Network Embedding (NE) is one of the most popular learning methods in complex networks. It aims at learning the low-dimensional representations of nodes in networks and has been applied in a variety of network analytic tasks. Most existing methods of NE are designed by merely using the local, high-order or global proximity to preserve the network structure; hence they are incapable of fully capturing the structural identity of nodes, which is a concept of symmetry defined by the network structure and their relationship to other nodes. There are two limitations to existing NE models. First, the local and global node dependency information is not considered simultaneously. Second, there is no adequate framework that can reveal the role property of each node. In this paper, we propose an intuitive and unified deep learning framework named DMER, short for Deep Mutual Encode for Embedding, to learn node embeddings from structural identity. In our model, Graph Convolution Network (GCN) is adopted to model the dependency relations between nodes from a global perspective. An Auto-Encoder (AE) framework is proposed to reconstruct the features of nodes, and it can conclusively reveal the structural identity from network structure. By integrating the GCN and AE components with a shared and constrained mechanism, the proposed model implements mutual enhancement for node embedding from structural identity. Experimental results based on structural role classification and visualization demonstrate that our model achieves better performance compared with the state-of-the-art methods.
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