CONSISTENT SPECTRAL CLUSTERING OF NETWORK BLOCK MODELS UNDER LOCAL DIFFERENTIAL PRIVACY

Jonathan Hehir, Aleksandra Slavković, Xiaoyue Niu

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 thann). We empirically demonstrate our results on a number of network examples.

Original languageEnglish (US)
Pages (from-to)1-22
Number of pages22
JournalJournal of Privacy and Confidentiality
Volume12
Issue number2
DOIs
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)
  • Statistics and Probability
  • Computer Science Applications

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