# Quaternion-Based Graph Convolution Network for Recommendation

arXiv: https://arxiv.org/abs/2111.10536 · HTML: https://mlsanity.com/paper/2111.10536/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 56 references that are in the map.
- First posted on arXiv 20 Nov 2021.

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

- [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)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [KGAT: Knowledge Graph Attention Network for Recommendation](https://mlsanity.com/paper/1905.07854/) (2019)
- [Variational Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/1802.05814/) (2018)
- [Self-supervised Graph Learning for Recommendation](https://mlsanity.com/paper/2010.10783/) (2020)
- [Adversarial Attack on Graph Structured Data](https://mlsanity.com/paper/1806.02371/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Quaternion Knowledge Graph Embeddings](https://mlsanity.com/paper/1904.10281/) (2019)
- [VBPR: Visual Bayesian Personalized Ranking from Implicit Feedback](https://mlsanity.com/paper/1510.01784/) (2015)
- [RippleNet: Propagating User Preferences on the Knowledge Graph for Recommender Systems](https://mlsanity.com/paper/1803.03467/) (2018)
- [NAIS: Neural Attentive Item Similarity Model for Recommendation](https://mlsanity.com/paper/1809.07053/) (2018)
- [Deep Quaternion Networks](https://mlsanity.com/paper/1712.04604/) (2017)
- [Quaternion Convolutional Neural Networks](https://mlsanity.com/paper/1903.00658/) (2019)
- [Quaternion Recurrent Neural Networks](https://mlsanity.com/paper/1806.04418/) (2018)
- [Interest-aware Message-Passing GCN for Recommendation](https://mlsanity.com/paper/2102.10044/) (2021)
- [Collaborative Memory Network for Recommendation Systems](https://mlsanity.com/paper/1804.10862/) (2018)
- [Lightweight and Efficient Neural Natural Language Processing with Quaternion Networks](https://mlsanity.com/paper/1906.04393/) (2019)
- [Heterogeneous Global Graph Neural Networks for Personalized Session-based Recommendation](https://mlsanity.com/paper/2107.03813/) (2021)
- [Quaternion Convolutional Neural Networks for End-to-End Automatic Speech Recognition](https://mlsanity.com/paper/1806.07789/) (2018)
- [Binarized Graph Neural Network](https://mlsanity.com/paper/2004.11147/) (2020)
- [Quaternion Graph Neural Networks](https://mlsanity.com/paper/2008.05089/) (2020)
- [Speech recognition with quaternion neural networks](https://mlsanity.com/paper/1811.09678/) (2018)
- [QuatRE: Relation-Aware Quaternions for Knowledge Graph Embeddings](https://mlsanity.com/paper/2009.12517/) (2020)

## Abstract (arXiv)

Graph Convolution Network (GCN) has been widely applied in recommender systems for its representation learning capability on user and item embeddings. However, GCN is vulnerable to noisy and incomplete graphs, which are common in real world, due to its recursive message propagation mechanism. In the literature, some work propose to remove the feature transformation during message propagation, but making it unable to effectively capture the graph structural features. Moreover, they model users and items in the Euclidean space, which has been demonstrated to have high distortion when modeling complex graphs, further degrading the capability to capture the graph structural features and leading to sub-optimal performance. To this end, in this paper, we propose a simple yet effective Quaternion-based Graph Convolution Network (QGCN) recommendation model. In the proposed model, we utilize the hyper-complex Quaternion space to learn user and item representations and feature transformation to improve both performance and robustness. Specifically, we first embed all users and items into the Quaternion space. Then, we introduce the quaternion embedding propagation layers with quaternion feature transformation to perform message propagation. Finally, we combine the embeddings generated at each layer with the mean pooling strategy to obtain the final embeddings for recommendation. Extensive experiments on three public benchmark datasets demonstrate that our proposed QGCN model outperforms baseline methods by a large margin.