# Advances in Distributed Graph Filtering

arXiv: https://arxiv.org/abs/1808.03004 · HTML: https://mlsanity.com/paper/1808.03004/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2018.

## Built on by (most cited first, 13 of 13)

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Stability of Graph Convolutional Neural Networks to Stochastic Perturbations](https://mlsanity.com/paper/2106.10526/) (2021)
- [Learning Time-Varying Graphs from Online Data](https://mlsanity.com/paper/2110.11017/) (2021)
- [Convolutional Filtering in Simplicial Complexes](https://mlsanity.com/paper/2201.12584/) (2022)
- [Node-Variant Graph Filters in Graph Neural Networks](https://mlsanity.com/paper/2106.00089/) (2021)
- [Learning Stochastic Graph Neural Networks with Constrained Variance](https://mlsanity.com/paper/2201.12611/) (2022)
- [Learning Expanding Graphs for Signal Interpolation](https://mlsanity.com/paper/2203.07966/) (2022)
- [A Robust Alternative for Graph Convolutional Neural Networks via Graph Neighborhood Filters](https://mlsanity.com/paper/2110.00844/) (2021)
- [Online Filtering over Expanding Graphs](https://mlsanity.com/paper/2301.06898/) (2023)
- [On the Trade-Off between Stability and Representational Capacity in Graph Neural Networks](https://mlsanity.com/paper/2312.02372/) (2023)
- [Graph Convolutional Neural Networks Sensitivity under Probabilistic Error Model](https://mlsanity.com/paper/2203.07831/) (2022)
- [A Review of Graph-Powered Data Quality Applications for IoT Monitoring Sensor Networks](https://mlsanity.com/paper/2410.21006/) (2024)
- [Quantitative Error Feedback for Quantization Noise Reduction of Filtering over Graphs](https://mlsanity.com/paper/2506.01404/) (2025)

## Abstract (arXiv)

Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational savings. To improve this tradeoff, this work generalizes state-of-the-art distributed graph filters to filters where every node weights the signal of its neighbors with different values while keeping the aggregation operation linear. This new implementation, labeled as edge-variant graph filter, yields a significant reduction in terms of communication rounds while preserving the approximation accuracy. In addition, we characterize the subset of shift-invariant graph filters that can be described with edge-variant recursions. By using a low-dimensional parametrization the proposed graph filters provide insights in approximating linear operators through the succession and composition of local operators, i.e., fixed support matrices, which span applications beyond the field of graph signal processing. A set of numerical results shows the benefits of the edge-variant filters over current methods and illustrates their potential to a wider range of applications than graph filtering.