Bounds on Perfect Node Classification: A Convex Graph Clustering Perspective

2025-08-27

AI Summary

This paper investigates exact community recovery in transductive node classification. For graphs where topology aligns with node features and labels, we propose a convex graph clustering optimization framework that jointly incorporates label and feature information. By co-modeling spectral graph structure and node attributes, our method captures their synergistic effects. We theoretically establish that integrating appropriately calibrated node information substantially relaxes classical requirements on intra-community edge density, enabling exact community recovery under milder conditions. We design an efficient convex optimization algorithm and derive sufficient conditions for perfect recovery. Experiments on synthetic and real-world networks demonstrate that our approach consistently outperforms existing baselines in both accuracy and robustness.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

Abstract

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.

Problem

• Analyzing transductive node classification with community-label alignment
• Proposing spectral clustering optimization incorporating node-specific information
• Establishing synergy between graph structure and node features

Innovation

• Convex graph clustering with node-specific information
• Spectral framework integrating labels and features
• Optimization problem ensuring perfect community recovery