[Paper Review] Hierarchical Graph Pooling with Structure Learning

Zhen Zhang, Jiajun Bu+5 more|arXiv (Cornell University)|Nov 14, 2019

Advanced Graph Neural Networks42 references120 citations

TL;DR

Proposes HGP-SL, a non-parametric graph pooling operator with a sparse-attention structure learning step to build hierarchical graph representations for graph classification, integrated into GNNs and tested on six benchmarks.

ABSTRACT

Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly focus on designing graph convolution operations. The graph pooling (or downsampling) operations, that play an important role in learning hierarchical representations, are usually overlooked. In this paper, we propose a novel graph pooling operator, called Hierarchical Graph Pooling with Structure Learning (HGP-SL), which can be integrated into various graph neural network architectures. HGP-SL incorporates graph pooling and structure learning into a unified module to generate hierarchical representations of graphs. More specifically, the graph pooling operation adaptively selects a subset of nodes to form an induced subgraph for the subsequent layers. To preserve the integrity of graph's topological information, we further introduce a structure learning mechanism to learn a refined graph structure for the pooled graph at each layer. By combining HGP-SL operator with graph neural networks, we perform graph level representation learning with focus on graph classification task. Experimental results on six widely used benchmarks demonstrate the effectiveness of our proposed model.

Motivation & Objective

• Motivate the need for hierarchical pooling in graph neural networks to capture both local and global graph structure for graph classification.
• Introduce a non-parametric graph pooling operator (HGP-SL) that selects informative nodes and forms induced subgraphs.
• Incorporate a structure learning mechanism with sparse attention to refine pooled graph topology.
• Demonstrate end-to-end trainability of HGP-SL within standard GNN architectures.
• Empirically validate the approach against diverse baselines on multiple benchmark datasets.

Proposed method

• Define node information score as the L1 distance between a node's representation and its neighborhood-reconstructed representation to guide pooling.
• Select top-rn_i^k nodes to form the induced subgraph at each pooling layer (non-parametric pooling).
• Introduce a sparse attention-based structure learning layer to compute a refined adjacency S_i^k using node features and existing edges, with sparsity via the sparsemax function.
• Integrate the learned S_i^k into subsequent graph convolutions (replacing the original adjacency in GCN/GNN layers).
• Compute a readout at each level by concatenating mean and max poolings, and sum over K layers to create the graph-level representation z_i.
• Train end-to-end with cross-entropy loss for graph classification.

Experimental results

Research questions

• RQ1 Can a non-parametric pooling operation that relies on node information scores preserve essential graph topology during hierarchical downsampling?
• RQ2 Does incorporating a sparse, learned graph structure in pooled subgraphs improve message passing and final graph classification performance compared to traditional pooling?
• RQ3 How does HGP-SL perform across different backbone GNN architectures and datasets compared to state-of-the-art pooling methods?

Key findings

• HGP-SL consistently outperforms state-of-the-art baselines across six benchmark datasets for graph classification.
• The structured pooling with learned sparse graphs yields better performance than NSL and HOP variants, validating the structure learning component.
• HGP-SL with dense vs. sparse structure learning shows that sparsity (via sparsemax) generally helps by reducing noise.
• Ablation shows combining pooling with structure learning outperforms using pooling alone or simple neighbor connections.
• HGP-SL achieves strong results across GCN, GAT, and GraphSAGE backbones, demonstrating architecture compatibility.