Privacy-Preserving Transfer Learning for Community Detection using Locally Distributed Multiple Networks

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Modern applications increasingly involve highly sensitive network data, where raw edges cannot be shared due to privacy constraints. We propose \texttt{TransNet}, a new spectral clustering-based transfer learning framework that improves community detection on a \emph{target network} by leveraging heterogeneous, locally stored, and privacy-preserved auxiliary \emph{source networks}. Our focus is the \textit{local differential privacy} regime, in which each local data provider perturbs edges via \textit{randomized response} before release, requiring no trusted third party. \texttt{TransNet} aggregates source eigenspaces through a novel adaptive weighting scheme that accounts for both privacy and heterogeneity, and then regularizes the weighted source eigenspace with the target eigenspace to optimally balance the two. Theoretically, we establish an error-bound-oracle property: the estimation error for the aggregated eigenspace depends only on \textit{informative sources}, ensuring robustness when some sources are highly heterogeneous or heavily privatized. We further show that the error bound of \texttt{TransNet} is no greater than that of estimators using only the target network or only (weighted) sources. Empirically, \texttt{TransNet} delivers strong gains across a range of privacy levels and heterogeneity patterns. For completeness, we also present \texttt{TransNetX}, an extension based on Gaussian perturbation of projection matrices under the assumption that trusted local data curators are available.