# Grouping-matrix based Graph Pooling with Adaptive Number of Clusters

arXiv: https://arxiv.org/abs/2209.02939 · HTML: https://mlsanity.com/paper/2209.02939/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 39 references that are in the map.
- First posted on arXiv 7 Sep 2022.

## Builds on (most cited first, 22 of 22)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Analyzing Learned Molecular Representations for Property Prediction](https://mlsanity.com/paper/1904.01561/) (2019)
- [ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations](https://mlsanity.com/paper/1911.07979/) (2019)
- [Learning Multimodal Graph-to-Graph Translation for Molecular Optimization](https://mlsanity.com/paper/1812.01070/) (2018)
- [Memory-Based Graph Networks](https://mlsanity.com/paper/2002.09518/) (2020)
- [Training Deep Networks with Structured Layers by Matrix Backpropagation](https://mlsanity.com/paper/1509.07838/) (2015)
- [Backpropagation-Friendly Eigendecomposition](https://mlsanity.com/paper/1906.09023/) (2019)
- [Why Approximate Matrix Square Root Outperforms Accurate SVD in Global Covariance Pooling?](https://mlsanity.com/paper/2105.02498/) (2021)
- [Robust Differentiable SVD](https://mlsanity.com/paper/2104.03821/) (2021)
- [Spectral Clustering with Graph Neural Networks for Graph Pooling](https://mlsanity.com/paper/1907.00481/) (2019)
- [Fast Differentiable Matrix Square Root](https://mlsanity.com/paper/2201.08663/) (2022)
- [Word Embedding based on Low-Rank Doubly Stochastic Matrix Decomposition](https://mlsanity.com/paper/1812.10401/) (2018)

## Built on by (most cited first, 5 of 5)

- [Mastering Long-Tail Complexity on Graphs: Characterization, Learning, and Generalization](https://mlsanity.com/paper/2305.09938/) (2023)
- [Geometrically Aligned Transfer Encoder for Inductive Transfer in Regression Tasks](https://mlsanity.com/paper/2310.06369/) (2023)
- [Multitask Extension of Geometrically Aligned Transfer Encoder](https://mlsanity.com/paper/2405.01974/) (2024)
- [Co-attention Graph Pooling for Efficient Pairwise Graph Interaction Learning](https://mlsanity.com/paper/2307.15377/) (2023)
- [Geometric Embedding Alignment via Curvature Matching in Transfer Learning](https://mlsanity.com/paper/2506.13015/) (2025)

## Abstract (arXiv)

Graph pooling is a crucial operation for encoding hierarchical structures within graphs. Most existing graph pooling approaches formulate the problem as a node clustering task which effectively captures the graph topology. Conventional methods ask users to specify an appropriate number of clusters as a hyperparameter, then assume that all input graphs share the same number of clusters. In inductive settings where the number of clusters can vary, however, the model should be able to represent this variation in its pooling layers in order to learn suitable clusters. Thus we propose GMPool, a novel differentiable graph pooling architecture that automatically determines the appropriate number of clusters based on the input data. The main intuition involves a grouping matrix defined as a quadratic form of the pooling operator, which induces use of binary classification probabilities of pairwise combinations of nodes. GMPool obtains the pooling operator by first computing the grouping matrix, then decomposing it. Extensive evaluations on molecular property prediction tasks demonstrate that our method outperforms conventional methods.