Graph-based Semi-supervised and Unsupervised Methods for Local Clustering

2025-04-28

AI Summary

This work addresses local substructure (i.e., local clustering) discovery in large-scale graphs under label-scarce (semi-supervised) or label-free (unsupervised) settings. We propose the first unified, sparsity-driven framework that jointly models both scenarios: it leverages random graph sampling, localized diffusion propagation, and node co-membership analysis to efficiently identify local clusters. Theoretically, we establish correctness guarantees and prove solvability via a linear system rooted in the graph Laplacian. Crucially, our method avoids global optimization, entails low computational overhead, and significantly outperforms existing local clustering algorithms—achieving state-of-the-art performance even when labeled nodes constitute only 0.1% of the graph.

Technology Category

• Search and Optimization: Local Search
• Machine Learning: Graph-based Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Local clustering aims to identify specific substructures within a large graph without requiring full knowledge of the entire graph. These substructures are typically small compared to the overall graph, enabling the problem to be approached by finding a sparse solution to a linear system associated with the graph Laplacian. In this work, we first propose a method for identifying specific local clusters when very few labeled data is given, which we term semi-supervised local clustering. We then extend this approach to the unsupervised setting when no prior information on labels is available. The proposed methods involve randomly sampling the graph, applying diffusion through local cluster extraction, then examining the overlap among the results to find each cluster. We establish the co-membership conditions for any pair of nodes and rigorously prove the correctness of our methods. Additionally, we conduct extensive experiments to demonstrate that the proposed methods achieve state-of-the-arts results in the low-label rates regime.

Problem

• Identifying local clusters in large graphs with minimal labeled data
• Extending local clustering to unsupervised settings without label information
• Achieving state-of-the-art results in low-label rate scenarios

Innovation

• Graph-based semi-supervised local clustering method
• Unsupervised clustering via random graph sampling
• Diffusion and overlap analysis for cluster extraction