Mixture Stochastic Block Model for Multi-Group Community Detection in Multiplex Graphs

Noureddine Henka, Mohamad Assaad, Sami Tazi

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Keywords: Stochastic Block Model, Mixture Model, Multi-Group Community Detection, Multiplex Graph

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Abstract: Multiplex graphs have emerged as a powerful tool for modeling complex data due to their capability to accommodate multi-relation structures. These graphs consist of multiple layers, where each layer represents a specific type of relation. Pillar community detection, a clustering approach that assigns vertices to clusters across all layers, has been employed to identify shared community structures. However, particular layers may possess distinct divisions, deviating from the pillar-based clustering. Consequently, it becomes crucial not to identify individual layer clusters, but a similar cluster for similar layers. In this paper, we propose an approach called the "Mixture Stochastic Block Model," which aims to group similar layers based on shared community structures. A common Stochastic Block Model represents each group's shared community structure. The model is rigorously defined, and an iterative technique is employed for computing the inference. We estimate the layer-to-group assignments using the expectation-maximization technique, while the vertex-to-block assignments within each group are determined using the variational estimation-maximization technique. We assess the identifiability of our proposed model and show the consistency of the maximum likelihood function. The performance of the method is evaluated using both synthetic graphs and real-world datasets, showing its efficacy in identifying consistent community structures across diverse multiplex graphs.

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Submission Number: 1813