# Irregularity-Aware Graph Fourier Transforms

arXiv: https://arxiv.org/abs/1802.10220 · HTML: https://mlsanity.com/paper/1802.10220/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2018.

## Built on by (most cited first, 8 of 8)

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Towards joint graph learning and sampling set selection from data](https://mlsanity.com/paper/2412.09753/) (2024)
- [Spend Bits Where Queries Look: KV Cache Vector Quantization with Attention-Preserving Transforms](https://mlsanity.com/paper/2608.04074/) (2026)
- [Motion estimation and filtered prediction for dynamic point cloud attribute compression](https://mlsanity.com/paper/2210.08262/) (2022)
- [Joint Graph and Vertex Importance Learning](https://mlsanity.com/paper/2303.08552/) (2023)
- [Haar-Laplacian for directed graphs](https://mlsanity.com/paper/2411.15527/) (2024)
- [Graph Distribution-valued Signals: A Wasserstein Space Perspective](https://mlsanity.com/paper/2509.25802/) (2025)
- [Large Graph Signal Denoising with Application to Differential Privacy](https://mlsanity.com/paper/2209.02043/) (2022)

## Abstract (arXiv)

In this paper, we present a novel generalization of the graph Fourier transform (GFT). Our approach is based on separately considering the definitions of signal energy and signal variation, leading to several possible orthonormal GFTs. Our approach includes traditional definitions of the GFT as special cases, while also leading to new GFT designs that are better at taking into account the irregular nature of the graph. As an illustration, in the context of sensor networks we use the Voronoi cell area of vertices in our GFT definition, showing that it leads to a more sensible definition of graph signal energy even when sampling is highly irregular.