[Paper Review] HyperGCN: A New Method of Training Graph Convolutional Networks on Hypergraphs

Naganand Yadati, Madhav Nimishakavi+4 more|arXiv (Cornell University)|Sep 7, 2018

Advanced Graph Neural Networks61 references205 citations

TL;DR

HyperGCN trains graph convolutional networks on hypergraphs by linear-edge approximations, outperforming HGNN on noisy hyperedges in SSL and enabling apps in combinatorial optimization.

ABSTRACT

In many real-world network datasets such as co-authorship, co-citation, email communication, etc., relationships are complex and go beyond pairwise. Hypergraphs provide a flexible and natural modeling tool to model such complex relationships. The obvious existence of such complex relationships in many real-world networks naturaly motivates the problem of learning with hypergraphs. A popular learning paradigm is hypergraph-based semi-supervised learning (SSL) where the goal is to assign labels to initially unlabeled vertices in a hypergraph. Motivated by the fact that a graph convolutional network (GCN) has been effective for graph-based SSL, we propose HyperGCN, a novel GCN for SSL on attributed hypergraphs. Additionally, we show how HyperGCN can be used as a learning-based approach for combinatorial optimisation on NP-hard hypergraph problems. We demonstrate HyperGCN's effectiveness through detailed experimentation on real-world hypergraphs.

Motivation & Objective

• Motivate learning on hypergraphs where relationships go beyond pairwise edges.
• Propose a graph-convolutional framework (HyperGCN) that uses hypergraph Laplacians to guide learning.
• Demonstrate HyperGCN's effectiveness in semi-supervised learning and combinatorial optimization on real-world hypergraphs.
• Compare HyperGCN against baselines including HGNN and MLP-based methods to identify regimes where HyperGCN excels.

Proposed method

• Define a hypergraph Laplacian-based approximation to transform each hyperedge into a linear set of edges.
• Propose 1-HyperGCN which uses exactly one representative edge per hyperedge for convolution.
• Enhance 1-HyperGCN with mediators to form a generalized hypergraph Laplacian (HyperGCN with mediators).
• Introduce FastHyperGCN which precomputes the Laplacian using initial features for faster training.
• Provide training algorithms (HyperGCN, FastHyperGCN, 1-HyperGCN) and analyze their time complexities.
• Show that HyperGCN reduces edge growth to linear per hyperedge compared to clique-based expansions.

Experimental results

Research questions

• RQ1 How can hypergraphs be leveraged effectively for semi-supervised learning with neural models?
• RQ2 When does HyperGCN outperform clique-based HGNN on real-world hypergraphs, particularly with large noisy hyperedges?
• RQ3 What is the computational trade-off between accuracy and training time for HyperGCN variants?
• RQ4 Can HyperGCN be applied to combinatorial optimization problems on hypergraphs beyond SSL?

Key findings

• HyperGCN, FastHyperGCN, and 1-HyperGCN outperform HGNN on real-world hypergraphs with noisy large hyperedges (DBLP, PubMed, Cora co-authorship).
• HyperGCN achieves the best mean test errors across most SSL datasets: DBLP 24.09±2.0, PubMed 25.56±1.6, Cora co-authorship 30.08±1.8, Cora co-citation 32.37±1.6, Citeseer 37.35±1.6.
• FastHyperGCN generally offers faster training times and strong performance, often close to HyperGCN.
• HGNN remains competitive on datasets with smaller or less noisy hyperedges (e.g., Cora/Citeseer co-citation).
• On synthetic/noisy hypergraphs, HyperGCN methods show robustness advantages over HGNN as hyperedge size and noise increase.
• In combinatorial optimization tasks on hypergraphs, HyperGCN-based approaches outperform several baselines in density.