融合图结构与节点信息，实现更优的社区精准分类。
Bounds on Perfect Node Classification: A Convex Graph Clustering Perspective
- 构建基于谱聚类的优化模型，整合节点标签与特征。
- 在较弱条件下即可完美恢复社区结构，优于纯图聚类方法。
- 适合研究图神经网络理论或社区发现的学者参考。
我们分析了归纳式节点分类问题，其底层图具有与节点标签一致的社区结构及节点特征。针对节点分类，提出一种新优化问题，将节点特异性信息（标签与特征）融入谱图聚类框架。研究表明，图结构与节点信息间存在协同效应：适当的节点信息可在比纯图聚类更宽松的条件下，保证所提优化问题的解能完美恢复社区结构。我们给出了该优化问题的算法求解方案，并通过数值实验验证了这种协同效应的存在。
原文摘要 · Abstract (English)
We present an analysis of the transductive node classification problem, where the underlying graph consists of communities that agree with the node labels and node features. For node classification, we propose a novel optimization problem that incorporates the node-specific information (labels and features) in a spectral graph clustering framework. Studying this problem, we demonstrate a synergy between the graph structure and node-specific information. In particular, we show that suitable node-specific information guarantees the solution of our optimization problem perfectly recovering the communities, under milder conditions than the bounds on graph clustering alone. We present algorithmic solutions to our optimization problem and numerical experiments that confirm such a synergy.
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