Brain networks have received considerable attention given the critical significance for understanding human brain organization, for investigating neurological disorders and for clinical diagnostic applications. Structural brain network (e.g. DTI) and functional brain network (e.g. fMRI) are the primary networks of interest. Most existing works in brain network analysis focus on either structural or functional connectivity, which cannot leverage the complementary information from each other. Although multi-view learning methods have been proposed to learn from both networks (or views), these methods aim to reach a consensus among multiple views, and thus distinct intrinsic properties of each view may be ignored. How to jointly learn representations from structural and functional brain networks while preserving their inherent properties is a critical problem. In this paper, we propose a framework of Siamese community-preserving graph convolutional network (SCP-GCN) to learn the structural and functional joint embedding of brain networks. Specifically, we use graph convolutions to learn the structural and functional joint embedding, where the graph structure is defined with structural connectivity and node features are from the functional connectivity. Moreover, we propose to preserve the community structure of brain networks in the graph convolutions by considering the intra-community and inter-community properties in the learning process. Furthermore, we use Siamese architecture which models the pair-wise similarity learning to guide the learning process. To evaluate the proposed approach, we conduct extensive experiments on two real brain network datasets. The experimental results demonstrate the superior performance of the proposed approach in structural and functional joint embedding for neurological disorder analysis, indicating its promising value for clinical applications.
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