# Co-Hub Node Based Multiview Graph Learning with Theoretical Guarantees

arXiv: https://arxiv.org/abs/2512.12435 · HTML: https://mlsanity.com/paper/2512.12435/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 66 references that are in the map.
- First posted on arXiv 13 Dec 2025.

## Builds on (most cited first, 19 of 19)

- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Network Inference via the Time-Varying Graphical Lasso](https://mlsanity.com/paper/1703.01958/) (2017)
- [A Unified Framework for Structured Graph Learning via Spectral Constraints](https://mlsanity.com/paper/1904.09792/) (2019)
- [Node-Based Learning of Multiple Gaussian Graphical Models](https://mlsanity.com/paper/1303.5145/) (2013)
- [Joint Inference of Multiple Graphs from Matrix Polynomials](https://mlsanity.com/paper/2010.08120/) (2020)
- [Identifying the Topology of Undirected Networks from Diffused Non-stationary Graph Signals](https://mlsanity.com/paper/1801.03862/) (2018)
- [Learning Time-Varying Graphs from Online Data](https://mlsanity.com/paper/2110.11017/) (2021)
- [Joint Network Topology Inference via a Shared Graphon Model](https://mlsanity.com/paper/2209.08223/) (2022)
- [Estimation of Graphical Models through Structured Norm Minimization](https://mlsanity.com/paper/1609.09010/) (2016)
- [Simultaneous Clustering and Estimation of Heterogeneous Graphical Models](https://mlsanity.com/paper/1611.09391/) (2016)
- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)
- [Learning Graphical Models With Hubs](https://mlsanity.com/paper/1402.7349/) (2014)
- [Multilayer Clustered Graph Learning](https://mlsanity.com/paper/2010.15456/) (2020)
- [Laplacian Constrained Precision Matrix Estimation: Existence and High Dimensional Consistency](https://mlsanity.com/paper/2111.00590/) (2021)
- [A Convex Formulation for Learning Scale-Free Networks via Submodular Relaxation](https://mlsanity.com/paper/1407.2697/) (2014)
- [Multiview Graph Learning with Consensus Graph](https://mlsanity.com/paper/2401.13769/) (2024)
- [Time-Varying Graph Learning for Data with Heavy-Tailed Distribution](https://mlsanity.com/paper/2501.00606/) (2024)
- [Graph Learning Across Data Silos](https://mlsanity.com/paper/2301.06662/) (2023)
- [Learning Graph Filters for Structure-Function Coupling based Hub Node Identification](https://mlsanity.com/paper/2410.17410/) (2024)

## Abstract (arXiv)

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.