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Brain network modularity analysis has attracted increasing interest due to its capability in measuring the level of integration and segregation across subnetworks. Most studies have focused on extracting modules at a single level, although brain network modules are known to be organized in a hierarchical manner. A few techniques have been developed to extract hierarchical modularity in human functional brain networks using resting-state functional magnetic resonance imaging (fMRI) data; however, the focus of those methods is binary networks produced by applying arbitrary thresholds of correlation coefficients to the connectivity matrices. In this study, we propose a new multisubject spectral clustering technique, called group-level network hierarchical clustering (GNetHiClus), to extract the hierarchical structure of the functional network based on full weighted connectivity information. The most reliable results of hierarchical clustering are then estimated using a bootstrap aggregation algorithm. Specifically, we employ a voting-based ensemble method, that is, majority voting; random subsamples with replacement are created for clustering brain regions, which are further aggregated to select the most reliable clustering results. The proposed method is evaluated over a range of group sample sizes, based on resting-state fMRI data from the Human Connectome Project. Our results show that GNetHiClus can extract relatively consistent hierarchical network structures across a range of sample sizes investigated. In addition, the results demonstrate that GNetHiClus can hierarchically cluster brain functional networks into specialized subnetworks from upper-to-lower level, including the high-level cognitive and the low-level perceptual networks. Conversely, from lower-to-upper level, information processed by specialized lower level subnetworks is integrated into upper level for achieving optimal efficiency for brain functional communications. Importantly, these findings are consistent with the concept of network segregation and integration, suggesting that the proposed technique can be helpful to promote the understanding of brain network from a hierarchical point of view.

A Novel Method for Extracting Hierarchical Functional Subnetworks Based on a Multisubject Spectral Clustering Approach