# Graph Convolutional Networks with EigenPooling

arXiv: https://arxiv.org/abs/1904.13107 · HTML: https://mlsanity.com/paper/1904.13107/

## Key facts

- Cited by 94 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2019.

## Built on by (most cited first, 30 of 94)

- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [GraphPrompt: Unifying Pre-Training and Downstream Tasks for Graph Neural Networks](https://mlsanity.com/paper/2302.08043/) (2023)
- [Accurate Learning of Graph Representations with Graph Multiset Pooling](https://mlsanity.com/paper/2102.11533/) (2021)
- [Machine Learning for Synthetic Data Generation: A Review](https://mlsanity.com/paper/2302.04062/) (2023)
- [GraphEBM: Molecular Graph Generation with Energy-Based Models](https://mlsanity.com/paper/2102.00546/) (2021)
- [SUGAR: Subgraph Neural Network with Reinforcement Pooling and Self-Supervised Mutual Information Mechanism](https://mlsanity.com/paper/2101.08170/) (2021)
- [A Comprehensive Survey on Deep Graph Representation Learning](https://mlsanity.com/paper/2304.05055/) (2023)
- [Understanding Pooling in Graph Neural Networks](https://mlsanity.com/paper/2110.05292/) (2021)
- [Graph-Based Deep Learning for Medical Diagnosis and Analysis: Past, Present and Future](https://mlsanity.com/paper/2105.13137/) (2021)
- [Structural Entropy Guided Graph Hierarchical Pooling](https://mlsanity.com/paper/2206.13510/) (2022)
- [A Survey on Graph Neural Networks and Graph Transformers in Computer Vision: A Task-Oriented Perspective](https://mlsanity.com/paper/2209.13232/) (2022)
- [Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2204.07321/) (2022)
- [Generalized Graph Prompt: Toward a Unification of Pre-Training and Downstream Tasks on Graphs](https://mlsanity.com/paper/2311.15317/) (2023)
- [Pooling Architecture Search for Graph Classification](https://mlsanity.com/paper/2108.10587/) (2021)
- [Graph Domain Adaptation: A Generative View](https://mlsanity.com/paper/2106.07482/) (2021)
- [Higher-order Clustering and Pooling for Graph Neural Networks](https://mlsanity.com/paper/2209.03473/) (2022)
- [AdaFGL: A New Paradigm for Federated Node Classification with Topology Heterogeneity](https://mlsanity.com/paper/2401.11750/) (2024)
- [Privacy-Preserving Representation Learning on Graphs: A Mutual Information Perspective](https://mlsanity.com/paper/2107.01475/) (2021)
- [Graph Transformer Networks: Learning Meta-path Graphs to Improve GNNs](https://mlsanity.com/paper/2106.06218/) (2021)
- [Model-Agnostic Augmentation for Accurate Graph Classification](https://mlsanity.com/paper/2202.10107/) (2022)
- [Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks](https://mlsanity.com/paper/2107.10234/) (2021)
- [Test-Time Training for Graph Neural Networks](https://mlsanity.com/paper/2210.08813/) (2022)
- [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)
- [Learnable Structural Semantic Readout for Graph Classification](https://mlsanity.com/paper/2111.11523/) (2021)
- [EvGNN: An Event-driven Graph Neural Network Accelerator for Edge Vision](https://mlsanity.com/paper/2404.19489/) (2024)
- [Tensor-view Topological Graph Neural Network](https://mlsanity.com/paper/2401.12007/) (2024)
- [LightDiC: A Simple yet Effective Approach for Large-scale Digraph Representation Learning](https://mlsanity.com/paper/2401.11772/) (2024)
- [Neural Atoms: Propagating Long-range Interaction in Molecular Graphs through Efficient Communication Channel](https://mlsanity.com/paper/2311.01276/) (2023)
- [A Graph is Worth K Words: Euclideanizing Graph using Pure Transformer](https://mlsanity.com/paper/2402.02464/) (2024)

## Abstract (arXiv)

Graph neural networks, which generalize deep neural network models to graph structured data, have attracted increasing attention in recent years. They usually learn node representations by transforming, propagating and aggregating node features and have been proven to improve the performance of many graph related tasks such as node classification and link prediction. To apply graph neural networks for the graph classification task, approaches to generate the textitgraph representation from node representations are demanded. A common way is to globally combine the node representations. However, rich structural information is overlooked. Thus a hierarchical pooling procedure is desired to preserve the graph structure during the graph representation learning. There are some recent works on hierarchically learning graph representation analogous to the pooling step in conventional convolutional neural (CNN) networks. However, the local structural information is still largely neglected during the pooling process. In this paper, we introduce a pooling operator pooling based on graph Fourier transform, which can utilize the node features and local structures during the pooling process. We then design pooling layers based on the pooling operator, which are further combined with traditional GCN convolutional layers to form a graph neural network framework m for graph classification. Theoretical analysis is provided to understand pooling from both local and global perspectives. Experimental results of the graph classification task on 6 commonly used benchmarks demonstrate the effectiveness of the proposed framework.