[论文解读] Hypergraph Convolution and Hypergraph Attention

Song Bai, Feihu Zhang+1 more|arXiv (Cornell University)|Jan 23, 2019

Advanced Graph Neural Networks参考文献 73被引用 39

一句话总结

本文介绍了超图卷积和超图注意力，将图神经网络扩展到高阶关系，并在半监督节点分类方面相较于成对 GNNs 显示出提升。

ABSTRACT

Recently, graph neural networks have attracted great attention and achieved prominent performance in various research fields. Most of those algorithms have assumed pairwise relationships of objects of interest. However, in many real applications, the relationships between objects are in higher-order, beyond a pairwise formulation. To efficiently learn deep embeddings on the high-order graph-structured data, we introduce two end-to-end trainable operators to the family of graph neural networks, i.e., hypergraph convolution and hypergraph attention. Whilst hypergraph convolution defines the basic formulation of performing convolution on a hypergraph, hypergraph attention further enhances the capacity of representation learning by leveraging an attention module. With the two operators, a graph neural network is readily extended to a more flexible model and applied to diverse applications where non-pairwise relationships are observed. Extensive experimental results with semi-supervised node classification demonstrate the effectiveness of hypergraph convolution and hypergraph attention.

研究动机与目标

• Motivate learning on high-order (non-pairwise) relationships beyond simple graphs.
• Introduce end-to-end trainable hypergraph convolution and hypergraph attention operators.
• Demonstrate improved semi-supervised node classification performance on benchmark datasets.

提出的方法

• Define hypergraph with incidence matrix H, vertex degrees D and hyperedge degrees B.
• Propose hypergraph convolution: X^{(l+1)} = σ(D^{-1/2} H W B^{-1} H^T D^{-1/2} X^{(l)} P) (symmetric normalization) or X^{(l+1)} = σ(D^{-1} H W B^{-1} H^T X^{(l)} P) (asymmetric normalization).
• Prove that standard graph convolution is a special case of hypergraph convolution when hyperedges are pairwise.
• Optionally enable hypergraph attention by learning a dynamic incidence matrix H via attention scores (Eq. 7–8).
• Discuss practical aspects: complexity, sparsity, skip connections, and multi-head extensions (Eq. 13).
• Show how to integrate with existing GNNs and leverage non-pairwise relationships.

实验结果

研究问题

• RQ1 Can hypergraph convolution generalize graph convolution to higher-order relationships?
• RQ2 Does hypergraph attention provide further performance gains by learning dynamic connectivity?
• RQ3 How do hypergraph operators perform on standard semi-supervised node classification benchmarks compared to GCN/GAT?
• RQ4 What are practical considerations (normalization, sparsity, training stability) for implementing hypergraph operators?

主要发现

方法	Cora	Citeseer	Pubmed
Multilayer Perceptron	55.1	46.5	71.4
Manifold Regularization	59.5	60.1	70.7
Semi-supervised Embedding	59.0	59.6	71.7
Label Propagation	68.0	45.3	63.0
DeepWalk	67.2	43.2	65.3
Iterative Classification Algorithm	75.1	69.1	73.9
Planetoid	75.7	64.7	77.2
Chebyshev	81.2	69.8	74.4
MoNet	81.7	-	78.8
Variance Reduction	82.0	70.9	79.0
Graph Convolutional Network	81.5	70.3	79.0
Feng et al.	81.6	-	-
Ours (Hypergraph Conv)	82.7 ±0.3	71.2 ±0.4	78.4 ±0.3

• Hypergraph convolution reduces to graph convolution when hyperedges are pairwise and normalized appropriately.
• Hypergraph attention further improves results by learning dynamic connectivity over hyperedges.
• On Cora and Citeseer, hypergraph-based methods outperform their pairwise counterparts (e.g., Hyper-Conv. vs GCN*, Hyper-Atten. vs GAT*).
• On Pubmed, hypergraph attention achieves competitive accuracy with state-of-the-art methods.
• Table-based comparisons show Ours achieves 82.7% (Cora), 71.2% (Citeseer), and 78.4% (Pubmed) in Table 5, closely matching or exceeding several baselines.