Consistent Spectral Clustering of Network Block Models under Local Differential Privacy
This work addresses privacy-preserving community detection in networks, offering incremental improvements by extending spectral clustering to private settings with theoretical guarantees.
The paper tackles spectral clustering of network block models under local differential privacy, using an edge-flip mechanism to achieve privacy while matching known non-private convergence rates for dense networks and weak consistency for sparse networks.
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.