Heuristic Learning with Graph Neural Networks: A Unified Framework for Link Prediction

TL;DR

This paper introduces HL-GNN, a unified graph neural network framework that generalizes and efficiently implements various heuristics for link prediction, outperforming existing methods in accuracy and speed.

Contribution

The paper proposes a unified matrix formulation for local and global heuristics and develops HL-GNN, a scalable, interpretable GNN model that surpasses prior approaches in performance and efficiency.

Findings

HL-GNN outperforms existing methods in prediction accuracy.

HL-GNN is significantly faster than heuristic-inspired methods.

The learned heuristics are highly interpretable.

Abstract

Link prediction is a fundamental task in graph learning, inherently shaped by the topology of the graph. While traditional heuristics are grounded in graph topology, they encounter challenges in generalizing across diverse graphs. Recent research efforts have aimed to leverage the potential of heuristics, yet a unified formulation accommodating both local and global heuristics remains undiscovered. Drawing insights from the fact that both local and global heuristics can be represented by adjacency matrix multiplications, we propose a unified matrix formulation to accommodate and generalize various heuristics. We further propose the Heuristic Learning Graph Neural Network (HL-GNN) to efficiently implement the formulation. HL-GNN adopts intra-layer propagation and inter-layer connections, allowing it to reach a depth of around 20 layers with lower time complexity than GCN. Extensive experiments on the Planetoid, Amazon, and OGB datasets underscore the effectiveness and efficiency of HL-GNN. It outperforms existing methods by a large margin in prediction performance. Additionally, HL-GNN is several orders of magnitude faster than heuristic-inspired methods while requiring only a few trainable parameters. The case study further demonstrates that the generalized heuristics and learned weights are highly interpretable.