# Sampling and Uniqueness Sets in Graphon Signal Processing

arXiv: https://arxiv.org/abs/2401.06279 · HTML: https://mlsanity.com/paper/2401.06279/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 45 references that are in the map.
- First posted on arXiv 11 Jan 2024.

## Builds on (most cited first, 18 of 18)

- [Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/1910.09658/) (2019)
- [Graphon Signal Processing](https://mlsanity.com/paper/2003.05030/) (2020)
- [Discrete Signal Processing on Graphs: Sampling Theory](https://mlsanity.com/paper/1503.05432/) (2015)
- [Algebraic Neural Networks: Stability to Deformations](https://mlsanity.com/paper/2009.01433/) (2020)
- [Sampling of graph signals with successive local aggregations](https://mlsanity.com/paper/1504.04687/) (2015)
- [Graphon Filters: Graph Signal Processing in the Limit](https://mlsanity.com/paper/2003.02099/) (2020)
- [Random sampling of bandlimited signals on graphs](https://mlsanity.com/paper/1511.05118/) (2015)
- [Unsupervised Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/2210.09277/) (2022)
- [Graphon Pooling in Graph Neural Networks](https://mlsanity.com/paper/2003.01795/) (2020)
- [Greedy Sampling of Graph Signals](https://mlsanity.com/paper/1704.01223/) (2017)
- [Stability of Algebraic Neural Networks to Small Perturbations](https://mlsanity.com/paper/2010.11544/) (2020)
- [Convolutional Filtering and Neural Networks with Non Commutative Algebras](https://mlsanity.com/paper/2108.09923/) (2021)
- [Graphon Pooling for Reducing Dimensionality of Signals and Convolutional Operators on Graphs](https://mlsanity.com/paper/2212.08171/) (2022)
- [Stability of Aggregation Graph Neural Networks](https://mlsanity.com/paper/2207.03678/) (2022)
- [Sampling and Recovery of Graph Signals](https://mlsanity.com/paper/1712.09310/) (2017)
- [Blue-Noise Sampling on Graphs](https://mlsanity.com/paper/1811.12542/) (2018)
- [Practical graph signal sampling with log-linear size scaling](https://mlsanity.com/paper/2102.10506/) (2021)
- [Graph sampling with determinantal processes](https://mlsanity.com/paper/1703.01594/) (2017)

## Built on by (most cited first, 5 of 5)

- [Convolutional Filtering with RKHS Algebras](https://mlsanity.com/paper/2411.01341/) (2024)
- [RKHS Representation of Algebraic Convolutional Filters with Integral Operators](https://mlsanity.com/paper/2602.19094/) (2026)
- [A Novel Unified Extended Matrix for Graph Signal Processing: Theory and Application](https://mlsanity.com/paper/2508.16633/) (2025)
- [A Generative Model for Controllable Feature Heterophily in Graphs](https://mlsanity.com/paper/2509.23230/) (2025)
- [Fundamental Limits of Transferability and Equivariance in Algebraic Signal Models I: Finite Dimensions](https://mlsanity.com/paper/2609.36106/) (2026)

## Abstract (arXiv)

In this work, we study the properties of sampling sets on families of large graphs by leveraging the theory of graphons and graph limits. To this end, we extend to graphon signals the notion of removable and uniqueness sets, which was developed originally for the analysis of signals on graphs. We state the formal definition of a Lambda-removable set and conditions under which a bandlimited graphon signal can be represented in a unique way when its samples are obtained from the complement of a given Lambda-removable set in the graphon. By leveraging such results we show that graphon representations of graphs and graph signals can be used as a common framework to compare sampling sets between graphs with different numbers of nodes and edges, and different node labelings. Additionally, given a sequence of graphs that converges to a graphon, we show that the sequences of sampling sets whose graphon representation is identical in [0,1] are convergent as well. We exploit the convergence results to provide an algorithm that obtains approximately close to optimal sampling sets. Performing a set of numerical experiments, we evaluate the quality of these sampling sets. Our results open the door for the efficient computation of optimal sampling sets in graphs of large size.