# Fast Semi-supervised Learning on Large Graphs: An Improved Green-function Method

arXiv: https://arxiv.org/abs/2411.01792 · HTML: https://mlsanity.com/paper/2411.01792/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 52 references that are in the map.
- First posted on arXiv 4 Nov 2024.

## Builds on (most cited first, 5 of 5)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Interpolation Consistency Training for Semi-Supervised Learning](https://mlsanity.com/paper/1903.03825/) (2019)
- [Semi-Supervised Sparse Representation Based Classification for Face Recognition with Insufficient Labeled Samples](https://mlsanity.com/paper/1609.03279/) (2016)

## Built on by (most cited first, 2 of 2)

- [ScaleGNN: Towards Scalable Graph Neural Networks via Adaptive High-order Neighboring Feature Fusion](https://mlsanity.com/paper/2504.15920/) (2025)
- [Adversarial Graph Fusion for Incomplete Multi-view Semi-supervised Learning with Tensorial Imputation](https://mlsanity.com/paper/2509.15955/) (2025)

## Abstract (arXiv)

In the graph-based semi-supervised learning, the Green-function method is a classical method that works by computing the Green's function in the graph space. However, when applied to large graphs, especially those sparse ones, this method performs unstably and unsatisfactorily. We make a detailed analysis on it and propose a novel method from the perspective of optimization. On fully connected graphs, the method is equivalent to the Green-function method and can be seen as another interpretation with physical meanings, while on non-fully connected graphs, it helps to explain why the Green-function method causes a mess on large sparse graphs. To solve this dilemma, we propose a workable approach to improve our proposed method. Unlike the original method, our improved method can also apply two accelerating techniques, Gaussian Elimination, and Anchored Graphs to become more efficient on large graphs. Finally, the extensive experiments prove our conclusions and the efficiency, accuracy, and stability of our improved Green's function method.