Privacy-preserving communication-efficient spectral clustering for distributed multiple networks

Multi-layer networks arise naturally in various scientific domains including social sciences, biology, neuroscience, among others. The network layers of a given multi-layer network are commonly stored in a local and distributed fashion because of the privacy, ownership, and communication costs. The literature on community detection based on these data is still limited. This paper proposes a new distributed spectral clustering-based algorithm for consensus community detection of the locally stored multi-layer network. The algorithm is based on the power method. It is communication-efficient by allowing multiple local power iterations before aggregation; and privacy-preserving by incorporating the notion of differential privacy. The convergence rate of the proposed algorithm is studied under the assumption that the multi-layer networks are generated from the multi-layer stochastic block models. Numerical studies show the superior performance of the proposed algorithm over competitive algorithms.