mlsanityData to 7 Oct 2026

Higher-order Clustering and Pooling for Graph Neural Networks

arXiv 2209.03473 ↗First posted 2 Sep 2022cs.LG cs.AIcited by 26

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Abstract (arXiv)

Graph Neural Networks achieve state-of-the-art performance on a plethora of graph classification tasks, especially due to pooling operators, which aggregate learned node embeddings hierarchically into a final graph representation. However, they are not only questioned by recent work showing on par performance with random pooling, but also ignore completely higher-order connectivity patterns. To tackle this issue, we propose HoscPool, a clustering-based graph pooling operator that captures higher-order information hierarchically, leading to richer graph representations. In fact, we learn a probabilistic cluster assignment matrix end-to-end by minimising relaxed formulations of motif spectral clustering in our objective function, and we then extend it to a pooling operator. We evaluate HoscPool on graph classification tasks and its clustering component on graphs with ground-truth community structure, achieving best performance. Lastly, we provide a deep empirical analysis of pooling operators' inner functioning.

Key facts. Cited by 26 papers in the map (data through 7 Oct 2026). Builds on 33 of its 56 references that are in the map. First posted on arXiv 2 Sep 2022.

Builds on

33 of 56 references.

References · 33

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Inductive Representation Learning on Large Graphscited by 6,284
  3. 2018How Powerful are Graph Neural Networks?cited by 4,355
  4. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  5. 2018Graph Neural Networks: A Review of Methods and Applicationscited by 1,571
  6. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 878
  7. 2018Hierarchical Graph Representation Learning with Differentiable Poolingcited by 786
  8. 2020TUDataset: A collection of benchmark datasets for learning with graphscited by 718
  9. 2019Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological Viewcited by 544
  10. 2019Graph U-Netscited by 489
  11. 2019Self-Attention Graph Poolingcited by 421
  12. 2017Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphscited by 307
21 more
  1. 2015Diffusion-Convolutional Neural Networkscited by 268
  2. 2020Graph Clustering with Graph Neural Networkscited by 163
  3. 2017SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernelscited by 160
  4. 2019ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representationscited by 156
  5. 2020Higher-Order Explanations of Graph Neural Networks via Relevant Walkscited by 138
  6. 2021Accurate Learning of Graph Representations with Graph Multiset Poolingcited by 120
  7. 2016Higher-order organization of complex networkscited by 109
  8. 2019Graph Convolutional Networks with EigenPoolingcited by 94
  9. 2020Rethinking pooling in graph neural networkscited by 73
  10. 2019Edge Contraction Pooling for Graph Neural Networkscited by 53
  11. 2021Higher-Order Attribute-Enhancing Heterogeneous Graph Neural Networkscited by 22
  12. 2016Scalable motif-aware graph clusteringcited by 15
  13. 2021Graph Pooling via Coarsened Graph Infomaxcited by 15
  14. 2021Hierarchical Adaptive Pooling by Capturing High-order Dependency for Graph Representation Learningcited by 14
  15. 2019Clique pooling for graph classificationcited by 13
  16. 2019Link Prediction via Higher-Order Motif Featurescited by 10
  17. 2020Higher-Order Label Homogeneity and Spreading in Graphscited by 9
  18. 2018Higher-order Graph Convolutional Networkscited by 8
  19. 2019Higher-Order Ranking and Link Prediction: From Closing Triangles to Closing Higher-Order Motifscited by 5
  20. 2014Using Triangles to Improve Community Detection in Directed Networkscited by 3
  21. 2021Higher-Order Relations Skew Link Prediction in Graphscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 6; 2024: 9; 2025: 6; 2026: 2.

26 papers.

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  1. 2022Explaining the Explainers in Graph Neural Networks: a Comparative Studycited by 34
  2. 2023Contrastive Graph Clustering in Curvature Spacescited by 15
  3. 2024DeepRicci: Self-supervised Graph Structure-Feature Co-Refinement for Alleviating Over-squashingcited by 15
  4. 2024Gegenbauer Graph Neural Networks for Time-varying Signal Reconstructioncited by 12
  5. 2023Bridged-GNN: Knowledge Bridge Learning for Effective Knowledge Transfercited by 10
  6. 2024Graph Pooling via Ricci Flowcited by 10
  7. 2023Transformer-Based Hierarchical Clustering for Brain Network Analysiscited by 8
  8. 2022Total Variation Graph Neural Networkscited by 7
  9. 2022PhAST: Physics-Aware, Scalable, and Task-specific GNNs for Accelerated Catalyst Designcited by 6
  10. 2024A Comprehensive Graph Pooling Benchmark: Effectiveness, Robustness and Generalizabilitycited by 6
  11. 2024MaxCutPool: differentiable feature-aware Maxcut for pooling in graph neural networkscited by 5
  12. 2023Time-varying Signals Recovery via Graph Neural Networkscited by 4
14 more
  1. 2023On Exploring Node-feature and Graph-structure Diversities for Node Drop Graph Poolingcited by 4
  2. 2024Graph Parsing Networkscited by 4
  3. 2025From GNNs to Trees: Multi-Granular Interpretability for Graph Neural Networkscited by 4
  4. 2024Differentiable Cluster Graph Neural Networkcited by 2
  5. 2024Graph Neural Network Generalization with Gaussian Mixture Model Based Augmentationcited by 2
  6. 2025BN-Pool: Bayesian Nonparametric Pooling for Graphscited by 2
  7. 2025Torch Geometric Pool: the PyTorch library for pooling in Graph Neural Networkscited by 2
  8. 2023Higher-order Sparse Convolutions in Graph Neural Networkscited by 1
  9. 2024Higher-Order GNNs Meet Efficiency: Sparse Sobolev Graph Neural Networkscited by 1
  10. 2025Efficient Knowledge Tracing Leveraging Higher-Order Information in Integrated Graphscited by 0
  11. 2025GraphPPD: Posterior Predictive Modelling for Graph-Level Inferencecited by 0
  12. 2025Benchmark-Ready 3D Anatomical Shape Classificationcited by 0
  13. 2026Beyond the Academic Monoculture: A Unified Framework and Industrial Perspective for Attributed Graph Clusteringcited by 0
  14. 2026Beyond Convolution: Advancing Hypergraph Neural Networks with Hypergraph U-Netscited by 0