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

Graph signal processing (GSP) has seen rapid developmentsin recent years. Since its introduction around ten years ago,we have seen numerous new ideas and practical applicationsrelated to the field. In this tutorial, we give an overviewof some recent advances in generalizing GSP, with a focuson the extension to high-dimensional spaces, models, andstructures. Alongside new frameworks proposed to tacklesuch problems, many new mathematical tools are beingintroduced. In the first part of the monograph, we willreview traditional GSP, highlight the challenges it faces, andmotivate efforts in overcoming such challenges, which willbe the theme of the rest of the monograph.