# Distributed Autoregressive Moving Average Graph Filters

arXiv: https://arxiv.org/abs/1508.05808 · HTML: https://mlsanity.com/paper/1508.05808/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2015.

## Built on by (most cited first, 6 of 6)

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks](https://mlsanity.com/paper/2107.10234/) (2021)
- [Joint Detection and Localization of Stealth False Data Injection Attacks in Smart Grids using Graph Neural Networks](https://mlsanity.com/paper/2104.11846/) (2021)
- [Two Trades is not Baffled: Condensing Graph via Crafting Rational Gradient Matching](https://mlsanity.com/paper/2402.04924/) (2024)
- [Deep representation learning: Fundamentals, Perspectives, Applications, and Open Challenges](https://mlsanity.com/paper/2211.14732/) (2022)
- [Infinite Impulse Response Graph Neural Networks for Cyberattack Localization in Smart Grids](https://mlsanity.com/paper/2206.12527/) (2022)

## Abstract (arXiv)

We introduce the concept of autoregressive moving average (ARMA) filters on a graph and show how they can be implemented in a distributed fashion. Our graph filter design philosophy is independent of the particular graph, meaning that the filter coefficients are derived irrespective of the graph. In contrast to finite-impulse response (FIR) graph filters, ARMA graph filters are robust against changes in the signal and/or graph. In addition, when time-varying signals are considered, we prove that the proposed graph filters behave as ARMA filters in the graph domain and, depending on the implementation, as first or higher ARMA filters in the time domain.