Spectral graph fractional Fourier transform for directed graphs and its application

TL;DR

This paper introduces a novel spectral graph fractional Fourier transform tailored for directed graphs, enabling advanced signal processing and noise reduction in real-world network applications.

Contribution

It proposes a new fractional Hermitian Laplacian for directed graphs and generalizes the spectral graph fractional Fourier transform to this domain.

Findings

Effective noise reduction in temperature data using DGFRFT

Successful application on real-world directed graphs

Demonstrates improved signal processing capabilities

Abstract

In graph signal processing, many studies assume that the underlying network is undirected. Although the digraph model is rarely adopted, it is more appropriate for many applications, especially for real world networks. In this paper, we present a general framework for extending the graph signal processing to directed graphs in graph fractional domain. For this purpose, we consider a new definition for fractional Hermitian Laplacian matrix on directed graph and generalize the spectral graph fractional Fourier transform to directed graph (DGFRFT). Based on our new transform, we then define filtering, which is used in reducing unnecessary noise superimposed on temperature data. Finally, the performance of the proposed DGFRFT approach is also evaluated through numerical experiments using real-world directed graphs.