Title: Enhancing Local Graph Clustering Through Compressive Sensing: Approaches for Semi-Supervised and Unsupervised Scenarios

Abstract: Local clustering focuses on detecting distinct substructures within extensive graphs, operating without reliance on external structural metadata. Given that these target substructures are generally small relative to the entire network, the challenge can be addressed by solving for a sparse solution to a linear system derived from the graph Laplacian. This study introduces a novel technique for pinpointing local clusters in scenarios with limited labeled data, a process we define as semi-supervised local clustering. Furthermore, we generalize this framework to an unsupervised context where no initial label information is present. Our methodology entails randomly sampling the graph, executing diffusion processes to extract local clusters, and analyzing the intersections of these outcomes to identify individual clusters. We define co-membership criteria for node pairs and provide a rigorous mathematical proof validating the accuracy of our proposed techniques. Extensive experimental evaluations confirm that our methods deliver state-of-the-art performance, particularly in regimes characterized by low label availability.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC