# Windowed Fourier Analysis for Signal Processing on Graph Bundles

arXiv: https://arxiv.org/abs/2302.05592 · HTML: https://mlsanity.com/paper/2302.05592/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 34 references that are in the map.
- First posted on arXiv 11 Feb 2023.

## Builds on (most cited first, 15 of 15)

- [Topological Signal Processing over Simplicial Complexes](https://mlsanity.com/paper/1907.11577/) (2019)
- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Flow Smoothing and Denoising: Graph Signal Processing in the Edge-Space](https://mlsanity.com/paper/1808.02111/) (2018)
- [Vertex-Frequency Analysis on Graphs](https://mlsanity.com/paper/1307.5708/) (2013)
- [Graph-based Semi-Supervised & Active Learning for Edge Flows](https://mlsanity.com/paper/1905.07451/) (2019)
- [Spectrum-Adapted Tight Graph Wavelet and Vertex-Frequency Frames](https://mlsanity.com/paper/1311.0897/) (2013)
- [Finite Impulse Response Filters for Simplicial Complexes](https://mlsanity.com/paper/2103.12587/) (2021)
- [Multi-way Graph Signal Processing on Tensors: Integrative analysis of irregular geometries](https://mlsanity.com/paper/2007.00041/) (2020)
- [Enhanced graph-learning schemes driven by similar distributions of motifs](https://mlsanity.com/paper/2207.04747/) (2022)
- [Approximate and discrete Euclidean vector bundles](https://mlsanity.com/paper/2104.07563/) (2021)
- [FibeRed: Fiberwise Dimensionality Reduction of Topologically Complex Data with Vector Bundles](https://mlsanity.com/paper/2206.06513/) (2022)
- [On Local Distributions in Graph Signal Processing](https://mlsanity.com/paper/2202.10649/) (2022)
- [Partition of Unity Methods for Signal Processing on Graphs](https://mlsanity.com/paper/2012.10636/) (2020)
- [Sampling and Reconstruction of Signals on Product Graphs](https://mlsanity.com/paper/1807.00145/) (2018)
- [Sampling Theory for Graph Signals on Product Graphs](https://mlsanity.com/paper/1809.10049/) (2018)

## Abstract (arXiv)

We consider the task of representing signals supported on graph bundles, which are generalizations of product graphs that allow for "twists" in the product structure. Leveraging the localized product structure of a graph bundle, we demonstrate how a suitable partition of unity over the base graph can be used to lift the signal on the graph into a space where a product factorization can be readily applied. Motivated by the locality of this procedure, we demonstrate that bases for the signal spaces of the components of the graph bundle can be lifted in the same way, yielding a basis for the signal space of the total graph. We demonstrate this construction on synthetic graphs, as well as with an analysis of the energy landscape of conformational manifolds in stereochemistry.