# Rotation-Parameterized Graph Fractional Fourier Transform: Definition, Properties, and Optimal Filtering

arXiv: https://arxiv.org/abs/2511.16111 · HTML: https://mlsanity.com/paper/2511.16111/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 69 references that are in the map.
- First posted on arXiv 20 Nov 2025.

## Builds on (most cited first, 24 of 24)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Discrete Signal Processing on Graphs: Frequency Analysis](https://mlsanity.com/paper/1307.0468/) (2013)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Graph Spectral Image Processing](https://mlsanity.com/paper/1801.04749/) (2018)
- [Graph Signal Processing: History, Development, Impact, and Outlook](https://mlsanity.com/paper/2303.12211/) (2023)
- [Learning parametric dictionaries for graph signals](https://mlsanity.com/paper/1401.0887/) (2014)
- [Bayesian Estimation of Graph Signals](https://mlsanity.com/paper/2103.15520/) (2021)
- [Graph Signal Processing -- Part I: Graphs, Graph Spectra, and Spectral Clustering](https://mlsanity.com/paper/1907.03467/) (2019)
- [A Directed Graph Fourier Transform with Spread Frequency Components](https://mlsanity.com/paper/1804.03000/) (2018)
- [Verifying the Smoothness of Graph Signals: A Graph Signal Processing Approach](https://mlsanity.com/paper/2305.19618/) (2023)
- [Graph Fourier Transform: A Stable Approximation](https://mlsanity.com/paper/2001.05042/) (2020)
- [Graph Signal Processing over a Probability Space of Shift Operators](https://mlsanity.com/paper/2108.09192/) (2021)
- [Signal Representations on Graphs: Tools and Applications](https://mlsanity.com/paper/1512.05406/) (2015)
- [Fast Graph Fourier Transforms Based on Graph Symmetry and Bipartition](https://mlsanity.com/paper/1907.07875/) (2019)
- [Non-Bayesian Estimation Framework for Signal Recovery on Graphs](https://mlsanity.com/paper/2005.01952/) (2020)
- [Kernel Based Reconstruction for Generalized Graph Signal Processing](https://mlsanity.com/paper/2308.06949/) (2023)
- [A Graph Signal Processing Perspective of Network Multiple Hypothesis Testing with False Discovery Rate Control](https://mlsanity.com/paper/2408.03142/) (2024)
- [Multi-dimensional graph fractional Fourier transform and its application](https://mlsanity.com/paper/2109.04358/) (2021)
- [Joint Time-Vertex Fractional Fourier Transform](https://mlsanity.com/paper/2203.07655/) (2022)

## Abstract (arXiv)

Graph spectral representations are fundamental in graph signal processing, providing a rigorous frameworkforanalyzing graph-structured data. The graph fractional Fourier transform (GFRFT) extends the graph Fourier transform (GFT) through a fractional-order parameter, enabling flexible spectral analysis with mathematical consistency. The angular graph Fourier transform (AGFT) further introduces angular control by rotating GFT eigenvectors; however, existing constructions may fail to reduce exactly to the GFT at zero angle, weakening theoretical consistency and interpretability. To address these complementary limitations, namely the lack of rotation-based basis control in GFRFT and the defective zero-angle degeneracy of AGFT, this paper proposes the rotation-parameterized graph fractional Fourier transform (RP-GFRFT), which unifies fractional order and rotation-parameterized spectral analysis. A degeneracy preserving rotation matrix family is constructed to guarantee exact GFT reduction at zero angle. TwoRP-GFRFTvariants,I-RP-GFRFTandII-RP-GFRFT,arethenformulated, with theoretical analyses confirming their unitarity, invertibility, reduction behavior, and smooth parameter dependence. The fractional order and rotation angle are jointly optimized for adaptive graph spectral filtering. Experiments on real-world signals, images, and point clouds demonstrate that RP-GFRFT improves denoising accuracy, reconstruction quality, and feature preservation over GFRFT, AGFT, and representative filtering baselines.