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Brain network analysis has been widely applied in neuroimaging studies. A hyper-network construction method was previously proposed to characterize the high-order relationships among multiple brain regions, where every edge is connected to more than two brain regions and can be represented by a hyper-graph. A brain functional hyper-network is constructed by a sparse linear regression model using resting-state functional magnetic resonance imaging (fMRI) time series, which in previous studies has been solved by the lasso method. Despite its successful application in many studies, the lasso method has some limitations, including an inability to explain the grouping effect. That is, using the lasso method may cause relevant brain regions be missed in selecting related regions. Ideally, a hyper-edge construction method should be able to select interacting brain regions as accurately as possible. To solve this problem, we took into account the grouping effect among brain regions and proposed two methods to improve the construction of the hyper-network: the elastic net and the group lasso. The three methods were applied to the construction of functional hyper-networks in depressed patients and normal controls. The results showed structural differences among the hyper-networks constructed by the three methods. The hyper-network structure obtained by the lasso was similar to that obtained by the elastic net method but very different from that obtained by the group lasso. The classification results indicated that the elastic net method achieved better classification results than the lasso method with the two proposed methods of hyper-network construction. The elastic net method can effectively solve the grouping effect and achieve better classification performance.

Resting-State Brain Functional Hyper-Network Construction Based on Elastic Net and Group Lasso Methods