# Hierarchical Graph Pooling with Structure Learning

arXiv: https://arxiv.org/abs/1911.05954 · HTML: https://mlsanity.com/paper/1911.05954/

## Key facts

- Cited by 81 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2019.

## Built on by (most cited first, 30 of 81)

- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [A Comprehensive Survey on Deep Clustering: Taxonomy, Challenges, and Future Directions](https://mlsanity.com/paper/2206.07579/) (2022)
- [Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2204.07321/) (2022)
- [GSLB: The Graph Structure Learning Benchmark](https://mlsanity.com/paper/2310.05174/) (2023)
- [Efficient Learning of Mesh-Based Physical Simulation with BSMS-GNN](https://mlsanity.com/paper/2210.02573/) (2022)
- [Position-aware Structure Learning for Graph Topology-imbalance by Relieving Under-reaching and Over-squashing](https://mlsanity.com/paper/2208.08302/) (2022)
- [DialoGraph: Incorporating Interpretable Strategy-Graph Networks into Negotiation Dialogues](https://mlsanity.com/paper/2106.00920/) (2021)
- [AdaFGL: A New Paradigm for Federated Node Classification with Topology Heterogeneity](https://mlsanity.com/paper/2401.11750/) (2024)
- [Molecular Representation Learning via Heterogeneous Motif Graph Neural Networks](https://mlsanity.com/paper/2202.00529/) (2022)
- [Distribution Knowledge Embedding for Graph Pooling](https://mlsanity.com/paper/2109.14333/) (2021)
- [Comprehensive Graph Gradual Pruning for Sparse Training in Graph Neural Networks](https://mlsanity.com/paper/2207.08629/) (2022)
- [Continual Graph Learning: A Survey](https://mlsanity.com/paper/2301.12230/) (2023)
- [Rethinking Node-wise Propagation for Large-scale Graph Learning](https://mlsanity.com/paper/2402.06128/) (2024)
- [Hierarchical Adaptive Pooling by Capturing High-order Dependency for Graph Representation Learning](https://mlsanity.com/paper/2104.05960/) (2021)
- [Projective Ranking-based GNN Evasion Attacks](https://mlsanity.com/paper/2202.12993/) (2022)
- [Boosting Graph Structure Learning with Dummy Nodes](https://mlsanity.com/paper/2206.08561/) (2022)
- [LightDiC: A Simple yet Effective Approach for Large-scale Digraph Representation Learning](https://mlsanity.com/paper/2401.11772/) (2024)
- [Label Contrastive Coding based Graph Neural Network for Graph Classification](https://mlsanity.com/paper/2101.05486/) (2021)
- [Live Graph Lab: Towards Open, Dynamic and Real Transaction Graphs with NFT](https://mlsanity.com/paper/2310.11709/) (2023)
- [Graph Pooling via Ricci Flow](https://mlsanity.com/paper/2407.04236/) (2024)
- [Contrastive Brain Network Learning via Hierarchical Signed Graph Pooling Model](https://mlsanity.com/paper/2207.07650/) (2022)
- [Graphcode: Learning from multiparameter persistent homology using graph neural networks](https://mlsanity.com/paper/2405.14302/) (2024)
- [A Comprehensive Graph Pooling Benchmark: Effectiveness, Robustness and Generalizability](https://mlsanity.com/paper/2406.09031/) (2024)
- [Localized Graph Collaborative Filtering](https://mlsanity.com/paper/2108.04475/) (2021)
- [Pooling Strategies for Simplicial Convolutional Networks](https://mlsanity.com/paper/2210.05490/) (2022)
- [Impact-Oriented Contextual Scholar Profiling using Self-Citation Graphs](https://mlsanity.com/paper/2304.12217/) (2023)
- [Contrastive Graph Pooling for Explainable Classification of Brain Networks](https://mlsanity.com/paper/2307.11133/) (2023)
- [MaxCutPool: differentiable feature-aware Maxcut for pooling in graph neural networks](https://mlsanity.com/paper/2409.05100/) (2024)
- [Graph-in-Graph (GiG): Learning interpretable latent graphs in non-Euclidean domain for biological and healthcare applications](https://mlsanity.com/paper/2204.00323/) (2022)
- [On Exploring Node-feature and Graph-structure Diversities for Node Drop Graph Pooling](https://mlsanity.com/paper/2306.12726/) (2023)

## Abstract (arXiv)

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.