[Paper Review] HNHN: Hypergraph Networks with Hyperedge Neurons

Yihe Dong, Will Sawin+1 more|arXiv (Cornell University)|Jun 22, 2020

Advanced Graph Neural Networks22 references47 citations

TL;DR

HNHN introduces a hypergraph convolution framework that assigns representations to both hypernodes and hyperedges with nonlinear activations, plus a flexible normalization scheme, achieving improved accuracy and speed over state-of-the-art methods on real datasets.

ABSTRACT

Hypergraphs provide a natural representation for many real world datasets. We propose a novel framework, HNHN, for hypergraph representation learning. HNHN is a hypergraph convolution network with nonlinear activation functions applied to both hypernodes and hyperedges, combined with a normalization scheme that can flexibly adjust the importance of high-cardinality hyperedges and high-degree vertices depending on the dataset. We demonstrate improved performance of HNHN in both classification accuracy and speed on real world datasets when compared to state of the art methods.

Motivation & Objective

• Motivate learning on hypergraphs by treating hyperedges as first-class entities with dedicated representations.
• Develop a hypergraph convolution method that uses incidence-based propagation with nonlinear activations on both hypernodes and hyperedges.
• Introduce a flexible normalization scheme to balance high-cardinality hyperedges and high-degree vertices based on dataset needs.
• Compare HNHN against clique and star expansions and existing hypergraph learning methods to demonstrate advantages in accuracy and efficiency.

Proposed method

• Define hypergraph with incidence matrix A and learn separate representations for hypernodes X_V and hyperedges X_E.
• Update rules: X_E' = sigma(A^T X_V W_E + b_E) and X_V' = sigma(A X_E' W_V + b_V).
• Incorporate nonlinear activation on both hypernodes and hyperedges to capture hyperedge-specific nonlinearities.
• Introduce normalization schemes D_{E,l,alpha}, D_{V,r,alpha}, D_{V,l,alpha}, D_{E,r,alpha} parameterized by alpha and beta to weight hyperedges and vertices by degree.
• Provide a practical implementation that computes normalization factors from hypergraph neighborhoods without explicitly forming the incidence matrix A.
• Discuss relationships to clique and star expansions and show how HNHN generalizes graph convolution on these expansions, with and without nonlinearities.
• Detail training procedure, hyperparameters, and convergence considerations (e.g., using Adam, dropout, ReLU).

Experimental results

Research questions

• RQ1 Can hyperedge-specific nonlinear activations improve predictive performance on hypergraph-structured data beyond traditional graph-convolution on clique/star expansions?
• RQ2 How does a flexible, degree-aware normalization affect learning on hypergraphs with varying hyperedge sizes and node degrees?
• RQ3 What are the comparative advantages in accuracy and speed of HNHN versus existing hypergraph convolution methods (e.g., HyperGCN, HGNN) across standard datasets?
• RQ4 Is it beneficial to maintain separate representations for hypernodes and hyperedges in learning tasks such as hypernode and hyperedge prediction?

Key findings

• HNHN outperforms state-of-the-art methods on several benchmark datasets for hypernode classification, with notable accuracy gains.
• The model provides competitive training speed due to avoidance of explicit incidence matrix instantiation and efficient GPU-based computations.
• Using nonlinear activations on both hypernodes and hyperedges yields better expressive power than linear or mono-entity approaches.
• The normalization scheme with tunable alpha and beta parameters significantly impacts performance, and default equal-weight normalization (alpha=beta=0) is not always optimal.
• HNHN enables simultaneous learning of hyperedge representations, enabling competitive hyperedge prediction alongside node prediction.