# From Cluster Assumption to Graph Convolution: Graph-based Semi-Supervised Learning Revisited

arXiv: https://arxiv.org/abs/2309.13599 · HTML: https://mlsanity.com/paper/2309.13599/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 58 of its 90 references that are in the map.
- First posted on arXiv 24 Sep 2023.

## Builds on (most cited first, 30 of 58)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [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)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Beyond neural scaling laws: beating power law scaling via data pruning](https://mlsanity.com/paper/2206.14486/) (2022)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications](https://mlsanity.com/paper/1709.07604/) (2017)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)

## Built on by (most cited first, 6 of 6)

- [GraphICL: Unlocking Graph Learning Potential in LLMs through Structured Prompt Design](https://mlsanity.com/paper/2501.15755/) (2025)
- [rLLM: Relational Table Learning with LLMs](https://mlsanity.com/paper/2407.20157/) (2024)
- [Improved Graph-based semi-supervised learning Schemes](https://mlsanity.com/paper/2407.00760/) (2024)
- [Chem-NMF: Multi-layer α-divergence Non-Negative Matrix Factorization for Cardiorespiratory Disease Clustering, with Improved Convergence Inspired by Chemical Catalysts and Rigorous Asymptotic Analysis](https://mlsanity.com/paper/2510.06632/) (2025)
- [InRTL: Effective Intra-Inter Interaction Learning for Relational Tables](https://mlsanity.com/paper/2609.12712/) (2026)
- [MetaRTL: Meta-path Attention Enhanced Relational Table Learning](https://mlsanity.com/paper/2609.19832/) (2026)

## Abstract (arXiv)

Graph-based semi-supervised learning (GSSL) has long been a hot research topic. Traditional methods are generally shallow learners, based on the cluster assumption. Recently, graph convolutional networks (GCNs) have become the predominant techniques for their promising performance. In this paper, we theoretically discuss the relationship between these two types of methods in a unified optimization framework. One of the most intriguing findings is that, unlike traditional ones, typical GCNs may not jointly consider the graph structure and label information at each layer. Motivated by this, we further propose three simple but powerful graph convolution methods. The first is a supervised method OGC which guides the graph convolution process with labels. The others are two unsupervised methods: GGC and its multi-scale version GGCM, both aiming to preserve the graph structure information during the convolution process. Finally, we conduct extensive experiments to show the effectiveness of our methods. Code is available at https://github.com/zhengwang100/ogc_ggcm.