Joint embedding of structure and features via graph convolutional networks

Abstract

The creation of social ties is largely determined by the entangled effects of people's 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 AN2VEC, 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 feature-network 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. communities of shared interest, age, gender, or socio-economic status, and so on [4,12]. Though these mechanisms are not independent and lead to correlations between feature and network communities, it is difficult to define the causal relationship between the two: first, because simultaneously characterising similarities between multiple features and a complex network structure is not an easy task; second, because it is difficult to determine which of the two types of information, features or structure, is driving network formation to a greater extent. Indeed, we do not know what fraction of similar people initially get connected through homophilic tie creation, versus the fraction that first get connected due to structural similarities before influencing each other to become more similar [13,14].Over the last decade popular methods have been developed to characterise structural and feature similarities and to identify these two notions of communities. The detection of network communities has been a major challenge in network science with various concepts proposed [15,16,17] to solve it as an unsupervised learning task [18,19]. Commonly, these algorithms rely solely on network information, and their output is difficult to cross-examine without additional meta-data which is usually disregarded in their description. On the other hand, methods grouping similar people into feature communities typically ignore network information, and exclusively rely on individual feat...

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