Title: Bounds on Perfect Node Classification: A Convex Graph Clustering Perspective
Primary area: optimization
Keywords: graph clustering, convex optimization, atomic norm, node classification, convex clustering

Abstract: We study the problem of transductive node classification in graphs where communities align with both node features and labels. We propose a novel convex optimization framework that integrates node-specific information (features and labels) into graph clustering via low-rank matrix estimation. Our analysis reveals a bidirectional interaction between graph structure and node information: not only can features aid clustering, but graph structure can also enhance node classification. In particular, we prove that incorporating suitable node information enables perfect recovery of communities under milder conditions than required by graph clustering alone. To make the framework practical, we develop efficient algorithmic solutions and validate our theory with experiments demonstrating the predicted improvements.