Principled Hyperedge Prediction with Structural Spectral Features and Neural Networks

Hypergraph offers a framework to depict the multilateral relationships in real-world complex data. Predicting higher-order relationships, i.e hyperedge, becomes a fundamental problem for the full understanding of complicated interactions. The development of graph neural network (GNN) has greatly advanced the analysis of ordinary graphs with pair-wise relations. However, these methods could not be easily extended to the case of hypergraph. In this paper, we generalize the challenges of GNN in representing higher-order data in principle, which are edge- and node-level ambiguities. To overcome the challenges, we present \textbf{SNALS} that utilizes bipartite graph neural network with structural features to collectively tackle the two ambiguity issues. SNALS captures the joint interactions of a hyperedge by its local environment, which is retrieved by collecting the spectrum information of their connections. As a result, SNALS achieves nearly 30% performance increase compared with most recent GNN-based models. In addition, we applied SNALS to predict genetic higher-order interactions on 3D genome organization data. SNALS showed consistently high prediction accuracy across different chromosomes, and generated novel findings on 4-way gene interaction, which is further validated by existing literature.