Summary of Sampling and Uniqueness Sets in Graphon Signal Processing, by Alejandro Parada-mayorga and Alejandro Ribeiro
Sampling and Uniqueness Sets in Graphon Signal Processing
by Alejandro Parada-Mayorga, Alejandro Ribeiro
First submitted to arxiv on: 11 Jan 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Signal Processing (eess.SP)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper explores the properties of sampling sets on large graphs by leveraging graphon theory and limits. It extends the concept of removable and uniqueness sets from signal analysis to graph signals, allowing for unique representations of bandlimited graphon signals based on samples from the complement of a given removable set. The results enable comparisons between sampling sets across graphs with varying node numbers, edge counts, and labelings. Additionally, the paper shows that sequences of graphs converging to a graphon also converge in terms of their sampling sets. An algorithm is proposed for obtaining approximately optimal sampling sets, which is evaluated through numerical experiments. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper looks at how we can take big groups of connected nodes (like social networks) and find the best way to get information from just some of those nodes. It uses a new way of looking at graphs, called graphons, that lets us compare different ways of getting information from these groups. The researchers also come up with a way to make this work even when we’re dealing with really big groups or ones with lots of different types of connections. They test their idea and find it works well. |
