Statistics Seminar: Topological Clustering: from Multilayer Networks to Climate Resiliency and Beyond
Presenter: Professor Yulia R. Gel, Virginia Tech
Description: Multilayer networks continue to gain significant attention in many areas of study, particularly, due to their high utility in modeling interdependent systems such as critical infrastructures, human brain connectome, and socio-environmental ecosystems. However, clustering of multilayer networks, especially, using the information on higher order interactions of the system entities, yet remains in its infancy. We discuss a new topological approach for multilayer network clustering, based on the rationale to group nodes not using the pairwise connectivity patterns or relationships between observations recorded at two individual nodes, but based on how similar in shape their local neighborhoods are at various resolution scales. We quantify shapes of local node neighborhoods using persistence diagrams and then consider either single linkage or k-means forms of topological clustering, which allows us to systematically account for the important heterogeneous higher-order properties of node interactions within and in-between network layers and to integrate information from the node neighbors. In case of topological k-means, we also show that casting it into an empirical risk minimization framework using reproducing kernel Hilbert spaces allows us to derive clustering stability guarantees, similarly to the Euclidean k-means, i.e., property that most existing topological clustering methods lack. We illustrate our topological clustering methods in application to assessing climate-induced risks in insurance and COVID-19 biosurveillance.
Bio: Yulia R. Gel is a Professor in the Department of Statistics at Virginia Tech. Her research interests focus on mathematical and statistical foundations of data science, topological and geometric methods in artificial intelligence and machine learning, risk analytics, and graph learning, with applications to assessing resilience of complex systems, digital twins, and early warning mechanisms. She holds a Ph.D in Mathematics, followed by a postdoctoral position in Statistics at the University of Washington. Prior to joining Virginia Tech, she was a tenured faculty member at the University of Waterloo, Canada and University of Texas at Dallas. She also held visiting positions at Johns Hopkins University, University of California, Berkeley, and the Isaac Newton Institute for Mathematical Sciences, Cambridge University, UK. In her recent stint (2021-2025) as Program Director in National Science Foundation (NSF) at the Division of Mathematical Sciences (DMS) and Directorate for Technology, Innovation and Partnerships (TIP), she has served as a cognizant officer for various inter-agency interdisciplinary research programs at the interface of mathematical sciences and artificial intelligence, including the NSF-FDA-NIH Foundations for Digital Twins as Catalyzers of Biomedical Technological Innovation (FDT-BioTech) and the NSF-NIH Smart Health and Biomedical Research in the Era of Artificial Intelligence and Advanced Data Science (SCH). She has authored more than 150 publications in top statistical, data mining and machine learning venues such as NeurIPS, ICML, ICLR, AAAI, KDD, IJCAI, and PNAS and served as senior area chair for ICML and NeurIPS. Her research has been continuously supported by ONR, NASA, and NSF. She is a Fellow of the American Statistical Association (ASA), recipient of the NSF2023 Director’s Award, NSF STARS Awards, and has multiple Best Paper Awards from the ASA Section on Statistics for Defense and National Security.
Hosted by: Professor Paul Parker
