Generalizing Graph Signal Processing: High Dimensional Spaces, Models and Structures

Graph signal processing (GSP) has seen rapid developments in recent years. Since its introduction around ten years ago, we have seen numerous new ideas and practical applications related to the field. In this tutorial, we give an overview of some recent advances in generalizing GSP, with a focus on the extension to high-dimensional spaces, models, and structures. Alongside new frameworks proposed to tackle such problems, many new mathematical tools are being introduced. In the first part of the monograph, we will review traditional GSP, highlight the challenges it faces, and motivate efforts in overcoming such challenges, which will be the theme of the rest of the monograph.