Decoupled Variational Graph Autoencoder for Link Prediction

Link prediction is an important learning task for graph-structured data, and has become increasingly popular due to its wide application areas. Graph Neural Network (GNN)-based approaches including Variational Graph Autoencoder (VGAE) have achieved promising performance on link prediction outperforming conventional models which use hand-crafted features. VGAE learns latent node representations and predicts links based on the similarities between nodes. While the inner product based decoder effectively utilizes the node representations for link prediction, it exhibits sub-optimal performance due to the intrinsic limitation of the inner product. We found that the the cosine similarity and norm simultaneously try to explain the link probability, which hinders the gradient flow during training. We also point out the message passing scheme is unexpectedly dominated by the nodes with large norm values. In this paper, we propose a stochastic VGAE-based method that can effectively decouple the norm and angle in the embeddings. Specifically, we relate the cosine similarity and norm to two fundamental principles in graph: homophily and node popularity respectively. Our learning scheme is based on a hard expectation maximization learning method; we infer which of the two has been exerted for link formation, and subsequently optimize based on this guess. Through extensive experiments on real-world datasets, we demonstrate our model outperforms the existing state-of-the-art methods on link prediction and achieves comparable performances on other downstream tasks such as node classification and clustering. Our code is at https://github.com/yoonsikcho/d-vgae.