The notion of graph filters can be used to define generative models for graph data. In fact, the data obtained from many examples of network dynamics may be viewed as the output of a graph filter. With this interpretation, classical signal processing tools such as frequency analysis have been successfully applied with analogous interpretation to graph data, generating new insights for data science. What follows is a user guide on a specific class of graph data, where the generating graph filters are low-pass, i.e., the filter attenuates contents in the higher graph frequencies while retaining contents in the lower frequencies. Our choice is motivated by the prevalence of low-pass models in application domains such as social networks, financial markets, and power systems. We illustrate how to leverage properties of low-pass graph filters to learn the graph topology or identify its community structure, efficiently represent graph data through sampling, recover missing measurements, de-noise graph data and perform a blind graph matching using graph signals.
Anna Scaglione (M.Sc.'95, Ph.D. '99) is currently a professor in electrical and computer at Cornell Tech, the New York City campus of Cornell University, Prior to that she held faculty positions at Arizona State University, the University of California at Davis, Cornell University (the first time) and the University of New Mexico. She is IEEE fellow since 2011 and received the 2013, IEEE Donald G. Fink Prize Paper Award, the 2000 IEEE Signal Processing Transactions Best Paper Award the NSF CAREER grant (2002). She is co-recipient with her students of several best student papers awards at conferences and received the 2013 IEEE Signal Processing Society Young Author Best Paper Award with one of the PhD students. She was Distinguished Lecturer of the Signal Processing Society in 2019 and 2020. Dr. Scaglione's expertise and research considers theoretical and applied problems is in statistical signal processing, communications theory and cyber-physical systems. Her talk includes research she has done on data that originate from networked systems.