The multiplex deep latent position model for the clustering of nodes in multiview networks

Multiplex networks capture multiple types of interactions among the same set of nodes, creating a complex, multi-relational framework. A typical example is a social network where nodes (actors) are connected by various types of ties, such as professional, familial, or social relationships. Clustering nodes in these networks is a key challenge in unsupervised learning, given the increasing prevalence of multiview data across domains. While previous research has focused on extending statistical models to handle such networks, these adaptations often struggle to fully capture complex network structures and rely on computationally intensive Markov chain Monte Carlo (MCMC) for inference, rendering them less feasible for effective network analysis. To overcome these limitations, we propose the multiplex deep latent position model (MDLPM), which generalizes and extends latent position models to multiplex networks. MDLPM combines deep learning with variational inference to effectively tackle both the modeling and computational challenges raised by multiplex networks. Unlike most existing deep learning models for graphs that require external clustering algorithms (e.g., k-means) to group nodes based on their latent embeddings, MDLPM integrates clustering directly into the learning process, enabling a fully unsupervised, end-to-end approach. This integration improves the ability to uncover and interpret clusters in multiplex networks without relying on external procedures. Numerical experiments across various synthetic data sets and two real-world networks demonstrate the performance of MDLPM compared to state-of-the-art methods, highlighting its applicability and effectiveness for multiplex network analysis.