# Principled Hyperedge Prediction with Structural Spectral Features and Neural Networks

arXiv: https://arxiv.org/abs/2106.04292 · HTML: https://mlsanity.com/paper/2106.04292/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 40 references that are in the map.
- First posted on arXiv 8 Jun 2021.

## Builds on (most cited first, 15 of 15)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [Drug discovery with explainable artificial intelligence](https://mlsanity.com/paper/2007.00523/) (2020)
- [HNHN: Hypergraph Networks with Hyperedge Neurons](https://mlsanity.com/paper/2006.12278/) (2020)
- [Simplicial Closure and higher-order link prediction](https://mlsanity.com/paper/1802.06916/) (2018)
- [Hyper-SAGNN: a self-attention based graph neural network for hypergraphs](https://mlsanity.com/paper/1911.02613/) (2019)
- [HyperSAGE: Generalizing Inductive Representation Learning on Hypergraphs](https://mlsanity.com/paper/2010.04558/) (2020)
- [Learning over Families of Sets -- Hypergraph Representation Learning for Higher Order Tasks](https://mlsanity.com/paper/2101.07773/) (2021)
- [Pairwise Link Prediction](https://mlsanity.com/paper/1907.04503/) (2019)

## Built on by (most cited first, 7 of 7)

- [A Survey on Hypergraph Neural Networks: An In-Depth and Step-By-Step Guide](https://mlsanity.com/paper/2404.01039/) (2024)
- [A Survey on Hyperlink Prediction](https://mlsanity.com/paper/2207.02911/) (2022)
- [A Hypergraph Neural Network Framework for Learning Hyperedge-Dependent Node Embeddings](https://mlsanity.com/paper/2212.14077/) (2022)
- [Union Subgraph Neural Networks](https://mlsanity.com/paper/2305.15747/) (2023)
- [Improving Graph Neural Networks on Multi-node Tasks with the Labeling Trick](https://mlsanity.com/paper/2304.10074/) (2023)
- [Expressive Higher-Order Link Prediction through Hypergraph Symmetry Breaking](https://mlsanity.com/paper/2402.11339/) (2024)
- [A Unified View Between Tensor Hypergraph Neural Networks And Signal Denoising](https://mlsanity.com/paper/2309.08385/) (2023)

## Abstract (arXiv)

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.