  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 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.
