GC-NLDP: A graph clustering algorithm with local differential privacy

Abstract

Clustering distributed star social graphs, which can offer useful insights into the structure of the data, has attracted considerable attention. Each star social graph often contains sensitive personal information. Unrestricted collection and analysis of such information by curators may reveal privacy. Local differential privacy (LDP), as a privacy model un-requiring any trusted third party, has been widely utilized in distributed privacy-preserving clustering. Most existing solutions adopt the edge-LDP model, compromising privacy strength for high utility. To enhance privacy, we turn to node-LDP and design a two-stage privacy-preserving graph clustering framework, achieving more robust privacy strength while keeping a higher clustering quality. Concretely, in the first stage, we design a node aggregation approach based on the silhouette coefficient measurement model and combine some connection information to form initial clusters. Besides, a novel cluster-based perturbation mechanism is developed to improve data statistics accuracy by leveraging an adaptive noise injecting method. The second stage develops a feedback loop strategy between clients and the curator. The curator iteratively optimizes the perturbation mechanism and node aggregation method based on the feedback information to improve the clustering quality further. Theoretical analysis and experimentation on real-world datasets demonstrate that our proposed method can obtain desirable clustering results while satisfying node-LDP.