Principled Hyperedge Prediction with Structural Spectral Features and Neural Networks

Abstract

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 edgeand 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.

T-HyperGNNs: Hypergraph Neural Networks via Tensor Representations

“…Another matrix descriptor known as the adjacency matrix of a hypergraph is defined as A = HH T , which projects out the hyperedge dimension but leads to clique expansion (see Fig. 2 (b)) that causes distortion of hypergraph structures [15], [16].…”

“…With such reduction, the small edge e 1 contained in e 2 is ignored. Thus the hypergraph expansion is not a one-to-one mapping, which could cause node-level and edgelevel ambiguities [16]. Other methods such as HyperGCN [10] and LEGCN [23] are developed following similar ideas with different variants of matrix descriptors.…”

“…Since the graph convolution operation is originally derived in the spectral domain [12], we call them spectral HyperGNNs. Despite the simplicity, these methods could cause topological distortion and difficulty in downstream tasks since the mapping from a hypergraph to its corresponding simple graph is not one-to-one [15], [16]. For example, if we consider the clique expansion that connects any two nodes in a hyperedge, it is easy to verify that hypergraphs G 1 in Fig.…”

T-HyperGNNs: Hypergraph Neural Networks Via Tensor Representations

“…With such reduction, the small edge e 1 contained in e 2 is ignored. Thus the hypergraph expansion is not a one-to-one mapping, which could cause node-level and edgelevel ambiguities [16]. Other methods such as HyperGCN [10] and LEGCN [23] are developed following similar ideas with different variants of matrix descriptors.…”

Union Subgraph Neural Networks

“…But the local structures they choose are not able to capture the complete picture of the 1-hop neighborhood of an edge. Some others incorporate shortest path information to edges in message passing via distance encoding (Li et al 2020), adaptive breath/depth functions (Liu et al 2019) and affinity matrix (Wan et al 2021) to control the message from neighbors at different distances. However, the descriptor used to encode the substructure may overlook some connectivities between neighbors.…”