Rethinking Degree-Corrected Spectral Clustering: a Pure Spectral Analysis & Extension

Meng QIN, Wei Li, Chaorui Zhang, Weixi Zhang, Yiwen Zhong, Jianfeng Hou

Keywords: Degree-corrected Spectral Clustering, Regularized Spectral Clustering, Graph Clustering, Spectral Graph Theory

Abstract: Spectral clustering is a representative graph clustering technique with strong interpretability and theoretical guarantees. Recently, degree-corrected spectral clustering (DCSC) has emerged as the state-of-the-art for this technique. While prior studies have provided several theoretical results for DCSC, their analysis relies on some random graph models (e.g., stochastic block models). In this study, we explore an alternative analysis of DCSC from a pure spectral view. It gives rigorous bounds for the mis-clustered volume and conductance w.r.t. the optimal solution while involving quantities that indicate impacts of (i) high degree heterogeneity and (ii) weak clustering structures to DCSC. Inspired by recent advances in graph neural networks (GNNs) and the associated over-smoothing issue, we propose ASCENT (Adaptive Spectral ClustEring with Node-wise correcTion), a simple yet effective extension of DCSC. Different from most DCSC methods with a constant degree correction for all nodes, ASCENT follows a node-wise correction scheme. It can assign different corrections for nodes via the mean aggregation of GNNs. We further demonstrate that (i) ASCENT reduces to conventional DCSC methods when encountering over-smoothing and (ii) some early stages before over-smoothing can potentially obtain better clustering quality.

Primary Area: other topics in machine learning (i.e., none of the above)

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Submission Number: 6551