# A Comprehensive Survey on Spectral Clustering with Graph Structure Learning

arXiv: https://arxiv.org/abs/2501.13597 · HTML: https://mlsanity.com/paper/2501.13597/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 151 references that are in the map.
- First posted on arXiv 23 Jan 2025.

## Builds on (most cited first, 15 of 15)

- [A Survey of Multi-View Representation Learning](https://mlsanity.com/paper/1610.01206/) (2016)
- [Deep Subspace Clustering Networks](https://mlsanity.com/paper/1709.02508/) (2017)
- [Deep Clustering: A Comprehensive Survey](https://mlsanity.com/paper/2210.04142/) (2022)
- [Robust and Efficient Subspace Segmentation via Least Squares Regression](https://mlsanity.com/paper/1404.6736/) (2014)
- [Structured Graph Learning for Scalable Subspace Clustering: From Single-view to Multi-view](https://mlsanity.com/paper/2102.07943/) (2021)
- [Multi-view Low-rank Sparse Subspace Clustering](https://mlsanity.com/paper/1708.08732/) (2017)
- [Multi-graph Fusion for Multi-view Spectral Clustering](https://mlsanity.com/paper/1909.06940/) (2019)
- [Hypergraph Spectral Clustering in the Weighted Stochastic Block Model](https://mlsanity.com/paper/1805.08956/) (2018)
- [Iterative Views Agreement: An Iterative Low-Rank based Structured Optimization Method to Multi-View Spectral Clustering](https://mlsanity.com/paper/1608.05560/) (2016)
- [Multi-View Spectral Clustering with High-Order Optimal Neighborhood Laplacian Matrix](https://mlsanity.com/paper/2008.13539/) (2020)
- [Hypergraph p-Laplacian: A Differential Geometry View](https://mlsanity.com/paper/1711.08171/) (2017)
- [Elastic Net Hypergraph Learning for Image Clustering and Semi-supervised Classification](https://mlsanity.com/paper/1603.01096/) (2016)
- [Unsupervised Multi-view Clustering by Squeezing Hybrid Knowledge from Cross View and Each View](https://mlsanity.com/paper/2008.09990/) (2020)
- [Image Segmentation Based on Multiscale Fast Spectral Clustering](https://mlsanity.com/paper/1812.04816/) (2018)
- [On The Effect of Hyperedge Weights On Hypergraph Learning](https://mlsanity.com/paper/1410.6736/) (2014)

## Built on by (most cited first, 10 of 10)

- [Large Language Models Meet Text-Attributed Graphs: A Survey of Integration Frameworks and Applications](https://mlsanity.com/paper/2510.21131/) (2025)
- [Kernel VICReg for Self-Supervised Learning in Reproducing Kernel Hilbert Space](https://mlsanity.com/paper/2509.07289/) (2025)
- [A Markov Categorical Framework for Language Modeling](https://mlsanity.com/paper/2507.19247/) (2025)
- [Graph-based Clustering Revisited: A Relaxation of Kernel k-Means Perspective](https://mlsanity.com/paper/2509.18826/) (2025)
- [Estimating Fair Graphs from Graph-Stationary Data](https://mlsanity.com/paper/2510.07536/) (2025)
- [Cyberswarm: a novel swarm intelligence algorithm inspired by cyber community dynamics](https://mlsanity.com/paper/2512.14752/) (2025)
- [Learning Superpixel Ensemble and Hierarchy Graphs for Melanoma Detection](https://mlsanity.com/paper/2604.03710/) (2026)
- [Minimum Description Length based Granular-Ball Tree Regularization for Spectral Clustering](https://mlsanity.com/paper/2605.22410/) (2026)
- [Continuous Cross-Domain Traffic State Prediction via Memory-Augmented Graph Liquid Time-Constant Networks](https://mlsanity.com/paper/2606.15807/) (2026)
- [An Auto-Scaling Approach for Serverless Environments Based on a Multi-Expert Consensus Mechanism](https://mlsanity.com/paper/2607.15511/) (2026)

## Abstract (arXiv)

Spectral clustering is a powerful technique for clustering high-dimensional data, utilizing graph-based representations to detect complex, non-linear structures and non-convex clusters. The construction of a similarity graph is essential for ensuring accurate and effective clustering, making graph structure learning (GSL) central for enhancing spectral clustering performance in response to the growing demand for scalable solutions. Despite advancements in GSL, there is a lack of comprehensive surveys specifically addressing its role within spectral clustering. To bridge this gap, this survey presents a comprehensive review of spectral clustering methods, emphasizing on the critical role of GSL. We explore various graph construction techniques, including pairwise, anchor, and hypergraph-based methods, in both fixed and adaptive settings. Additionally, we categorize spectral clustering approaches into single-view and multi-view frameworks, examining their applications within one-step and two-step clustering processes. We also discuss multi-view information fusion techniques and their impact on clustering data. By addressing current challenges and proposing future research directions, this survey provides valuable insights for advancing spectral clustering methodologies and highlights the pivotal role of GSL in tackling large-scale and high-dimensional data clustering tasks.