Constructing high-order functional networks based on hypergraph for diagnosis of autism spectrum disorders

High-order functional connectivity networks (FCNs) that reflect the connection relationships among multiple brain regions have become important tools for exploring the deep workings of the brain and revealing the mechanisms of brain diseases. The traditional high-order FCN constructed based on the "correlation of correlations" strategy, is a representative method for conducting whole-brain connectivity analysis and revealing global network characteristics. However, whole-brain connectivity analysis may be affected by noise carried by less important brain regions, resulting in redundant information and affecting the accuracy and reliability of the analysis. Moreover, this type of analysis has a high computational complexity.To address these issues, a new method for constructing high-order FCN based on hypergraphs is proposed in this article, which is used to accurately capture the real interaction relationships among brain regions. Specifically, first, a low-order FCN reflecting the connection relationships between pairs of brain regions based on resting-state functional Magnetic Resonance Imaging (rs-fMRI) time series is constructed, the method first constructs the low-order FCN that reflects the connection relationships between pairs of brain regions based on rs-fMRI time series, and then selects the "good friends" of each brain region from hypergraph perspective, which refers to the local friend circles with closer relationships. Then, the rs-fMRI time series corresponding to the "good friends" in each brain region's friend circle are averaged to obtain a sequence that reflects the intimacy between brain regions in each friend circle. Finally, hypergraph high-order FCN, which reflects the interaction relationships among multiple brain regions, is obtained by calculating the correlations based on the sequence of friend circles.The experimental results demonstrate that the proposed method outperforms traditional high-order FCN construction methods. Furthermore, integrating the high-order FCN constructed based on hypergraphs and the low-order FCN through feature fusion to achieve complementary information improves the accuracy of assisting in the diagnosis of brain diseases.In addition, the effectiveness of our method has only been validated in the diagnosis of ASD. For future work, we plan to extend this method to other brain connectivity patterns.