Learning graphs from data: A signal representation perspective
This is an incremental tutorial that surveys existing techniques for graph learning, which is important for researchers in signal processing and machine learning dealing with structured data representation.
The paper provides a tutorial overview of methods for learning graph topologies from data, comparing classical statistical and physics-based approaches with newer graph signal processing (GSP) perspectives, and highlights the advantages of GSP-based methods in various scenarios.
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.