A short-graph Fourier transform via personalized PageRank vectors

TL;DR

This paper introduces a novel short-time Fourier transform for graph signals using personalized PageRank vectors, bridging local spectral graph theory and spectral analysis to better analyze complex graph-based data.

Contribution

It proposes a new graph STFT formulation based on personalized PageRank vectors, connecting local spectral theory with localized spectral analysis.

Findings

Effective analysis of synthetic graph signals

Successful application to real-world data

Demonstrates improved spectral localization

Abstract

The short-time Fourier transform (STFT) is widely used to analyze the spectra of temporal signals that vary through time. Signals defined over graphs, due to their intrinsic complexity, exhibit large variations in their patterns. In this work we propose a new formulation for an STFT for signals defined over graphs. This formulation draws on recent ideas from spectral graph theory, using personalized PageRank vectors as its fundamental building block. Furthermore, this work establishes and explores the connection between local spectral graph theory and localized spectral analysis of graph signals. We accompany the presentation with synthetic and real-world examples, showing the suitability of the proposed approach.