B1908
Title: Optimal clustering in mixtures of multi-layer networks
Authors: Dong Xia - Hong Kong University of Science and Technology (Hong Kong) [presenting]
Abstract: Network clustering represents a critical problem with wide-ranging applications across various domains. The minimax lower bound is examined on the clustering error rate, which is characterized by the Renyi divergence of order 1/2 between the connectivity probabilities of the component networks. In the context of the mixture multi-layer stochastic block model (MMSBM), a two-stage procedure is proposed. The procedure involves a tensor-based spectral initialization method, followed by a network-wise local refinement step based on maximum likelihood estimation. Under certain conditions, the proposed algorithm is revealed to achieve the optimal exponential decay rate in terms of network divergence, thereby aligning with the information-theoretic limits. This optimality of the algorithm finds validation both in numerical experiments and real-world data applications.
