Table_3_Hypernetwork Construction and Feature Fusion Analysis Based on Sparse Group Lasso Method on fMRI Dataset.docx

Recent works have shown that the resting-state brain functional connectivity hypernetwork, where multiple nodes can be connected, are an effective technique for brain disease diagnosis and classification research. The lasso method was used to construct hypernetworks by solving sparse linear regression models in previous research. But, constructing a hypernetwork based on the lasso method simply selects a single variable, in that it lacks the ability to interpret the grouping effect. Considering the group structure problem, the previous study proposed to create a hypernetwork based on the elastic net and the group lasso methods, and the results showed that the former method had the best classification performance. However, the highly correlated variables selected by the elastic net method were not necessarily in the active set in the group. Therefore, we extended our research to address this issue. Herein, we propose a new method that introduces the sparse group lasso method to improve the construction of the hypernetwork by solving the group structure problem of the brain regions. We used the traditional lasso, group lasso method, and sparse group lasso method to construct a hypernetwork in patients with depression and normal subjects. Meanwhile, other clustering coefficients (clustering coefficients based on pairs of nodes) were also introduced to extract features with traditional clustering coefficients. Two types of features with significant differences obtained after feature selection were subjected to multi-kernel learning for feature fusion and classification using each method, respectively. The network topology results revealed differences among the three networks, where hypernetwork using the lasso method was the strictest; the group lasso, most lenient; and the sgLasso method, moderate. The network topology of the sparse group lasso method was similar to that of the group lasso method but different from the lasso method. The classification results show that the sparse group lasso method achieves the best classification accuracy by using multi-kernel learning, which indicates that better classification performance can be achieved when the group structure exists and is properly extended.