Spectral Graph Clustering under Differential Privacy: Balancing Privacy, Accuracy, and Efficiency

2025-10-08

AI Summary

This paper addresses spectral graph clustering under edge differential privacy (edge-DP), balancing privacy preservation, clustering accuracy, and computational efficiency. To this end, we propose three synergistic mechanisms: (1) graph structure perturbation via randomized edge flipping and adjacency matrix shuffling; (2) private graph projection into a low-dimensional space with calibrated Gaussian noise; and (3) a private power iteration algorithm incorporating iterative distributed noise injection. We theoretically establish that the proposed framework satisfies $(varepsilon,delta)$-edge-DP and derive an error bound that vanishes asymptotically with increasing node count. Extensive experiments on synthetic and real-world networks demonstrate that our method significantly outperforms existing baselines—achieving high community detection accuracy even under stringent privacy budgets. The framework thus provides a scalable, analytically grounded paradigm for privacy-preserving clustering of large-scale graph data.

Technology Category

• Machine Learning: Privacy
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Privacy-enhancing technologies
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

We study the problem of spectral graph clustering under edge differential privacy (DP). Specifically, we develop three mechanisms: (i) graph perturbation via randomized edge flipping combined with adjacency matrix shuffling, which enforces edge privacy while preserving key spectral properties of the graph. Importantly, shuffling considerably amplifies the guarantees: whereas flipping edges with a fixed probability alone provides only a constant epsilon edge DP guarantee as the number of nodes grows, the shuffled mechanism achieves (epsilon, delta) edge DP with parameters that tend to zero as the number of nodes increase; (ii) private graph projection with additive Gaussian noise in a lower-dimensional space to reduce dimensionality and computational complexity; and (iii) a noisy power iteration method that distributes Gaussian noise across iterations to ensure edge DP while maintaining convergence. Our analysis provides rigorous privacy guarantees and a precise characterization of the misclassification error rate. Experiments on synthetic and real-world networks validate our theoretical analysis and illustrate the practical privacy-utility trade-offs.

Problem

• Achieving edge differential privacy in spectral graph clustering
• Balancing privacy guarantees with clustering accuracy and efficiency
• Developing private mechanisms preserving spectral properties of graphs

Innovation

• Randomized edge flipping with adjacency matrix shuffling for privacy
• Private graph projection using additive Gaussian noise in lower-dimensional space
• Noisy power iteration method distributing Gaussian noise across iterations