Signal Processing on Signed Graphs: Fundamentals and Potentials

A wide range of data science problems can be modeled in terms of a graph (or network), e.g., social, sensor, communication, infrastructure, and biological networks. The nodes in a graph/network represent the entities of interest, and the edges reflect relations between these entities, such as geographic proximity (e.g., wireless networks), social relations (e.g., Facebook), biological mechanisms (e.g., brain networks), similarity (e.g., texts by identical authors), and statistical dependencies (e.g., gene expression data). Graph signal processing (GSP) advocates the use of graphs as combined data and computation models and has become a groundbreaking and powerful paradigm for solving diverse learning and inference tasks in the area of data science. GSP uses tools from linear algebra, (spectral) graph theory, computational harmonic analysis, and optimization theory to extend conventional signal processing concepts to data located on irregular domains that are characterized by graphs (networks). For entry-level expositions of GSP fundamentals and the relevant state of the art, we refer to [1]-[4] and the May 2018 Proceedings of the IEEE.