# A Non-Negative Factorization approach to node pooling in Graph Convolutional Neural Networks

arXiv: https://arxiv.org/abs/1909.03287 · HTML: https://mlsanity.com/paper/1909.03287/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Sep 2019.

## Built on by (most cited first, 14 of 14)

- [Understanding Pooling in Graph Neural Networks](https://mlsanity.com/paper/2110.05292/) (2021)
- [Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2204.07321/) (2022)
- [The expressive power of pooling in Graph Neural Networks](https://mlsanity.com/paper/2304.01575/) (2023)
- [Pyramidal Reservoir Graph Neural Network](https://mlsanity.com/paper/2104.04710/) (2021)
- [Graph Pooling via Ricci Flow](https://mlsanity.com/paper/2407.04236/) (2024)
- [Boosting Graph Pooling with Persistent Homology](https://mlsanity.com/paper/2402.16346/) (2024)
- [Cluster-wise Graph Transformer with Dual-granularity Kernelized Attention](https://mlsanity.com/paper/2410.06746/) (2024)
- [Generalizing Downsampling from Regular Data to Graphs](https://mlsanity.com/paper/2208.03523/) (2022)
- [Geometry-Aware Edge Pooling for Graph Neural Networks](https://mlsanity.com/paper/2506.11700/) (2025)
- [On Exploring Node-feature and Graph-structure Diversities for Node Drop Graph Pooling](https://mlsanity.com/paper/2306.12726/) (2023)
- [Survey of Graph Neural Network for Internet of Things and NextG Networks](https://mlsanity.com/paper/2405.17309/) (2024)
- [Everybody Needs a Little HELP: Explaining Graphs via Hierarchical Concepts](https://mlsanity.com/paper/2311.15112/) (2023)
- [Torch Geometric Pool: the PyTorch library for pooling in Graph Neural Networks](https://mlsanity.com/paper/2512.12642/) (2025)
- [NervePool: A Simplicial Pooling Layer](https://mlsanity.com/paper/2305.06315/) (2023)

## Abstract (arXiv)

The paper discusses a pooling mechanism to induce subsampling in graph structured data and introduces it as a component of a graph convolutional neural network. The pooling mechanism builds on the Non-Negative Matrix Factorization (NMF) of a matrix representing node adjacency and node similarity as adaptively obtained through the vertices embedding learned by the model. Such mechanism is applied to obtain an incrementally coarser graph where nodes are adaptively pooled into communities based on the outcomes of the non-negative factorization. The empirical analysis on graph classification benchmarks shows how such coarsening process yields significant improvements in the predictive performance of the model with respect to its non-pooled counterpart.