# Structural Adversarial Variational Auto-Encoder for Attributed Network Embedding
###### Abstract  
As most networks come with some content in each node, attributed network embedding has aroused much research interest. Most existing attributed network embedding methods aim at learning a fixed representation for each node encoding its local proximity. However, those methods usually neglect the global information between nodes distant from each other and distribution of the latent codes. We propose Structural Adversarial Variational Graph Auto-Encoder (SAVGAE), a novel framework which encodes the network structure and node content into low-dimensional embeddings. On one hand, our model captures the local proximity and proximities at any distance of a network by exploiting a high-order proximity indicator named Rooted Pagerank. On the other hand, our method learns the data distribution of each node representation while circumvents the side effect its sampling process causes on learning a robust embedding through adversarial training. On benchmark datasets, we demonstrate that our method performs competitively compared with state-of-the-art models.  
network embedding; adversarial training; variational auto-encoder; graph convolutional network +
Footnote †: journal:  
(VAE) ([10; 11]) and GCN to learn great node representation. Then ARVGA [12] and CAN [13] improve it by adding GAN or changing learning aim. GCN-based models inherit some common defects. VGAE and ARVGA use variational auto-encoders (VAE) to encode the data distribution of the latent codes in graphs while suffering from the drawback of the sampling process in VAE, which makes the latent representation not repeatable for the same sample and harms the performance in related tasks. These typical methods mostly ignore the global information between nodes.  
To overcome the deficits mentioned before, we propose a framework (SAVGAE) to encode the graph structure and node attribute of attributed networks into compact representation. We use the higher proximity metric Rooted PageRank to include the local and global information between each pair of nodes. We design a delicate structure to employ the strong learning ability of VAE while circumventing the effect brought by the inner core sampling process through an adversarial training module. The delicate structure makes the representation exclusive for each node and the adversarial training module prevents the performance declining it may cause. We evaluate our model on three typical graph analysis tasks including link prediction, node clustering, and graph visualization meanwhile get competitive performance. In summary, our contributions are as follows:  
1. We propose to use Rooted PageRank (RPR) rather than adjacency matrix as the reconstruction objective so as to preserve local and global proximity simultaneously in node representation.
2. We develop a novel graph autoencoder model combining generative adversarial networks and variational autoencoder, where we use the great learning ability of VAE and avoid the side effect it may cause on learning graph embedding.
3. We evaluate the proposed model over two tasks on three widely used graph benchmarks, and get competitive results.  
We organize the rest of our paper as follows. In Section 2, we introduce the work related to our model. In Section 3, we detail our model SAVGAE. In Section 4, we introduce the experiments setup and experiments results. Finally, in Section 5, we draw our conclusions.