# Joint Network Topology Inference via Structured Fusion Regularization

arXiv: https://arxiv.org/abs/2103.03471 · HTML: https://mlsanity.com/paper/2103.03471/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 49 references that are in the map.
- First posted on arXiv 5 Mar 2021.

## Builds on (most cited first, 16 of 16)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Learning graphs from data: A signal representation perspective](https://mlsanity.com/paper/1806.00848/) (2018)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [Network Inference via the Time-Varying Graphical Lasso](https://mlsanity.com/paper/1703.01958/) (2017)
- [Learning Sparse Graphs Under Smoothness Prior](https://mlsanity.com/paper/1609.03448/) (2016)
- [Joint Inference of Multiple Graphs from Matrix Polynomials](https://mlsanity.com/paper/2010.08120/) (2020)
- [Graph Learning from Filtered Signals: Graph System and Diffusion Kernel Identification](https://mlsanity.com/paper/1803.02553/) (2018)
- [Learning Graphs with Monotone Topology Properties and Multiple Connected Components](https://mlsanity.com/paper/1705.10934/) (2017)
- [Learning Undirected Graphs in Financial Markets](https://mlsanity.com/paper/2005.09958/) (2020)
- [Localized Spectral Graph Filter Frames: A Unifying Framework, Survey of Design Considerations, and Numerical Comparison (Extended Cut)](https://mlsanity.com/paper/2006.11220/) (2020)
- [Online Discriminative Graph Learning from Multi-Class Smooth Signals](https://mlsanity.com/paper/2101.00184/) (2021)
- [Time-Varying Graph Learning with Constraints on Graph Temporal Variation](https://mlsanity.com/paper/2001.03346/) (2020)
- [Covariance Matrix Estimation under Total Positivity for Portfolio Selection](https://mlsanity.com/paper/1909.04222/) (2019)
- [Tracking Switched Dynamic Network Topologies from Information Cascades](https://mlsanity.com/paper/1606.08882/) (2016)
- [Multi-layer graph analysis for dynamic social networks](https://mlsanity.com/paper/1309.5124/) (2013)

## Built on by (most cited first, 1 of 1)

- [Graph Learning Across Data Silos](https://mlsanity.com/paper/2301.06662/) (2023)

## Abstract (arXiv)

Joint network topology inference represents a canonical problem of jointly learning multiple graph Laplacian matrices from heterogeneous graph signals. In such a problem, a widely employed assumption is that of a simple common component shared among multiple networks. However, in practice, a more intricate topological pattern, comprising simultaneously of sparse, homogeneity and heterogeneity components, would exhibit in multiple networks. In this paper, we propose a general graph estimator based on a novel structured fusion regularization that enables us to jointly learn multiple graph Laplacian matrices with such complex topological patterns, and enjoys both high computational efficiency and rigorous theoretical guarantee. Moreover, in the proposed regularization term, the topological pattern among networks is characterized by a Gram matrix, endowing our graph estimator with the ability of flexible modelling different types of topological patterns by different choices of the Gram matrix. Computationally, the regularization term, coupling the parameters together, makes the formulated optimization problem intractable and thus, we develop a computationally-scalable algorithm based on the alternating direction method of multipliers (ADMM) to solve it efficiently. Theoretically, we provide a theoretical analysis of the proposed graph estimator, which establishes a non-asymptotic bound of the estimation error under the high-dimensional setting and reflects the effect of several key factors on the convergence rate of our algorithm. Finally, the superior performance of the proposed method is illustrated through simulated and real data examples.