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Graph Attention for Heterogeneous Graphs with Positional Encoding

Nikhil Shivakumar Nayak

TL;DR

This work tackles heterogeneity in graphs by benchmarking attention-based GNNs and identifying RGAT, GTN, and HGT as strong baselines for node classification and link prediction. It introduces spectral positional encoding (LPE) derived from the full Laplacian spectrum, leveraging eigenvalues $\lambda_i$ and eigenvectors $\phi_i$, and integrates it into RGAT, GTN, and HGT to provide both absolute and relative node positions. Empirical results show general performance gains across diverse datasets, with particularly strong improvements for HGT on $Tox21$ and $IMDB$ and for GTN on $ACM$, while RGAT can occasionally decline on $AIFB$. The work highlights the value of combining spectral embeddings with attention mechanisms and points to scalable transformer variants and broader tasks as promising future directions, with code made available.

Abstract

Graph Neural Networks (GNNs) have emerged as the de facto standard for modeling graph data, with attention mechanisms and transformers significantly enhancing their performance on graph-based tasks. Despite these advancements, the performance of GNNs on heterogeneous graphs often remains complex, with networks generally underperforming compared to their homogeneous counterparts. This work benchmarks various GNN architectures to identify the most effective methods for heterogeneous graphs, with a particular focus on node classification and link prediction. Our findings reveal that graph attention networks excel in these tasks. As a main contribution, we explore enhancements to these attention networks by integrating positional encodings for node embeddings. This involves utilizing the full Laplacian spectrum to accurately capture both the relative and absolute positions of each node within the graph, further enhancing performance on downstream tasks such as node classification and link prediction.

Graph Attention for Heterogeneous Graphs with Positional Encoding

TL;DR

This work tackles heterogeneity in graphs by benchmarking attention-based GNNs and identifying RGAT, GTN, and HGT as strong baselines for node classification and link prediction. It introduces spectral positional encoding (LPE) derived from the full Laplacian spectrum, leveraging eigenvalues and eigenvectors , and integrates it into RGAT, GTN, and HGT to provide both absolute and relative node positions. Empirical results show general performance gains across diverse datasets, with particularly strong improvements for HGT on and and for GTN on , while RGAT can occasionally decline on . The work highlights the value of combining spectral embeddings with attention mechanisms and points to scalable transformer variants and broader tasks as promising future directions, with code made available.

Abstract

Graph Neural Networks (GNNs) have emerged as the de facto standard for modeling graph data, with attention mechanisms and transformers significantly enhancing their performance on graph-based tasks. Despite these advancements, the performance of GNNs on heterogeneous graphs often remains complex, with networks generally underperforming compared to their homogeneous counterparts. This work benchmarks various GNN architectures to identify the most effective methods for heterogeneous graphs, with a particular focus on node classification and link prediction. Our findings reveal that graph attention networks excel in these tasks. As a main contribution, we explore enhancements to these attention networks by integrating positional encodings for node embeddings. This involves utilizing the full Laplacian spectrum to accurately capture both the relative and absolute positions of each node within the graph, further enhancing performance on downstream tasks such as node classification and link prediction.

Paper Structure

This paper contains 14 sections, 23 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Background and Notation
  3. Relational Graph Attention Networks (RGAT)
  4. Graph Transformer Networks (GTN)
  5. Heterogeneous Graph Transformer (HGT)
  6. Learned Positional Encoding in Spectral Attention Network (SAN)
  7. Proposed Approach
  8. Datasets
  9. Benchmarking Methodology
  10. Spectral Positional Encoding
  11. Integration of Spectral Positional Encoding
  12. Results
  13. Discussion and Conclusion
  14. Appendix: Code Implementation

Figures (3)

  • Figure 1: Schema and meta relations of a heterogeneous graph. Figure taken from hu2020heterogeneous.
  • Figure 2: Learned positional encoding (LPE) architectures, with the model being aware of the graph's Laplace spectrum by considering $m$ eigenvalues and eigenvectors, where we permit $m \leq N$, with $N$ denoting the number of nodes. Figure taken from kreuzer2021rethinking.
  • Figure 3: Standard view of the eigenvectors as a matrix on the left and eigenvectors $\phi_i$ viewed as vectors positioned on the axis of frequencies (eigenvalues) on the right. Figure taken from kreuzer2021rethinking.