Hierarchical Synchronization Estimation of Low- and High-Order Functional Connectivity Based on Sub-Network Division for the Diagnosis of Autism Spectrum Disorder.

Functional connectivity network (FCN) calculated by resting-state functional magnetic resonance imaging (rs-fMRI) plays an increasingly important role in the exploration of neurologic and mental diseases. Among the presented researches, the method of constructing FCN based on Matrix Variate Normal Distribution (MVND) theory provides a novel perspective, which can capture both low- and high-order correlations simultaneously with a clear mathematical interpretability. However, when fitting MVND model, the dimension of the parameters (i.e., population mean and population covariance) to be estimated is too high, but the number of samples is relatively quite small, which is insufficient to achieve accurate fitting. To address the issue, we divide the brain network into several sub-networks, and then the MVND based FCN construction algorithm is implemented in each sub-network, thus the spatial dimension of MVND is reduced and more accurate estimates of low- and high-order FCNs is obtained. Furthermore, for making up the functional connectivity which is lost because of the sub-network division, the rs-fMRI mean series of all sub-networks are calculated, and the low- and high-order FCN across sub-networks are estimated with the MVND based FCN construction method. In order to prove the superiority and effectiveness of this method, we design and conduct classification experiments on ASD patients and normal controls. The experimental results show that the classification accuracy of "hierarchical sub-network method" is greatly improved, and the sub-network found most related to ASD in our experiment is consistent with other related medical researches.