# Diffusion Maps for Signal Filtering in Graph Learning

arXiv: https://arxiv.org/abs/2312.14758 · HTML: https://mlsanity.com/paper/2312.14758/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 32 references that are in the map.
- First posted on arXiv 22 Dec 2023.

## Builds on (most cited first, 12 of 12)

- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [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 Signal Processing: History, Development, Impact, and Outlook](https://mlsanity.com/paper/2303.12211/) (2023)
- [Graph Learning from Filtered Signals: Graph System and Diffusion Kernel Identification](https://mlsanity.com/paper/1803.02553/) (2018)
- [Stationary time-vertex signal processing](https://mlsanity.com/paper/1611.00255/) (2016)
- [Complex-Value Spatio-temporal Graph Convolutional Neural Networks and its Applications to Electric Power Systems AI](https://mlsanity.com/paper/2208.08485/) (2022)
- [A Markov Variation Approach to Smooth Graph Signal Interpolation](https://mlsanity.com/paper/1806.03174/) (2018)
- [Wireless localization with diffusion maps](https://mlsanity.com/paper/1908.05216/) (2019)

## Abstract (arXiv)

This paper explores the application diffusion maps as graph shift operators in understanding the underlying geometry of graph signals. The study evaluates the improvements in graph learning when using diffusion map generated filters to the Markov Variation minimization problem. The paper showcases the effectiveness of this approach through examples involving synthetically generated and real-world temperature sensor data. These examples also compare the diffusion map graph signal model with other commonly used graph signal operators. The results provide new approaches for the analysis and understanding of complex, non-Euclidean data structures.