# Topology-Aware Joint Graph Filter and Edge Weight Identification for Network Processes

arXiv: https://arxiv.org/abs/2007.03266 · HTML: https://mlsanity.com/paper/2007.03266/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2020.

## Built on by (most cited first, 8 of 8)

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Robust Graph Neural Network based on Graph Denoising](https://mlsanity.com/paper/2312.06557/) (2023)
- [A Robust Alternative for Graph Convolutional Neural Networks via Graph Neighborhood Filters](https://mlsanity.com/paper/2110.00844/) (2021)
- [Distributed Graph Learning with Smooth Data Priors](https://mlsanity.com/paper/2112.05887/) (2021)
- [Precision Neural Networks: Joint Graph And Relational Learning](https://mlsanity.com/paper/2509.14821/) (2025)
- [Forecasting Graph Signals with Recursive MIMO Graph Filters](https://mlsanity.com/paper/2210.15258/) (2022)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)
- [Joint Precision Neural Networks: Task-Aware Dependency and Predictive Learning](https://mlsanity.com/paper/2610.06023/) (2026)

## Abstract (arXiv)

Data defined over a network have been successfully modelled by means of graph filters. However, although in many scenarios the connectivity of the network is known, e.g., smart grids, social networks, etc., the lack of well-defined interaction weights hinders the ability to model the observed networked data using graph filters. Therefore, in this paper, we focus on the joint identification of coefficients and graph weights defining the graph filter that best models the observed input/output network data. While these two problems have been mostly addressed separately, we here propose an iterative method that exploits the knowledge of the support of the graph for the joint identification of graph filter coefficients and edge weights. We further show that our iterative scheme guarantees a non-increasing cost at every iteration, ensuring a globally-convergent behavior. Numerical experiments confirm the applicability of our proposed approach.