# Poisson Learning: Graph Based Semi-Supervised Learning At Very Low Label Rates

arXiv: https://arxiv.org/abs/2006.11184 · HTML: https://mlsanity.com/paper/2006.11184/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2020.

## Built on by (most cited first, 30 of 49)

- [Graph-based Semi-supervised Learning: A Comprehensive Review](https://mlsanity.com/paper/2102.13303/) (2021)
- [Deep Metric Learning for Few-Shot Image Classification: A Review of Recent Developments](https://mlsanity.com/paper/2105.08149/) (2021)
- [GraphHop: An Enhanced Label Propagation Method for Node Classification](https://mlsanity.com/paper/2101.02326/) (2021)
- [From Coupled Oscillators to Graph Neural Networks: Reducing Over-smoothing via a Kuramoto Model-based Approach](https://mlsanity.com/paper/2311.03260/) (2023)
- [Few-shot Node Classification with Extremely Weak Supervision](https://mlsanity.com/paper/2301.02708/) (2023)
- [Uniform Convergence Rates for Lipschitz Learning on Graphs](https://mlsanity.com/paper/2111.12370/) (2021)
- [Model-Change Active Learning in Graph-Based Semi-Supervised Learning](https://mlsanity.com/paper/2110.07739/) (2021)
- [Hamilton-Jacobi equations on graphs with applications to semi-supervised learning and data depth](https://mlsanity.com/paper/2202.08789/) (2022)
- [Graph-based Active Learning for Semi-supervised Classification of SAR Data](https://mlsanity.com/paper/2204.00005/) (2022)
- [Cluster-aware Semi-supervised Learning: Relational Knowledge Distillation Provably Learns Clustering](https://mlsanity.com/paper/2307.11030/) (2023)
- [Poisson Reweighted Laplacian Uncertainty Sampling for Graph-based Active Learning](https://mlsanity.com/paper/2210.15786/) (2022)
- [Random Matrix Analysis to Balance between Supervised and Unsupervised Learning under the Low Density Separation Assumption](https://mlsanity.com/paper/2310.13434/) (2023)
- [PoissonSeg: Semi-Supervised Few-Shot Medical Image Segmentation via Poisson Learning](https://mlsanity.com/paper/2108.11694/) (2021)
- [Novel Batch Active Learning Approach and Its Application to Synthetic Aperture Radar Datasets](https://mlsanity.com/paper/2307.10495/) (2023)
- [A mean curvature flow arising in adversarial training](https://mlsanity.com/paper/2404.14402/) (2024)
- [PPGN: Physics-Preserved Graph Networks for Real-Time Fault Location in Distribution Systems with Limited Observation and Labels](https://mlsanity.com/paper/2107.02275/) (2021)
- [Label Efficient Regularization and Propagation for Graph Node Classification](https://mlsanity.com/paper/2204.08646/) (2022)
- [Consistency of semi-supervised learning, stochastic tug-of-war games, and the p-Laplacian](https://mlsanity.com/paper/2401.07463/) (2024)
- [Joint reconstruction-segmentation on graphs](https://mlsanity.com/paper/2208.05834/) (2022)
- [Persistent Laplacian-enhanced Algorithm for Scarcely Labeled Data Classification](https://mlsanity.com/paper/2305.16239/) (2023)
- [Multi-class Graph Clustering via Approximated Effective p-Resistance](https://mlsanity.com/paper/2306.08617/) (2023)
- [Improved Graph-based semi-supervised learning Schemes](https://mlsanity.com/paper/2407.00760/) (2024)
- [Dual GNNs: Graph Neural Network Learning with Limited Supervision](https://mlsanity.com/paper/2106.15755/) (2021)
- [Eikonal depth: an optimal control approach to statistical depths](https://mlsanity.com/paper/2201.05274/) (2022)
- [Digital Fingerprinting of Microstructures](https://mlsanity.com/paper/2203.13718/) (2022)
- [Hypergraph p-Laplacian regularization on point clouds for data interpolation](https://mlsanity.com/paper/2405.01109/) (2024)
- [MALADY: Multiclass Active Learning with Auction Dynamics on Graphs](https://mlsanity.com/paper/2409.09475/) (2024)
- [Graph-Based Semi-Supervised Segregated Lipschitz Learning](https://mlsanity.com/paper/2411.03273/) (2024)
- [Advancing Local Clustering on Graphs via Compressive Sensing: Semi-supervised and Unsupervised Methods](https://mlsanity.com/paper/2504.19419/) (2025)
- [Sparse Techniques for Regression in Deep Gaussian Processes](https://mlsanity.com/paper/2505.11355/) (2025)

## Abstract (arXiv)

We propose a new framework, called Poisson learning, for graph based semi-supervised learning at very low label rates. Poisson learning is motivated by the need to address the degeneracy of Laplacian semi-supervised learning in this regime. The method replaces the assignment of label values at training points with the placement of sources and sinks, and solves the resulting Poisson equation on the graph. The outcomes are provably more stable and informative than those of Laplacian learning. Poisson learning is efficient and simple to implement, and we present numerical experiments showing the method is superior to other recent approaches to semi-supervised learning at low label rates on MNIST, FashionMNIST, and Cifar-10. We also propose a graph-cut enhancement of Poisson learning, called Poisson MBO, that gives higher accuracy and can incorporate prior knowledge of relative class sizes.