Learning graphs from data: A signal representation perspective

TL;DR

This paper surveys methods for inferring graph structures from data, comparing classical and graph signal processing approaches, and discusses their advantages, challenges, and future research directions.

Contribution

It provides a comprehensive overview of graph learning techniques from both classical and GSP perspectives, highlighting their differences and potential benefits.

Findings

GSP-based methods offer advantages in certain scenarios.

Classical and GSP approaches have conceptual similarities and differences.

Open issues include challenges in designing future algorithms.

Abstract

The construction of a meaningful graph topology plays a crucial role in the effective representation, processing, analysis and visualization of structured data. When a natural choice of the graph is not readily available from the data sets, it is thus desirable to infer or learn a graph topology from the data. In this tutorial overview, we survey solutions to the problem of graph learning, including classical viewpoints from statistics and physics, and more recent approaches that adopt a graph signal processing (GSP) perspective. We further emphasize the conceptual similarities and differences between classical and GSP-based graph inference methods, and highlight the potential advantage of the latter in a number of theoretical and practical scenarios. We conclude with several open issues and challenges that are keys to the design of future signal processing and machine learning algorithms for learning graphs from data.