Accounting for the Complex Hierarchical Topology of EEG Functional Connectivity in Network Binarisation

All files are MATLAB files.

EyesOpenClosedData.mat contains the adjacency matrices of data processed as in the manuscript. The data comes from the Neurophysiological Biomarker Toolbox, available from www.nbtwiki.net. SpainADdata.mat contains the adjacency matrices of data processed as in the manuscript. The description of the signals can be found in Escudero J, Abasolo D, Hornero R, Espino P, Lopez M. Analysis of electroencephalograms in Alzheimer's disease patients with multiscale entropy. Physiological Measurement. 2016;27(11):1091-1106.

YHAshapeBindData.mat contains the adjacency matrices of data processed as in the manuscript. The signals are described in Smith K, Azami H, Escudero J, Parra MA, Starr JM. Comparison of network analysis approaches on EEG connectivity in beta during Visual Short-term Memory binding tasks. IEEE Proc. EMBC 2015. 2015;doi:10.1109/EMBC.2015.7318829. They were provided by Mario A. Parra, supported by the Alzheimer's Society, grant # AS-R42303 and MRC grant # MRC-R42552.

Scripts 1-5 provide the m-files for running the network analyses presented in the manuscript:
Script1_runComplexHierarchySimulations.m runs the simulations and computes results for the complex hierarchy models.
Script2_RunNetworkAttacks.m runs the network attack results.
Script3_RunEyesOpenClosedData runs analysis of the EyesOpenClosedData.mat file.
Script4_runVSTMdata runs analysis of the YHAshapeBindData.mat file.
Script5_runADdata runs analysis of the SpainADdata.mat file.

The other files pertain to MATLAB functions used to implement these scripts. Necessary citations can be found inside the function files.
randomHierarchy.m- computes weighted complex hierarchy models.
PhaseLagIndex_Stam.m- computes the phase lag index of MEG/EEG signals.
CST.m- computes the cluster-span threshold of a weighted adjacency matrix.
unionofshortestpaths.m- computes the union of shortest paths of a weighted adjacency matrix.
ECOfilter.m- computes the efficiency-cost optimisation threshold of a weighted adjacency matrix.
leafFraction.m- computes the leaf fraction of a binary minimum spanning tree.
FIRfiltersEOEC.mat- provides the alpha and beta filter coefficients for use in Script 3.

Herein are the network adjacency matrices, scripts and MATLAB functions used to provide the results in "Accounting for the complex hierarchical topology of EEG functional connectivity in network binarisation". Research into binary network analysis of brain function faces a methodological challenge in selecting an appropriate threshold to binarise edge weights. For EEG, such binarisation should take into account the complex hierarchical structure found in functional connectivity. We explore the density range suitable for such structure and provide a comparison of state-of-the-art binarisation techniques, the recently proposed Cluster-Span Threshold (CST), minimum spanning trees, efficiency-cost optimisation and union of shortest path graphs, with arbitrary proportional thresholds and weighted networks. We test these techniques on weighted complex hierarchy models by contrasting model realisations with small parametric differences. We also test the robustness of these techniques to random and targeted topological attacks. We reveal that complex hierarchical topology requires a medium-density range binarisation solution, such as the CST which proves near maximal for distinguishing differences when compared with arbitrary proportional thresholding. Simulated results are validated with the analysis of three relevant EEG datasets: eyes open and closed resting states; visual short-term memory tasks; and resting state Alzheimer's disease with a healthy control group. The CST consistently outperforms other state-of-the-art binarisation methods for topological accuracy and robustness in both synthetic and real data. We provide insights into how the complex hierarchical structure of functional networks is best revealed in medium density ranges and how it safeguards against targeted attacks.

Smith, Keith. (2017). Accounting for the Complex Hierarchical Topology of EEG Functional Connectivity in Network Binarisation, 2017 [software]. University of Edinburgh. School of Engineering. Institute for Digital Communications.. http://dx.doi.org/10.7488/ds/2109.