# Second-Order Pooling for Graph Neural Networks

arXiv: https://arxiv.org/abs/2007.10467 · HTML: https://mlsanity.com/paper/2007.10467/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2020.

## Built on by (most cited first, 30 of 33)

- [Self-Supervised Learning of Graph Neural Networks: A Unified Review](https://mlsanity.com/paper/2102.10757/) (2021)
- [Learning to Match Features with Seeded Graph Matching Network](https://mlsanity.com/paper/2108.08771/) (2021)
- [Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2204.07321/) (2022)
- [High-Order Pooling for Graph Neural Networks with Tensor Decomposition](https://mlsanity.com/paper/2205.11691/) (2022)
- [Distribution Knowledge Embedding for Graph Pooling](https://mlsanity.com/paper/2109.14333/) (2021)
- [BrainIB: Interpretable Brain Network-based Psychiatric Diagnosis with Graph Information Bottleneck](https://mlsanity.com/paper/2205.03612/) (2022)
- [Hierarchical Adaptive Pooling by Capturing High-order Dependency for Graph Representation Learning](https://mlsanity.com/paper/2104.05960/) (2021)
- [Learnable Structural Semantic Readout for Graph Classification](https://mlsanity.com/paper/2111.11523/) (2021)
- [Less Can Be More: Unsupervised Graph Pruning for Large-scale Dynamic Graphs](https://mlsanity.com/paper/2305.10673/) (2023)
- [State of the Art and Potentialities of Graph-level Learning](https://mlsanity.com/paper/2301.05860/) (2023)
- [Self-Discriminative Modeling for Anomalous Graph Detection](https://mlsanity.com/paper/2310.06261/) (2023)
- [Clustering for Protein Representation Learning](https://mlsanity.com/paper/2404.00254/) (2024)
- [Node2Seq: Towards Trainable Convolutions in Graph Neural Networks](https://mlsanity.com/paper/2101.01849/) (2021)
- [Group Contrastive Self-Supervised Learning on Graphs](https://mlsanity.com/paper/2107.09787/) (2021)
- [On Exploring Node-feature and Graph-structure Diversities for Node Drop Graph Pooling](https://mlsanity.com/paper/2306.12726/) (2023)
- [MHNet: Multi-view High-order Network for Diagnosing Neurodevelopmental Disorders Using Resting-state fMRI](https://mlsanity.com/paper/2407.03217/) (2024)
- [Tree-Constrained Graph Neural Networks For Argument Mining](https://mlsanity.com/paper/2110.00124/) (2021)
- [MSHCNet: Multi-Stream Hybridized Convolutional Networks with Mixed Statistics in Euclidean/Non-Euclidean Spaces and Its Application to Hyperspectral Image Classification](https://mlsanity.com/paper/2110.03346/) (2021)
- [Embedding Graphs on Grassmann Manifold](https://mlsanity.com/paper/2205.15068/) (2022)
- [Regularized Optimal Transport Layers for Generalized Global Pooling Operations](https://mlsanity.com/paper/2212.06339/) (2022)
- [Scalable Graph Compressed Convolutions](https://mlsanity.com/paper/2407.18480/) (2024)
- [Revisiting 2D Convolutional Neural Networks for Graph-based Applications](https://mlsanity.com/paper/2105.11016/) (2021)
- [Careful Selection and Thoughtful Discarding: Graph Explicit Pooling Utilizing Discarded Nodes](https://mlsanity.com/paper/2311.12644/) (2023)
- [Tackling Oversmoothing in GNN via Graph Sparsification: A Truss-based Approach](https://mlsanity.com/paper/2407.11928/) (2024)
- [Structural Optimization Makes Graph Classification Simpler and Better](https://mlsanity.com/paper/2109.02027/) (2021)
- [An attention-driven hierarchical multi-scale representation for visual recognition](https://mlsanity.com/paper/2110.12178/) (2021)
- [Adaptive Critical Subgraph Mining for Cognitive Impairment Conversion Prediction with T1-MRI-based Brain Network](https://mlsanity.com/paper/2403.13338/) (2024)
- [GvT: A Graph-based Vision Transformer with Talking-Heads Utilizing Sparsity, Trained from Scratch on Small Datasets](https://mlsanity.com/paper/2404.04924/) (2024)
- [On GNN explanability with activation rules](https://mlsanity.com/paper/2406.11594/) (2024)
- [Enhance Hyperbolic Representation Learning via Second-order Pooling](https://mlsanity.com/paper/2410.22026/) (2024)

## Abstract (arXiv)

Graph neural networks have achieved great success in learning node representations for graph tasks such as node classification and link prediction. Graph representation learning requires graph pooling to obtain graph representations from node representations. It is challenging to develop graph pooling methods due to the variable sizes and isomorphic structures of graphs. In this work, we propose to use second-order pooling as graph pooling, which naturally solves the above challenges. In addition, compared to existing graph pooling methods, second-order pooling is able to use information from all nodes and collect second-order statistics, making it more powerful. We show that direct use of second-order pooling with graph neural networks leads to practical problems. To overcome these problems, we propose two novel global graph pooling methods based on second-order pooling; namely, bilinear mapping and attentional second-order pooling. In addition, we extend attentional second-order pooling to hierarchical graph pooling for more flexible use in GNNs. We perform thorough experiments on graph classification tasks to demonstrate the effectiveness and superiority of our proposed methods. Experimental results show that our methods improve the performance significantly and consistently.