Consistent Spectral Clustering of Network Block Models under Local Differential Privacy

TL;DR

This paper develops a differentially private spectral clustering method for network models like SBM and DCBM, achieving strong theoretical guarantees and empirical validation under local privacy constraints.

Contribution

It introduces a privacy-preserving spectral clustering approach using the edge-flip mechanism with proven convergence guarantees for dense and sparse networks.

Findings

Achieves spectral clustering convergence rates matching non-private methods for dense networks.

Ensures weak consistency under mild sparsity conditions.

Empirically validates theoretical results on various network examples.

Abstract

The stochastic block model (SBM) and degree-corrected block model (DCBM) are network models often selected as the fundamental setting in which to analyze the theoretical properties of community detection methods. We consider the problem of spectral clustering of SBM and DCBM networks under a local form of edge differential privacy. Using a randomized response privacy mechanism called the edge-flip mechanism, we develop theoretical guarantees for differentially private community detection, demonstrating conditions under which this strong privacy guarantee can be upheld while achieving spectral clustering convergence rates that match the known rates without privacy. We prove the strongest theoretical results are achievable for dense networks (those with node degree linear in the number of nodes), while weak consistency is achievable under mild sparsity (node degree greater than $\sqrt{n}$). We empirically demonstrate our results on a number of network examples.