Variational autoencoder based bipartite network embedding by integrating local and global structure Abstract   As a powerful tool for machine learning on the graph, network embedding, which projects nodes into lowdimensional spaces, has a variety of applications on complex networks. Most current methods and models are not suitable for bipartite networks, which have two different types of nodes and there are no links between nodes of the same type. Furthermore, the only existing methods for bipartite network embedding ignore the internal mechanism and highly nonlinear structures of links. Therefore, in this paper, we propose a new deep learning method to learn the node embedding for bipartite networks based on the widely used autoencoder framework. Moreover, we carefully devise a nodelevel triplet including two types of nodes to assign the embedding by integrating the local and global structures. Meanwhile, we apply the variational autoencoder (VAE), a deep generation model with natural advantages in data generation and reconstruction, to enhance the node embedding for the highly nonlinear relationships between nodes and complex features. Experiments on some widely used datasets show the effectiveness of the proposed model and corresponding algorithm compared with some baseline network (and bipartite) embedding techniques.

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.