Locally Differentially Private Graph Clustering via the Power Iteration Method

2025-05-16

AI Summary

Existing local differential privacy (LDP) graph clustering methods require Ω(log n) privacy budget to ensure accuracy, failing to meet constant-budget privacy requirements. This work proposes the first interactive power iteration algorithm for high-accuracy LDP graph clustering under constant privacy budget. By integrating spectral analysis and noise suppression techniques, our method eliminates constant-level noise terms in the estimation of the leading eigenvector, thereby circumventing reliance on the stochastic block model and extending applicability to general well-clustered graphs with minimum degree Õ(√n). We provide rigorous theoretical guarantees showing that the algorithm achieves provably accurate clustering even under constant privacy budget. Empirical evaluations demonstrate significant improvements over existing LDP spectral clustering approaches based on randomized response, particularly in clustering quality and robustness.

Technology Category

• Machine Learning: Privacy
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Search and Optimization: Local Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Privacy-enhancing technologies
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

We propose a locally differentially private graph clustering algorithm. Previous works have explored this problem, including approaches that apply spectral clustering to graphs generated via the randomized response algorithm. However, these methods only achieve accurate results when the privacy budget is in $Omega(log n)$, which is unsuitable for many practical applications. In response, we present an interactive algorithm based on the power iteration method. Given that the noise introduced by the largest eigenvector constant can be significant, we incorporate a technique to eliminate this constant. As a result, our algorithm attains local differential privacy with a constant privacy budget when the graph is well-clustered and has a minimum degree of $ ilde{Omega}(sqrt{n})$. In contrast, while randomized response has been shown to produce accurate results under the same minimum degree condition, it is limited to graphs generated from the stochastic block model. We perform experiments to demonstrate that our method outperforms spectral clustering applied to randomized response results.

Problem

• Develop private graph clustering with constant privacy budget
• Overcome noise in largest eigenvector for accurate results
• Improve accuracy beyond stochastic block model limitations

Innovation

• Locally differentially private graph clustering algorithm
• Power iteration method with noise elimination
• Constant privacy budget for well-clustered graphs