AI 中文总结
研究从纯谱视角对度校正谱聚类进行无条件分析，给出错分节点数界限。受图神经网络启发，提出ASCENT对其进行扩展，采用节点级校正方案，实验证明ASCENT在过平滑时可简化为传统方法，过平滑前某些阶段可能提升聚类质量。
AI 中文摘要
谱聚类是一种具有强解释性和理论保证的代表性图聚类技术，度校正谱聚类（DCSC）是该技术的最新方法。以往研究对DCSC的分析依赖特定概率框架和条件，本文从纯谱视角探索无条件分析，给出错分节点数界限。受图神经网络启发，提出ASCENT，它是DCSC的简单有效扩展，采用节点级校正方案，通过GNN平均聚合器为节点分配不同校正。实验表明，ASCENT在过平滑时可简化为传统DCSC方法，过平滑前的某些早期阶段可能带来更好聚类质量。
英文摘要
Spectral clustering is a representative graph clustering technique with strong interpretability and theoretical guarantees. Degree-corrected spectral clustering (DCSC) has emerged as the state-of-the-art for this technique. While prior studies have provided impressive theoretical insights for DCSC, their analyses typically depend on specific probabilistic frameworks (e.g., stochastic block models) and conditions. In this study, we explore an alternative condition-free analysis for the clustering quality of DCSC from a pure spectral view, without any random graph models. It gives bounds for the number of mis-clustered nodes w.r.t. the optimal partition of conductance minimization while involving quantities that indicate impacts of (\romannumeral1) degree heterogeneity and (\romannumeral2) weakness of clustering structures to the clustering quality. Inspired by graph neural networks (GNNs) and their over-smoothing effect, 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, ASCENT follows a node-wise correction scheme. It can assign different corrections for nodes via a GNN mean aggregator. We demonstrate that (\romannumeral1) ASCENT reduces to conventional DCSC methods when encountering over-smoothing; (\romannumeral2) some early stages before over-smoothing can potentially result in better clustering quality.
