---
title: "Beyond Implicit Constraint: Explicit Low-Rank Structured Subspace Learning for Fast Attributed Graph Clustering"
authors:
  - "Yaoming Cai"
  - "Song Liu"
  - "Zijia Zhang"
  - "You Wu"
  - "Xiaobo Liu"
  - "Yao Ding"
  - "Fei Li"
doi: "10.24963/ijcai.2026/463"
url: "https://ijcai.org/proceedings/2026/463"
pdf: "https://ijcai.org/proceedings/2026/0463.pdf"
venue: "Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence"
year: 2026
pages: "4161-4169"
track: "Main Track"
keywords:
  - "Machine Learning: Clustering"
  - "Machine Learning: Unsupervised learning"
  - "Machine Learning: Geometric learning"
  - "Machine Learning: Kernel methods"
---

# Beyond Implicit Constraint: Explicit Low-Rank Structured Subspace Learning for Fast Attributed Graph Clustering

Yaoming Cai, Song Liu, Zijia Zhang, You Wu, Xiaobo Liu, Yao Ding, Fei Li

*Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence*, pages 4161-4169. DOI: [10.24963/ijcai.2026/463](https://doi.org/10.24963/ijcai.2026/463)

## Abstract

Attributed graph clustering has achieved remarkable success by synergistically integrating topological structures and node attributes. While subspace learning has emerged as a dominant paradigm for node partitioning, most existing methods rely on implicit low-rank constraints, which often fail to capture complex nonlinear manifolds and suffer from prohibitive computational overhead on large-scale graphs. In this paper, we propose ELSS (Explicit Low-rank Structured Subspace learning), a scalable and robust framework that transcends implicit formulations. Specifically, ELSS learns an explicit and nonlinear low-rank subspace within a graph-structured embedding space, effectively uncovering latent cluster structures. To effectively mitigate the pervasive oversmoothing issue, we introduce a homophily-aware adaptive graph filter, which dynamically calibrates smoothing intensity to preserve discriminative ego-information. Furthermore, to ensure linear scalability, we develop a PageRank-guided structural sampling strategy for anchor-based approximation, which identifies pivotal landmarks based on their global topological prestige. Theoretical analysis guarantees that ELSS effectively mitigates spectral collapse while maintaining a linear complexity. Extensive experiments on diverse benchmarks demonstrate that ELSS consistently delivers superior clustering accuracy over state-of-the-art methods.