# Online Graph Filtering Over Expanding Graphs

arXiv: https://arxiv.org/abs/2409.07204 · HTML: https://mlsanity.com/paper/2409.07204/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 48 references that are in the map.
- First posted on arXiv 11 Sep 2024.

## Builds on (most cited first, 20 of 20)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Discrete Signal Processing on Graphs: Frequency Analysis](https://mlsanity.com/paper/1307.0468/) (2013)
- [Graph signal processing for machine learning: A review and new perspectives](https://mlsanity.com/paper/2007.16061/) (2020)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Kernel-based Reconstruction of Graph Signals](https://mlsanity.com/paper/1605.07174/) (2016)
- [Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information](https://mlsanity.com/paper/2007.03653/) (2020)
- [Reconstruction of Time-varying Graph Signals via Sobolev Smoothness](https://mlsanity.com/paper/2207.06439/) (2022)
- [Adaptive Diffusions for Scalable Learning over Graphs](https://mlsanity.com/paper/1804.02081/) (2018)
- [Networked Signal and Information Processing](https://mlsanity.com/paper/2210.13767/) (2022)
- [Online Non-linear Topology Identification from Graph-connected Time Series](https://mlsanity.com/paper/2104.00030/) (2021)
- [Online Graph-Adaptive Learning with Scalability and Privacy](https://mlsanity.com/paper/1812.00974/) (2018)
- [Prediction-Correction Algorithms for Time-Varying Constrained Optimization](https://mlsanity.com/paper/1611.03681/) (2016)
- [Recursive Prediction of Graph Signals with Incoming Nodes](https://mlsanity.com/paper/1911.11542/) (2019)
- [Graph filtering over expanding graphs](https://mlsanity.com/paper/2203.08058/) (2022)
- [Learning Expanding Graphs for Signal Interpolation](https://mlsanity.com/paper/2203.07966/) (2022)
- [Online Distributed Learning over Graphs with Multitask Graph-Filter Models](https://mlsanity.com/paper/1912.05805/) (2019)
- [Streaming Network Embedding through Local Actions](https://mlsanity.com/paper/1811.05932/) (2018)
- [Online Filtering over Expanding Graphs](https://mlsanity.com/paper/2301.06898/) (2023)

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

- [Stochastic Sequential Decision Making over Expanding Networks with Graph Filtering](https://mlsanity.com/paper/2603.19501/) (2026)

## Abstract (arXiv)

Graph filters are a staple tool for processing signals over graphs in a multitude of downstream tasks. However, they are commonly designed for graphs with a fixed number of nodes, despite real-world networks typically grow over time. This topological evolution is often known up to a stochastic model, thus, making conventional graph filters ill-equipped to withstand such topological changes, their uncertainty, as well as the dynamic nature of the incoming data. To tackle these issues, we propose an online graph filtering framework by relying on online learning principles. We design filters for scenarios where the topology is both known and unknown, including a learner adaptive to such evolution. We conduct a regret analysis to highlight the role played by the different components such as the online algorithm, the filter order, and the growing graph model. Numerical experiments with synthetic and real data corroborate the proposed approach for graph signal inference tasks and show a competitive performance w.r.t. baselines and state-of-the-art alternatives.