Robust Self-Supervised Structural Graph Neural Network for Social Network Prediction

The self-supervised graph representation learning has achieved much success in recent web based research and applications, such as recommendation system, social networks, and anomaly detection. However, existing works suffer from two problems. Firstly, in social networks, the influential neighbors are important, but the overwhelming routine in graph representation-learning utilizes the node-wise similarity metric defined on embedding vectors that cannot exactly capture the subtle local structure and the network proximity. Secondly, existing works implicitly assume a universal distribution across datasets, which presumably leads to sub-optimal models considering the potential distribution shift. To address these problems, in this paper, we learn structural embeddings in which the proximity is characterized by 1-Wasserstein distance. We propose a distributionally robust self-supervised graph neural network framework to learn the representations. More specifically, in our method, the embeddings are computed based on subgraphs centering at the node of interest and represent both the node of interest and its neighbors, which better preserves the local structure of nodes. To make our model end-to-end trainable, we adopt a deep implicit layer to compute the Wasserstein distance, which can be formulated as a differentiable convex optimization problem. Meanwhile, our distributionally robust formulation explicitly constrains the maximal diversity for matched queries and keys. As such, our model is insensitive to the data distributions and has better generalization abilities. Extensive experiments demonstrate that the graph encoder learned by our approach can be utilized for various downstream analyses, including node classification, graph classification, and top-k similarity search. The results show our algorithm outperforms state-of-the-art baselines, and the ablation study validates the effectiveness of our design.