# HyReaL: Clustering Attributed Graph via Hyper-Complex Space Representation Learning

arXiv: https://arxiv.org/abs/2411.14727 · HTML: https://mlsanity.com/paper/2411.14727/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 45 references that are in the map.
- First posted on arXiv 22 Nov 2024.

## Builds on (most cited first, 24 of 24)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [Attributed Graph Clustering: A Deep Attentional Embedding Approach](https://mlsanity.com/paper/1906.06532/) (2019)
- [Structural Deep Clustering Network](https://mlsanity.com/paper/2002.01633/) (2020)
- [Graph-Coupled Oscillator Networks](https://mlsanity.com/paper/2202.02296/) (2022)
- [PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/2108.01938/) (2021)
- [Dirichlet Energy Constrained Learning for Deep Graph Neural Networks](https://mlsanity.com/paper/2107.02392/) (2021)
- [A Comprehensive Survey on Deep Clustering: Taxonomy, Challenges, and Future Directions](https://mlsanity.com/paper/2206.07579/) (2022)
- [Deep Fusion Clustering Network](https://mlsanity.com/paper/2012.09600/) (2020)
- [Cluster-guided Contrastive Graph Clustering Network](https://mlsanity.com/paper/2301.01098/) (2023)
- [Quaternion Convolutional Neural Networks](https://mlsanity.com/paper/1903.00658/) (2019)
- [Quaternion Recurrent Neural Networks](https://mlsanity.com/paper/1806.04418/) (2018)
- [Rethinking Graph Auto-Encoder Models for Attributed Graph Clustering](https://mlsanity.com/paper/2107.08562/) (2021)
- [Quaternion Convolutional Neural Networks for Heterogeneous Image Processing](https://mlsanity.com/paper/1811.02656/) (2018)
- [CONVERT:Contrastive Graph Clustering with Reliable Augmentation](https://mlsanity.com/paper/2308.08963/) (2023)
- [Quaternion Convolutional Neural Networks for Detection and Localization of 3D Sound Events](https://mlsanity.com/paper/1812.06811/) (2018)
- [Quaternion-valued Correlation Learning for Few-Shot Semantic Segmentation](https://mlsanity.com/paper/2305.07283/) (2023)

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

- [Bridge the Gaps: Heterogeneous Attributed Graph Clustering via Quaternion Representation Learning](https://mlsanity.com/paper/2606.23199/) (2026)

## Abstract (arXiv)

Clustering complex data in the form of attributed graphs has attracted increasing attention, where powerful graph representation is a critical prerequisite. However, the well-known Over-Smoothing (OS) effect makes Graph Convolutional Networks tend to homogenize the representation of graph nodes, while the existing OS solutions focus on alleviating the homogeneity of nodes' embeddings from the aspect of graph topology information, which is inconsistent with the attributed graph clustering objective. Therefore, we introduce hyper-complex space with powerful quaternion feature transformation to enhance the representation learning of the attributes. A generalized Hyper-complex space Representation Learning (HyReaL) model is designed to: 1) bridge arbitrary dimensional attributes to the well-developed quaternion algebra with four parts, and 2) connect the learned representations to more generalized clustering objective without being restricted to a given number of clusters k. The novel introduction of quaternion benefits attributed graph clustering from two aspects: 1) enhanced attribute coupling learning capability allows complex attribute information to be sufficiently exploited in clustering, and 2) stronger learning capability makes it unnecessary to stack too many graph convolution layers, naturally alleviating the OS problem. It turns out that the node representations learned by HyReaL are more discriminative and widely suit downstream clustering with different ks. Extensive experiments including significance tests, ablation studies, qualitative results, etc., show the superiority of HyReaL.