Mixture Degree-Corrected Stochastic Block Model for Multi-Group Community Detection in Multiplex Graphs
Abstract: Multiplex graphs have emerged as a powerful tool for modeling complex data structures due to their ability to handle multiple relational layers. Clustering within a multiplex graph can involve merging vertices into communities that are consistent across all layers, grouping similar layers into clusters, or creating overlapping clusters among vertices and layers. However, a multiplex graph may exhibit distinct vertex communities based on the specific layers to which a vertex is connected. This scenario, termed multi-group community detection, significantly enhances the accuracy of clustering processes and aids in the interpretation of partitions. To date, the current literature on state-of-the-art community detection has not extensively addressed this modeling approach. In this paper, we introduce a novel methodology referred to as the "Mixture Degree-Corrected Stochastic Block Model." This generative model, an extension of the widely utilized Degree-Corrected Stochastic Block Model (DCSBM), is designed to cluster similar layers by their community structures while simultaneously identifying communities within each layer's group. We provide a rigorous definition of the model and utilize an iterative technique to perform inference computations. Furthermore, we assess the identifiability of our proposed model and demonstrate the consistency of the maximum likelihood function through analytical analysis. The effectiveness of our method is evaluated using both real-word data sets and synthetic graphs.
Submission Length: Long submission (more than 12 pages of main content)
Assigned Action Editor: ~Seungjin_Choi1
Submission Number: 2996
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