Mapping Brain Structural Connectivities to Functional Networks Via Graph EncoderDecoder With Interpretable Latent Embeddings In this paper, the relationship between functional and structural brain networks is investigated by training a graph encoderdecoder system to learn the mapping from brain structural connectivity (SC) to functional connectivity (FC). Our work leverages a graph convolutional network (GCN) model in the encoder which integrates both nodal attributes and the network topology information to generate new graph representations in lower dimensions. Using brain SC graphs as inputs, the novel GCNbased encoderdecoder system manages to account for both direct and indirect interactions between brain regions to reconstruct the empirical FC networks. In doing so, the latent variables within the system (i.e., the learnt lowdimensional embeddings) capture important information regarding the relation between functional and structural networks. By decomposing the reconstructed functional networks in terms of the output of each graph convolution filter, we can extract those brain regions which contribute most to the generation of FC networks from their SC counterparts. Experiments on a large population of healthy subjects from the Human Connectome Project show our model can learn a generalizable and interpretable SCFC relationship. Overall, results here support the promising prospect of using GCNs to discover more about the complex nature of human brain activity and function.

Joint embedding of structure and features via graph convolutional networks The creation of social ties is largely determined by the entangled effects of peopleu0027s similarities in terms of individual characters and friends. However, feature and structural characters of people usually appear to be correlated, making it difficult to determine which has greater responsibility in the formation of the emergent network structure. We propose emphAN2VEC, a node embedding method which ultimately aims at disentangling the information shared by the structure of a network and the features of its nodes. Building on the recent developments of Graph Convolutional Networks (GCN), we develop a multitask GCN Variational Autoencoder where different dimensions of the generated embeddings can be dedicated to encoding feature information, network structure, and shared featurenetwork information. We explore the interaction between these disentangled characters by comparing the embedding reconstruction performance to a baseline case where no shared information is extracted. We use synthetic datasets with different levels of interdependency between feature and network characters and show (i) that shallow embeddings relying on shared information perform better than the corresponding reference with unshared information, (ii) that this performance gap increases with the correlation between network and feature structure, and (iii) that our embedding is able to capture joint information of structure and features. Our method can be relevant for the analysis and prediction of any featured network structure ranging from online social systems to network medicine.