[Paper Review] Topology-Aware Graph Pooling Networks

Hongyang Gao, Yi Liu+1 more|arXiv (Cornell University)|Oct 19, 2020

Advanced Graph Neural Networks32 references7 citations

TL;DR

This paper proposes a topology-aware pooling (TAP) layer that enhances graph neural network performance by explicitly incorporating local and global graph topology into node ranking for graph coarsening. The method uses a two-stage voting mechanism—local voting via node neighborhood similarity and global voting via a trainable projection—combined with a graph connectivity term to improve coarsened graph connectivity, achieving state-of-the-art performance on graph classification benchmarks with minimal parameter overhead.

ABSTRACT

Pooling operations have shown to be effective on computer vision and natural language processing tasks. One challenge of performing pooling operations on graph data is the lack of locality that is not well-defined on graphs. Previous studies used global ranking methods to sample some of the important nodes, but most of them are not able to incorporate graph topology. In this work, we propose the topology-aware pooling (TAP) layer that explicitly considers graph topology. Our TAP layer is a two-stage voting process that selects more important nodes in a graph. It first performs local voting to generate scores for each node by attending each node to its neighboring nodes. The scores are generated locally such that topology information is explicitly considered. In addition, graph topology is incorporated in global voting to compute the importance score of each node globally in the entire graph. Altogether, the final ranking score for each node is computed by combining its local and global voting scores. To encourage better graph connectivity in the sampled graph, we propose to add a graph connectivity term to the computation of ranking scores. Results on graph classification tasks demonstrate that our methods achieve consistently better performance than previous methods.

Motivation & Objective

• To address the limitation of existing graph pooling methods that fail to explicitly encode graph topology in node ranking.
• To improve graph coarsening quality by incorporating both local neighborhood structure and global graph topology.
• To reduce the risk of isolated nodes in coarsened graphs through a connectivity regularization term.
• To develop a scalable, parameter-efficient pooling mechanism that enhances graph neural network performance.
• To validate the effectiveness of the proposed TAP layer through ablation and comparative studies on diverse graph datasets.

Proposed method

• The TAP layer performs local voting by computing similarity scores between each node and its neighbors using dot product attention, then averages these scores to determine local importance.
• Global voting uses a trainable projection vector to compute a global importance score for each node by projecting its feature vector into a scalar.
• Final ranking scores are computed as a weighted combination of local and global voting scores to balance local and global topology awareness.
• A graph connectivity term is introduced, using node degree as a bias to favor selection of highly connected nodes and prevent isolated components in the coarsened graph.
• The TAP layer is integrated into a topology-aware pooling network (TAPNet) with an auxiliary link prediction objective to improve training stability and representation learning.
• The method is trained end-to-end and evaluated on standard graph classification datasets including PTC, MUTAG, IMDB-BINARY, and REDDIT-BINARY.

Experimental results

Research questions

• RQ1 Can explicit modeling of local and global graph topology improve node selection in graph pooling operations?
• RQ2 How does the inclusion of a graph connectivity term affect the quality and connectivity of coarsened graphs?
• RQ3 What is the impact of the hyperparameter λ balancing local topology and connectivity in the TAP layer?
• RQ4 Does the TAP layer lead to consistent performance gains across diverse graph classification datasets?
• RQ5 How does the TAP layer compare in performance and parameter efficiency to existing pooling methods like top-k and SortPool?

Key findings

• The TAP layer achieves a 3.6% accuracy improvement over TAPNet without TAP layers on the REDDIT-BINARY dataset, demonstrating its effectiveness.
• TAPNet with auxiliary link prediction achieves better performance than TAPNet without it, confirming the benefit of the similarity score matrix for training.
• The ablation study shows that both local and global voting components significantly contribute to performance, with TAPNet w/o LV&GV underperforming the full model.
• The optimal λ value for the connectivity term is 0.1, as higher values degrade performance, indicating that topology encoding should dominate over connectivity bias.
• The TAP layer adds only 2.29% more parameters than the baseline, showing minimal computational overhead despite significant performance gains.
• Visualizations confirm that TAP produces better-connected coarsened graphs than TAP without the connectivity term, reducing isolated node issues.