# Distributional Signals for Node Classification in Graph Neural Networks

arXiv: https://arxiv.org/abs/2304.03507 · HTML: https://mlsanity.com/paper/2304.03507/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 48 references that are in the map.
- First posted on arXiv 7 Apr 2023.

## Builds on (most cited first, 29 of 29)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [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)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View](https://mlsanity.com/paper/1909.03211/) (2019)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Graph-Coupled Oscillator Networks](https://mlsanity.com/paper/2202.02296/) (2022)
- [Hyperbolic Attention Networks](https://mlsanity.com/paper/1805.09786/) (2018)
- [Graph Adversarial Training: Dynamically Regularizing Based on Graph Structure](https://mlsanity.com/paper/1902.08226/) (2019)
- [Break the Ceiling: Stronger Multi-scale Deep Graph Convolutional Networks](https://mlsanity.com/paper/1906.02174/) (2019)
- [Graph Geometry Interaction Learning](https://mlsanity.com/paper/2010.12135/) (2020)
- [Rethinking Graph Regularization for Graph Neural Networks](https://mlsanity.com/paper/2009.02027/) (2020)
- [Batch Virtual Adversarial Training for Graph Convolutional Networks](https://mlsanity.com/paper/1902.09192/) (2019)
- [Signal Recovery on Graphs: Variation Minimization](https://mlsanity.com/paper/1411.7414/) (2014)
- [Node Masking: Making Graph Neural Networks Generalize and Scale Better](https://mlsanity.com/paper/2001.07524/) (2020)
- [A Hilbert Space Theory of Generalized Graph Signal Processing](https://mlsanity.com/paper/1904.11655/) (2019)
- [On distributional graph signals](https://mlsanity.com/paper/2302.11104/) (2023)
- [On the Properties of Gromov Matrices and their Applications in Network Inference](https://mlsanity.com/paper/1810.05333/) (2018)
- [LEReg: Empower Graph Neural Networks with Local Energy Regularization](https://mlsanity.com/paper/2203.10565/) (2022)

## Built on by (most cited first, 1 of 1)

- [Leveraging Label Non-Uniformity for Node Classification in Graph Neural Networks](https://mlsanity.com/paper/2305.00139/) (2023)

## Abstract (arXiv)

In graph neural networks (GNNs), both node features and labels are examples of graph signals, a key notion in graph signal processing (GSP). While it is common in GSP to impose signal smoothness constraints in learning and estimation tasks, it is unclear how this can be done for discrete node labels. We bridge this gap by introducing the concept of distributional graph signals. In our framework, we work with the distributions of node labels instead of their values and propose notions of smoothness and non-uniformity of such distributional graph signals. We then propose a general regularization method for GNNs that allows us to encode distributional smoothness and non-uniformity of the model output in semi-supervised node classification tasks. Numerical experiments demonstrate that our method can significantly improve the performance of most base GNN models in different problem settings.