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The paper considers a Mixture Multilayer Stochastic Block Model (MMLSBM),where layers can be partitioned into groups of similar networks, and networksin each group are equipped with a distinct Stochastic Block Model. The goal isto partition the multilayer network into clusters of similar layers, and toidentify communities in those layers. Jing et al. (2020) introduced the MMLSBMand developed a clustering methodology, TWIST, based on regularized tensordecomposition. The present paper proposes a different technique, an alternatingminimization algorithm (ALMA), that aims at simultaneous recovery of the layerpartition, together with estimation of the matrices of connection probabilitiesof the distinct layers. Compared to TWIST, ALMA achieves higher accuracy boththeoretically and numerically.

ALMA: Alternating Minimization Algorithm for Clustering Mixture Multilayer Network