SC-4: Graph Signal Processing and Geometric Learning: A Foundational Approach (Day 1)

This course presents a novel data analytics perspective to deal with signals and data supported by graphs. Such data occurs in many application domains from traditional physics-based signals like time series, images, or video to data traveling on telecom networks, to gene networks, chemical networks, or arising in social networks, marketing, corporate, financial, health care domains. Graph Signal Processing (GSP) extends traditional Digital Signal Processing (DSP) to data supported by graphs. Contrary to what is commonly believed in the SP community, GSP is not simply extending DSP approaches to arbitrary graphs. This course builds GSP from first principles and presents recent foundational results from GSP as an intuitive, direct extension of Digital Signal Processing concepts. Using this novel approach, this course introduces a canonical model, a new way to design and understand GSP concepts. It sheds new light on DSP interpretations and assumptions commonly taken for granted, providing new, valuable interpretations and perspectives in both DSP and GSP. Finally, the course considers Geometric Learning combining GSP and Deep Learning (DL), in particular, graph neural networks (GNN). This course is designed to be self-contained (with no required prerequisites), providing something for both those new to GSP and GSP veterans alike.