A User Guide to Low-Pass Graph Signal Processing and its Applications

TL;DR

This paper provides a comprehensive user guide on low-pass graph signal processing, demonstrating its applications in graph topology learning, data representation, denoising, and anomaly detection across various network domains.

Contribution

It introduces a detailed methodology for applying low-pass graph filters to analyze and process network data, highlighting its practical utility and effectiveness.

Findings

Low-pass graph filters help identify community structures.

Efficient sampling and recovery of graph data are achieved.

Anomaly detection is enhanced using low-pass filter properties.

Abstract

The notion of graph filters can be used to define generative models for graph data. In fact, the data obtained from many examples of network dynamics may be viewed as the output of a graph filter. With this interpretation, classical signal processing tools such as frequency analysis have been successfully applied with analogous interpretation to graph data, generating new insights for data science. What follows is a user guide on a specific class of graph data, where the generating graph filters are low-pass, i.e., the filter attenuates contents in the higher graph frequencies while retaining contents in the lower frequencies. Our choice is motivated by the prevalence of low-pass models in application domains such as social networks, financial markets, and power systems. We illustrate how to leverage properties of low-pass graph filters to learn the graph topology or identify its community structure; efficiently represent graph data through sampling, recover missing measurements, and de-noise graph data; the low-pass property is also used as the baseline to detect anomalies.