# Wasserstein Graph Neural Networks for Graphs with Missing Attributes

arXiv: https://arxiv.org/abs/2102.03450 · HTML: https://mlsanity.com/paper/2102.03450/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 39 references that are in the map.
- First posted on arXiv 6 Feb 2021.

## Builds on (most cited first, 20 of 20)

- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [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)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Handling Missing Data with Graph Representation Learning](https://mlsanity.com/paper/2010.16418/) (2020)
- [Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares](https://mlsanity.com/paper/1410.2596/) (2014)
- [Missing Data Imputation using Optimal Transport](https://mlsanity.com/paper/2002.03860/) (2020)
- [Geometric Matrix Completion with Recurrent Multi-Graph Neural Networks](https://mlsanity.com/paper/1704.06803/) (2017)
- [Inductive Matrix Completion Based on Graph Neural Networks](https://mlsanity.com/paper/1904.12058/) (2019)
- [Deep Models of Interactions Across Sets](https://mlsanity.com/paper/1803.02879/) (2018)
- [Missing Data Imputation with Adversarially-trained Graph Convolutional Networks](https://mlsanity.com/paper/1905.01907/) (2019)
- [Learning on Attribute-Missing Graphs](https://mlsanity.com/paper/2011.01623/) (2020)
- [Learning Embeddings into Entropic Wasserstein Spaces](https://mlsanity.com/paper/1905.03329/) (2019)

## Built on by (most cited first, 3 of 3)

- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [Incomplete Graph Learning: A Comprehensive Survey](https://mlsanity.com/paper/2502.12412/) (2025)
- [Multi-Task Learning on Networks](https://mlsanity.com/paper/2112.04891/) (2021)

## Abstract (arXiv)

Missing node attributes is a common problem in real-world graphs. Graph neural networks have been demonstrated power in graph representation learning while their performance is affected by the completeness of graph information. Most of them are not specified for missing-attribute graphs and fail to leverage incomplete attribute information effectively. In this paper, we propose an innovative node representation learning framework, Wasserstein Graph Neural Network (WGNN), to mitigate the problem. To make the most of limited observed attribute information and capture the uncertainty caused by missing values, we express nodes as low-dimensional distributions derived from the decomposition of the attribute matrix. Furthermore, we strengthen the expressiveness of representations by developing a novel message passing schema that aggregates distributional information from neighbors in the Wasserstein space. We test WGNN in node classification tasks under two missing-attribute cases on both synthetic and real-world datasets. In addition, we find WGNN suitable to recover missing values and adapt them to tackle matrix completion problems with graphs of users and items. Experimental results on both tasks demonstrate the superiority of our method.