Trivial bundle embeddings for learning graph representations

Embedding real-world networks presents challenges because it is not clear how to identify their latent geometries. Embedding some disassortative networks, such as scale-free networks, to the Euclidean space has been shown to incur distortions. Embedding scale-free networks to hyperbolic spaces offer an exciting alternative but incurs distortions when embedding assortative networks with latent geometries not hyperbolic. We propose an inductive model that leverages both the expressiveness of GCNs and trivial bundle to learn inductive node representations for networks with or without node features. A trivial bundle is a simple case of fiber bundles,a space that is globally a product space of its base space and fiber. The coordinates of base space and those of fiber can be used to express the assortative and disassortative factors in generating edges. Therefore, the model has the ability to learn embeddings that can express those factors. In practice, it reduces errors for link prediction and node classification when compared to the Euclidean and hyperbolic GCNs.