# Bespoke multiresolution analysis of graph signals

arXiv: https://arxiv.org/abs/2507.19181 · HTML: https://mlsanity.com/paper/2507.19181/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 44 references that are in the map.
- First posted on arXiv 25 Jul 2025.

## Builds on (most cited first, 10 of 10)

- [CoLight: Learning Network-level Cooperation for Traffic Signal Control](https://mlsanity.com/paper/1905.05717/) (2019)
- [A Recurrent Graph Neural Network for Multi-Relational Data](https://mlsanity.com/paper/1811.02061/) (2018)
- [Perturbation Bounds for Procrustes, Classical Scaling, and Trilateration, with Applications to Manifold Learning](https://mlsanity.com/paper/1810.09569/) (2018)
- [Multiresolution kernel matrix algebra](https://mlsanity.com/paper/2211.11681/) (2022)
- [ERGNN: Spectral Graph Neural Network With Explicitly-Optimized Rational Graph Filters](https://mlsanity.com/paper/2412.19106/) (2024)
- [Anisotropic multiresolution analyses for deepfake detection](https://mlsanity.com/paper/2210.14874/) (2022)
- [Samplet basis pursuit: Multiresolution scattered data approximation with sparsity constraints](https://mlsanity.com/paper/2306.10180/) (2023)
- [Multiscale scattered data analysis in samplet coordinates](https://mlsanity.com/paper/2409.14791/) (2024)
- [Multiresolution local smoothness detection in non-uniformly sampled multivariate signals](https://mlsanity.com/paper/2507.13480/) (2025)
- [Graph Wedgelets: Adaptive Data Compression on Graphs based on Binary Wedge Partitioning Trees and Geometric Wavelets](https://mlsanity.com/paper/2110.08843/) (2021)

## Built on by (most cited first, 2 of 2)

- [Data-intrinsic approximation in metric spaces](https://mlsanity.com/paper/2510.13496/) (2025)
- [Samplet limits and multiwavelets](https://mlsanity.com/paper/2604.02150/) (2026)

## Abstract (arXiv)

We present a novel framework for discrete multiresolution analysis of graph signals. The main analytical tool is the samplet transform, originally defined in the Euclidean framework as a discrete wavelet-like construction, tailored to the analysis of scattered data. The first contribution of this work is defining samplets on graphs. To this end, we subdivide the graph into a fixed number of patches, embed each patch into a Euclidean space, where we construct samplets, and eventually pull the construction back to the graph. This ensures orthogonality, locality, and the vanishing moments property with respect to properly defined polynomial spaces on graphs. Compared to classical Haar wavelets, this framework broadens the class of graph signals that can efficiently be compressed and analyzed. Along this line, we provide a definition of a class of signals that can be compressed using our construction. We support our findings with different examples of signals defined on graphs whose vertices lie on smooth manifolds. For efficient numerical implementation, we combine heavy edge clustering, to partition the graph into meaningful patches, with landmark textttIsomap, which provides low-dimensional embeddings for each patch. Our results demonstrate the method's robustness, scalability, and ability to yield sparse representations with controllable approximation error, significantly outperforming traditional Haar wavelet approaches in terms of compression efficiency and multiresolution fidelity.