Simultaneous global and local clustering in multiplex networks with covariate information
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908794942914560 |
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| author | Corneck, Joshua Cohen, Edward A. K. Martin, James S. Patel, Lekha Shuler, Kurtis W. Passino, Francesco Sanna |
| author_facet | Corneck, Joshua Cohen, Edward A. K. Martin, James S. Patel, Lekha Shuler, Kurtis W. Passino, Francesco Sanna |
| contents | Understanding both global and layer-specific group structures is useful for uncovering complex patterns in networks with multiple interaction types. In this work, we introduce a new model, the hierarchical multiplex stochastic blockmodel (HMPSBM), that simultaneously detects communities within individual layers of a multiplex network while inferring a global node clustering across the layers. A stochastic blockmodel is assumed in each layer, with probabilities of layer-level group memberships determined by a node's global group assignment. Our model uses a Bayesian framework, employing a probit stick-breaking process to construct node-specific mixing proportions over a set of shared Griffiths-Engen-McCloseky (GEM) distributions. These proportions determine layer-level community assignment, allowing for an unknown and varying number of groups across layers, while incorporating nodal covariate information to inform the global clustering. We propose a scalable variational inference procedure with parallelisable updates for application to large networks. Extensive simulation studies demonstrate our model's ability to accurately recover both global and layer-level clusters in complicated settings, and applications to real data showcase the model's effectiveness in uncovering interesting latent network structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03441 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simultaneous global and local clustering in multiplex networks with covariate information Corneck, Joshua Cohen, Edward A. K. Martin, James S. Patel, Lekha Shuler, Kurtis W. Passino, Francesco Sanna Methodology Understanding both global and layer-specific group structures is useful for uncovering complex patterns in networks with multiple interaction types. In this work, we introduce a new model, the hierarchical multiplex stochastic blockmodel (HMPSBM), that simultaneously detects communities within individual layers of a multiplex network while inferring a global node clustering across the layers. A stochastic blockmodel is assumed in each layer, with probabilities of layer-level group memberships determined by a node's global group assignment. Our model uses a Bayesian framework, employing a probit stick-breaking process to construct node-specific mixing proportions over a set of shared Griffiths-Engen-McCloseky (GEM) distributions. These proportions determine layer-level community assignment, allowing for an unknown and varying number of groups across layers, while incorporating nodal covariate information to inform the global clustering. We propose a scalable variational inference procedure with parallelisable updates for application to large networks. Extensive simulation studies demonstrate our model's ability to accurately recover both global and layer-level clusters in complicated settings, and applications to real data showcase the model's effectiveness in uncovering interesting latent network structure. |
| title | Simultaneous global and local clustering in multiplex networks with covariate information |
| topic | Methodology |
| url | https://arxiv.org/abs/2505.03441 |