# Geometric Matrix Completion via Sylvester Multi-Graph Neural Network

arXiv: https://arxiv.org/abs/2206.09477 · HTML: https://mlsanity.com/paper/2206.09477/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 42 references that are in the map.
- First posted on arXiv 19 Jun 2022.

## Builds on (most cited first, 12 of 12)

- [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)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Graph Matching Networks for Learning the Similarity of Graph Structured Objects](https://mlsanity.com/paper/1904.12787/) (2019)
- [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)
- [Distance Metric Learning for Graph Structured Data](https://mlsanity.com/paper/2002.00727/) (2020)
- [Cross-Graph Learning of Multi-Relational Associations](https://mlsanity.com/paper/1605.01832/) (2016)
- [Convolutional Geometric Matrix Completion](https://mlsanity.com/paper/1803.00754/) (2018)

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

- [Beyond RMSE and MAE: Introducing EAUC to unmask hidden bias and unfairness in dyadic regression models](https://mlsanity.com/paper/2401.10690/) (2024)
- [Contrastive Matrix Completion with Denoising and Augmented Graph Views for Robust Recommendation](https://mlsanity.com/paper/2506.10658/) (2025)

## Abstract (arXiv)

Despite the success of the Sylvester equation empowered methods on various graph mining applications, such as semi-supervised label learning and network alignment, there also exists several limitations. The Sylvester equation's inability of modeling non-linear relations and the inflexibility of tuning towards different tasks restrict its performance. In this paper, we propose an end-to-end neural framework, SYMGNN, which consists of a multi-network neural aggregation module and a prior multi-network association incorporation learning module. The proposed framework inherits the key ideas of the Sylvester equation, and meanwhile generalizes it to overcome aforementioned limitations. Empirical evaluations on real-world datasets show that the instantiations of SYMGNN overall outperform the baselines in geometric matrix completion task, and its low-rank instantiation could further reduce the memory consumption by 16.98% on average.