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

TL;DR

This paper studies how to perform spectral clustering for community detection in stochastic block models while ensuring edge differential privacy, analyzing the trade-offs and providing theoretical guarantees.

Contribution

It introduces private algorithms for community recovery under edge DP and establishes conditions for accurate community detection with privacy guarantees.

Findings

Proposes new privacy-preserving spectral clustering algorithms.

Derives theoretical bounds linking privacy budget and recovery accuracy.

Provides conditions guaranteeing successful community detection under edge DP.

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.