# Natural Graph Wavelet Packet Dictionaries

arXiv: https://arxiv.org/abs/2009.09020 · HTML: https://mlsanity.com/paper/2009.09020/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2020.

## Built on by (most cited first, 3 of 3)

- [VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks](https://mlsanity.com/paper/2510.01022/) (2025)
- [eGHWT: The Extended Generalized Haar-Walsh Transform](https://mlsanity.com/paper/2107.05121/) (2021)
- [StreaMRAK a Streaming Multi-Resolution Adaptive Kernel Algorithm](https://mlsanity.com/paper/2108.10411/) (2021)

## Abstract (arXiv)

We introduce a set of novel multiscale basis transforms for signals on graphs that utilize their "dual" domains by incorporating the "natural" distances between graph Laplacian eigenvectors, rather than simply using the eigenvalue ordering. These basis dictionaries can be seen as generalizations of the classical Shannon wavelet packet dictionary to arbitrary graphs, and do not rely on the frequency interpretation of Laplacian eigenvalues. We describe the algorithms (involving either vector rotations or orthogonalizations) to construct these basis dictionaries, use them to efficiently approximate graph signals through the best basis search, and demonstrate the strengths of these basis dictionaries for graph signals measured on sunflower graphs and street networks.