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Abstract:
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The stochastic block model (SBM) and degree-corrected block model (DCBM)---network models featuring community structure---are often selected as fundamental settings in which to analyze the theoretical properties of community detection methods. We consider the problem of privacy-preserving spectral clustering of SBM and DCBM under a strong formal privacy guarantee for networks, $\eps$--edge local differential privacy (DP), which protects the privacy of relationships between network participants. Using a randomized response privacy mechanism called the edge-flip mechanism, we take a first step toward theoretical analysis of differentially private community detection by demonstrating conditions under which this 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 $n^{-1/2}$ for SBM). We empirically demonstrate our results on a number of network examples.
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