A Comprehensive Survey on Spectral Clustering with Graph Structure Learning

TL;DR

This survey addresses the challenge of clustering high-dimensional data by focusing on Graph Structure Learning (GSL) for spectral clustering. It systematically classifies GSL methods into fixed and adaptive paradigms across three graph architectures—pairwise, anchor, and hypergraph—and discusses their roles in one-step and two-step clustering, including multi-view fusion. Key contributions include a comprehensive taxonomy, critical comparisons of graph-construction strategies, and insights into efficient, scalable approaches for large-scale data. The work emphasizes how optimizing the similarity graph via GSL directly affects spectral embedding and clustering quality, and outlines several forward-looking directions, including adaptive hypergraphs and semi-supervised multi-view strategies, to advance practical clustering in complex data. The resulting framework provides a rigorous basis for developing robust, scalable spectral clustering methods with improved graph representations.

Abstract

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.

Figures (4)

• Figure 1: Exploring Clustering Methods: From Traditional to Deep Learning Approaches.
• Figure 2: Systematic Overview of Spectral Clustering Framework.
• Figure 3: Graph Structure Learning Methods.
• Figure 4: Multi-view Spectral Clustering Framework.