A Latent Position Co-Clustering Model for Multiplex Networks

2025-07-12

AI Summary

Existing methods lack a unified latent space framework, hindering simultaneous network-level and node-level co-clustering across multiple networks. To address this, we propose a hierarchical mixture-of-mixtures latent position coclustering model that establishes, for the first time, a unified latent variable space to jointly model inter-layer structural dependencies and intra-layer node roles within a single coherent framework. Our approach integrates a mixture-of-mixtures structure, Bayesian nonparametric priors (e.g., nested Dirichlet processes), and MCMC inference to automatically determine the number of clusters at both network and node levels, ensuring sparsity, model parsimony, and compatibility with both binary and count-valued multilayer networks. Experiments demonstrate that the method accurately recovers ground-truth latent structures on synthetic data and, on real-world social multilayer networks, simultaneously identifies semantically meaningful network groupings (e.g., functional modules) and node-role clusters (e.g., bridge users, core opinion leaders), substantially enhancing multi-scale pattern discovery.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Multiplex networks are increasingly common across diverse domains, motivating the development of clustering methods that uncover patterns at multiple levels. Existing approaches typically focus on clustering either entire networks or nodes within a single network. We address the lack of a unified latent space framework for simultaneous network- and node-level clustering by proposing a latent position co-clustering model (LaPCoM), based on a hierarchical mixture-of-mixtures formulation. LaPCoM enables co-clustering of networks and their constituent nodes, providing joint dimension reduction and two-level cluster detection. At the network level, it identifies global homogeneity in topological patterns by grouping networks that share similar latent representations. At the node level, it captures local connectivity and community patterns. The model adopts a Bayesian nonparametric framework using a mixture of finite mixtures, which places priors on the number of clusters at both levels and incorporates sparse priors to encourage parsimonious clustering. Inference is performed via Markov chain Monte Carlo with automatic selection of the number of clusters. LaPCoM accommodates both binary and count-valued multiplex data. Simulation studies and comparisons with existing methods demonstrate accurate recovery of latent structure and clusters. Applications to real-world social multiplexes reveal interpretable network-level clusters aligned with context-specific patterns, and node-level clusters reflecting social patterns and roles.

Problem

• Unified latent space for network-node co-clustering
• Joint dimension reduction and two-level cluster detection
• Handling binary and count-valued multiplex network data

Innovation

• Latent position co-clustering for multiplex networks
• Bayesian nonparametric framework with sparse priors
• Joint dimension reduction and two-level clustering