PriME: Privacy-aware Membership profile Estimation in networks

TL;DR

This paper introduces a privacy-preserving method for estimating community memberships in networks using differential privacy, spectral clustering, and optimal algorithms, validated through simulations and real data.

Contribution

It proposes an optimal private algorithm for community membership estimation under local differential privacy, combining spectral clustering with a symmetric edge flip mechanism.

Findings

Achieves accurate community estimation while preserving privacy.

Provides theoretical bounds showing optimality of the method.

Demonstrates effectiveness through simulations and real-world data.

Abstract

This paper presents a novel approach to estimating community membership probabilities for network vertices generated by the Degree Corrected Mixed Membership Stochastic Block Model while preserving individual edge privacy. Operating within the $\varepsilon$-edge local differential privacy framework, we introduce an optimal private algorithm based on a symmetric edge flip mechanism and spectral clustering for accurate estimation of vertex community memberships. We conduct a comprehensive analysis of the estimation risk and establish the optimality of our procedure by providing matching lower bounds to the minimax risk under privacy constraints. To validate our approach, we demonstrate its performance through numerical simulations and its practical application to real-world data. This work represents a significant step forward in balancing accurate community membership estimation with stringent privacy preservation in network data analysis.