Co-Hub Node Based Multiview Graph Learning with Theoretical Guarantees

2025-12-13

AI Summary

This work addresses heterogeneous multi-view graph structure learning, focusing on identifying shared node-level structures—specifically “co-hub nodes” exhibiting cross-view centrality—across multiple closely related graphs. We propose a node-level cross-view sharing mechanism, replacing conventional edge-level regularization. We establish a layer-wise identifiability theory and derive an estimation error bound. By integrating structured sparsity optimization with multi-view graph regularization, our framework enables interpretable and verifiable joint graph learning. Experiments on synthetic data and multi-subject fMRI time-series demonstrate significant improvements in graph structure recovery accuracy. Empirical results substantiate the statistical identifiability, generalizability, and neuroscientific interpretability of the co-hub hypothesis.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Reasoning under Uncertainty: Graphical Models
• Computer Vision: Multi-modal Vision

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Identifying the graphical structure underlying the observed multivariate data is essential in numerous applications. Current methodologies are predominantly confined to deducing a singular graph under the presumption that the observed data are uniform. However, many contexts involve heterogeneous datasets that feature multiple closely related graphs, typically referred to as multiview graphs. Previous research on multiview graph learning promotes edge-based similarity across layers using pairwise or consensus-based regularizers. However, multiview graphs frequently exhibit a shared node-based architecture across different views, such as common hub nodes. Such commonalities can enhance the precision of learning and provide interpretive insight. In this paper, we propose a co-hub node model, positing that different views share a common group of hub nodes. The associated optimization framework is developed by enforcing structured sparsity on the connections of these co-hub nodes. Moreover, we present a theoretical examination of layer identifiability and determine bounds on estimation error. The proposed methodology is validated using both synthetic graph data and fMRI time series data from multiple subjects to discern several closely related graphs.

Problem

• Identifies multiview graph structures from heterogeneous datasets
• Models common hub nodes across different graph views
• Provides theoretical guarantees for layer identifiability and error bounds

Innovation

• Co-hub node model for multiview graph learning
• Structured sparsity optimization on co-hub connections
• Theoretical guarantees on layer identifiability and error bounds