Privacy-Preserving Community Detection for Locally Distributed Multiple Networks

TL;DR

This paper introduces a privacy-preserving community detection method for multi-layer networks, utilizing a novel distributed spectral clustering algorithm that ensures differential privacy while accurately estimating communities.

Contribution

It proposes the ppDSC algorithm that combines randomized response privacy mechanism with spectral clustering, including bias correction and theoretical error analysis for multi-layer networks.

Findings

The ppDSC algorithm effectively preserves privacy during community detection.

Theoretical bounds on eigenvector estimation errors are established.

The method handles network heterogeneity with clear error bounds.

Abstract

Modern multi-layer networks are commonly stored and analyzed in a local and distributed fashion because of the privacy, ownership, and communication costs. The literature on the model-based statistical methods for community detection based on these data is still limited. This paper proposes a new method for consensus community detection and estimation in a multi-layer stochastic block model using locally stored and computed network data with privacy protection. A novel algorithm named privacy-preserving Distributed Spectral Clustering (ppDSC) is developed. To preserve the edges' privacy, we adopt the randomized response (RR) mechanism to perturb the network edges, which satisfies the strong notion of differential privacy. The ppDSC algorithm is performed on the squared RR-perturbed adjacency matrices to prevent possible cancellation of communities among different layers. To remove the bias incurred by RR and the squared network matrices, we develop a two-step bias-adjustment procedure. Then we perform eigen-decomposition on the debiased matrices, aggregation of the local eigenvectors using an orthogonal Procrustes transformation, and k-means clustering. We provide theoretical analysis on the statistical errors of ppDSC in terms of eigen-vector estimation. In addition, the blessings and curses of network heterogeneity are well-explained by our bounds.