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

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Objective: Research into network analysis of brain function faces a methodological challenge in selecting an appropriate threshold to binarise edge weights. 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 including the recently proposed Cluster-Span Threshold (CST). Methods: We compare CST networks with weighted networks, minimum spanning trees, union of shortest path graphs and arbitrary proportional thresholds. 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. Simulated results are confirmed 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. Results: The CST consistently outperforms other state-of-the-art binarisation methods for topological accuracy and robustness in both synthetic and real data. In fact, it proves near maximal for distinguishing differences when compared with arbitrary proportional thresholding. Conclusion: Complex hierarchical topology requires a medium-density range binarisation solution, such as the CST. Significance: 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. We explore the effects of network size and density on the topological accuracy of binarised networks.