# Graph filtering over expanding graphs

arXiv: https://arxiv.org/abs/2203.08058 · HTML: https://mlsanity.com/paper/2203.08058/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 32 references that are in the map.
- First posted on arXiv 15 Mar 2022.

## Builds on (most cited first, 9 of 9)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks](https://mlsanity.com/paper/2003.03777/) (2020)
- [Signal Processing on Graphs: Causal Modeling of Unstructured Data](https://mlsanity.com/paper/1503.00173/) (2015)
- [Forecasting Time Series with VARMA Recursions on Graphs](https://mlsanity.com/paper/1810.08581/) (2018)
- [Learning parametric dictionaries for graph signals](https://mlsanity.com/paper/1401.0887/) (2014)
- [Adaptive Diffusions for Scalable Learning over Graphs](https://mlsanity.com/paper/1804.02081/) (2018)
- [Online Graph-Adaptive Learning with Scalability and Privacy](https://mlsanity.com/paper/1812.00974/) (2018)
- [Recursive Prediction of Graph Signals with Incoming Nodes](https://mlsanity.com/paper/1911.11542/) (2019)

## Built on by (most cited first, 5 of 5)

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Continual Learning on Graphs: Challenges, Solutions, and Opportunities](https://mlsanity.com/paper/2402.11565/) (2024)
- [Online Filtering over Expanding Graphs](https://mlsanity.com/paper/2301.06898/) (2023)
- [Online Graph Filtering Over Expanding Graphs](https://mlsanity.com/paper/2409.07204/) (2024)
- [Stochastic Sequential Decision Making over Expanding Networks with Graph Filtering](https://mlsanity.com/paper/2603.19501/) (2026)

## Abstract (arXiv)

Our capacity to learn representations from data is related to our ability to design filters that can leverage their coupling with the underlying domain. Graph filters are one such tool for network data and have been used in a myriad of applications. But graph filters work only with a fixed number of nodes despite the expanding nature of practical networks. Learning filters in this setting is challenging not only because of the increased dimensions but also because the connectivity is known only up to an attachment model. We propose a filter learning scheme for data over expanding graphs by relying only on such a model. By characterizing the filter stochastically, we develop an empirical risk minimization framework inspired by multi-kernel learning to balance the information inflow and outflow at the incoming nodes. We particularize the approach for denoising and semi-supervised learning (SSL) over expanding graphs and show near-optimal performance compared with baselines relying on the exact topology. For SSL, the proposed scheme uses the incoming node information to improve the task on the existing ones. These findings lay the foundation for learning representations over expanding graphs by relying only on the stochastic connectivity model.