To further understand graph signals

TL;DR

This paper emphasizes understanding the intrinsic geometric information within graph signals, proposing a framework to uncover hidden structures that can enhance signal processing techniques beyond traditional Fourier-based methods.

Contribution

It introduces a new framework to analyze the geometric aspects of graph signals, independent of Fourier theories, advancing the understanding of their intrinsic properties.

Findings

Graph signals contain hidden geometric information.

A new framework to analyze intrinsic properties of graph signals.

Potential improvements in signal processing methods.

Abstract

Graph signal processing (GSP) is a framework to analyze and process graph-structured data. Many research works focus on developing tools such as Graph Fourier transforms (GFT), filters, and neural network models to handle graph signals. Such approaches have successfully taken care of ``signal processing'' in many circumstances. In this paper, we want to put emphasis on ``graph signals'' themselves. Although there are characterizations of graph signals using the notion of bandwidth derived from GFT, we want to argue here that graph signals may contain hidden geometric information of the network, independent of (graph) Fourier theories. We shall provide a framework to understand such information, and demonstrate how new knowledge on ``graph signals'' can help with ``signal processing''.