ALMA: Alternating Minimization Algorithm for Clustering Mixture Multilayer Network
This work addresses network analysis for researchers in statistics and machine learning, offering an incremental improvement over prior methods.
The paper tackles the problem of clustering layers and identifying communities in multilayer networks under the Mixture Multilayer Stochastic Block Model, proposing the ALMA algorithm which achieves higher accuracy than the existing TWIST method both theoretically and numerically.
The paper considers a Mixture Multilayer Stochastic Block Model (MMLSBM), where layers can be partitioned into groups of similar networks, and networks in each group are equipped with a distinct Stochastic Block Model. The goal is to partition the multilayer network into clusters of similar layers, and to identify communities in those layers. Jing et al. (2020) introduced the MMLSBM and developed a clustering methodology, TWIST, based on regularized tensor decomposition. The present paper proposes a different technique, an alternating minimization algorithm (ALMA), that aims at simultaneous recovery of the layer partition, together with estimation of the matrices of connection probabilities of the distinct layers. Compared to TWIST, ALMA achieves higher accuracy both theoretically and numerically.