Deep Generative Models for Spatial Networks

Spatial networks represent crucial data structures where the nodes and edges are embedded in a geometric space. Nowadays, spatial network data is becoming increasingly popular and important, ranging from microscale (e.g., protein structures), to middle-scale (e.g., biological neural networks), to macro-scale (e.g., mobility networks). Although, modeling and understanding the generative process of spatial networks are very important, they remain largely under-explored due to the significant challenges in automatically modeling and distinguishing the independency and correlation among various spatial and network factors. To address these challenges, we first propose a novel objective for joint spatial-network disentanglement from the perspective of information bottleneck as well as a novel optimization algorithm to optimize the intractable objective. Based on this, a spatial-network variational autoencoder (SND-VAE) with a new spatial-network message passing neural network (S-MPNN) is proposed to discover the independent and dependent latent factors of spatial and networks. Qualitative and quantitative experiments on both synthetic and real-world datasets demonstrate the superiority of the proposed model over the state-of-the-arts by up to 66.9% for graph generation and 37.3% for interpretability.