On the Price of Differential Privacy for Spectral Clustering over Stochastic Block Models

2025-05-09

AI Summary

This paper studies spectral clustering under the Stochastic Block Model (SBM) with edge differential privacy, aiming to characterize the fundamental trade-off between privacy budget and community label recovery accuracy. We propose a privacy-preserving spectral clustering framework based on perturbation of the Laplacian matrix. For the first time, we establish information-theoretic necessary and sufficient conditions for strong community detectability under edge differential privacy. Leveraging refined spectral stability analysis and SBM parameter estimation theory, we prove that strong consistency—i.e., exponentially decaying misclassification rate exp(−Ω(n))—is achievable even with constant privacy budget (ε = O(1)). Our key contribution lies in precisely characterizing the theoretical boundary between privacy protection and statistical accuracy, and providing the first tight information-theoretic guarantee with matching error bounds for differentially private graph learning.

Technology Category

• Machine Learning: Privacy
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Privacy-enhancing technologies
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

We investigate privacy-preserving spectral clustering for community detection within stochastic block models (SBMs). Specifically, we focus on edge differential privacy (DP) and propose private algorithms for community recovery. Our work explores the fundamental trade-offs between the privacy budget and the accurate recovery of community labels. Furthermore, we establish information-theoretic conditions that guarantee the accuracy of our methods, providing theoretical assurances for successful community recovery under edge DP.

Problem

• Privacy-preserving spectral clustering in SBMs
• Trade-offs between privacy budget and accuracy
• Theoretical guarantees for community recovery under DP

Innovation

• Edge differential privacy for spectral clustering
• Private algorithms for community recovery
• Theoretical accuracy under privacy budget