# Nonlinear Correct and Smooth for Semi-Supervised Learning

arXiv: https://arxiv.org/abs/2310.05757 · HTML: https://mlsanity.com/paper/2310.05757/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 33 references that are in the map.
- First posted on arXiv 9 Oct 2023.

## Builds on (most cited first, 19 of 19)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [Combining Label Propagation and Simple Models Out-performs Graph Neural Networks](https://mlsanity.com/paper/2010.13993/) (2020)
- [Attention-based Graph Neural Network for Semi-supervised Learning](https://mlsanity.com/paper/1803.03735/) (2018)
- [Tackling Over-Smoothing for General Graph Convolutional Networks](https://mlsanity.com/paper/2008.09864/) (2020)
- [Understanding and Resolving Performance Degradation in Graph Convolutional Networks](https://mlsanity.com/paper/2006.07107/) (2020)
- [Bag of Tricks for Training Deeper Graph Neural Networks: A Comprehensive Benchmark Study](https://mlsanity.com/paper/2108.10521/) (2021)
- [Meta Propagation Networks for Graph Few-shot Semi-supervised Learning](https://mlsanity.com/paper/2112.09810/) (2021)
- [Nonlinear Higher-Order Label Spreading](https://mlsanity.com/paper/2006.04762/) (2020)
- [A Unifying Generative Model for Graph Learning Algorithms: Label Propagation, Graph Convolutions, and Combinations](https://mlsanity.com/paper/2101.07730/) (2021)
- [Higher-Order Label Homogeneity and Spreading in Graphs](https://mlsanity.com/paper/2002.07833/) (2020)
- [Why Propagate Alone? Parallel Use of Labels and Features on Graphs](https://mlsanity.com/paper/2110.07190/) (2021)
- [Alternately Optimized Graph Neural Networks](https://mlsanity.com/paper/2206.03638/) (2022)

## Abstract (arXiv)

Graph-based semi-supervised learning (GSSL) has been used successfully in various applications. Existing methods leverage the graph structure and labeled samples for classification. Label Propagation (LP) and Graph Neural Networks (GNNs) both iteratively pass messages on graphs, where LP propagates node labels through edges and GNN aggregates node features from the neighborhood. Recently, combining LP and GNN has led to improved performance. However, utilizing labels and features jointly in higher-order graphs has not been explored. Therefore, we propose Nonlinear Correct and Smooth (NLCS), which improves the existing post-processing approach by incorporating non-linearity and higher-order representation into the residual propagation to handle intricate node relationships effectively. Systematic evaluations show that our method achieves remarkable average improvements of 13.71% over base prediction and 2.16% over the state-of-the-art post-processing method on six commonly used datasets. Comparisons and analyses show our method effectively utilizes labels and features jointly in higher-order graphs to resolve challenging graph relationships.