hubs in Brain Networks , 2007, PloS one.

[51]  Angelo Bifone,et al.  Community structure and modularity in networks of correlated brain activity. , 2007, Magnetic resonance imaging.

[52]  Albert-László Barabási,et al.  Hierarchical organization in complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[53]  Rodrigo Quian Quiroga,et al.  Nonlinear multivariate analysis of neurophysiological signals , 2005, Progress in Neurobiology.

[54]  Martin J. McKeown,et al.  Dynamic Bayesian network modeling of fMRI: A comparison of group-analysis methods , 2008, NeuroImage.

[55]  Bin He,et al.  Electrophysiological Imaging of Brain Activity and Connectivity—Challenges and Opportunities , 2011, IEEE Transactions on Biomedical Engineering.

[56]  M. Barthelemy.  Betweenness centrality in large complex networks , 2003, cond-mat/0309436.

[57]  Stefan Haufe,et al.  A critical assessment of connectivity measures for EEG data: A simulation study , 2013, NeuroImage.

[58]  E Donchin,et al.  A new method for off-line removal of ocular artifact. , 1983, Electroencephalography and clinical neurophysiology.

[59]  E. Miller,et al.  An integrative theory of prefrontal cortex function. , 2001, Annual review of neuroscience.

[60]  Ying Liu,et al.  Directed information measure for quantifying the information flow in the brain , 2009, 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[61]  Joydeep Ghosh,et al.  Cluster Ensembles --- A Knowledge Reuse Framework for Combining Multiple Partitions , 2002, J. Mach. Learn. Res..

[62]  Ying Liu,et al.  Quantification of Effective Connectivity in the Brain Using a Measure of Directed Information , 2012, Comput. Math. Methods Medicine.

[63]  Erik G. Miller.  A new class of entropy estimators for multi-dimensional densities , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[64]  Hans-Jochen Heinze,et al.  Directed information flow—A model free measure to analyze causal interactions in event related EEG‐MEG‐experiments , 2008, Human brain mapping.

[65]  Vince D. Calhoun,et al.  Canonical Correlation Analysis for Data Fusion and Group Inferences , 2010, IEEE Signal Processing Magazine.

[66]  Ulrike von Luxburg,et al.  A tutorial on spectral clustering , 2007, Stat. Comput..

[67]  Igor Vajda,et al.  Estimation of the Information by an Adaptive Partitioning of the Observation Space , 1999, IEEE Trans. Inf. Theory.

[68]  M. Botvinick,et al.  Conflict monitoring and cognitive control. , 2001, Psychological review.

[69]  J. Martinerie,et al.  Statistical assessment of nonlinear causality: application to epileptic EEG signals , 2003, Journal of Neuroscience Methods.

[70]  Yu-Hao Lee,et al.  Mind Your Errors , 2011, Psychological science.

[71]  Karl J. Friston,et al.  Dynamic causal modelling , 2003, NeuroImage.

[72]  Selin Aviyente,et al.  A phase synchrony measure for quantifying dynamic functional integration in the brain , 2011, Human brain mapping.

[73]  R. Willison.  Recent Advances in EEG and EMG Data Processing , 1982 .

[74]  Karl J. Friston.  Functional and Effective Connectivity: A Review , 2011, Brain Connect..

[75]  Ying Liu,et al.  Community detection for directional neural networks inferred from EEG data , 2011, 2011 Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[76]  D. Perkel,et al.  Simultaneously Recorded Trains of Action Potentials: Analysis and Functional Interpretation , 1969, Science.

[77]  Changsong Zhou,et al.  Hierarchical organization unveiled by functional connectivity in complex brain networks. , 2006, Physical review letters.

[78]  Edward T. Bullmore,et al.  Neuroinformatics Original Research Article , 2022 .

[79]  C. Tenke,et al.  Generator localization by current source density (CSD): Implications of volume conduction and field closure at intracranial and scalp resolutions , 2012, Clinical Neurophysiology.

[80]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

[81]  V. Latora,et al.  Detecting complex network modularity by dynamical clustering. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[82]  Gary H. Glover,et al.  Grand Challenges in Mapping the Human Brain: NSF Workshop Report , 2013, IEEE Transactions on Biomedical Engineering.