Topological and Geometric Methods for Graph Analysis
Link to talk video: https://compsci.capture.duke.edu/Panopto/Pages/Viewer.aspx?id=28895c92-0b4b-475c-8f51-ab8a01771bcb
In recent years, topological and geometric data analysis (TGDA) has emerged as a new and promising field for processing, analyzing and understanding complex data. Indeed, geometry and topology form natural platforms for data analysis, with geometry describing the "shape" and "structure" behind data; and topology characterizing / summarizing both the domain where data are sampled from, as well as functions and maps associated to them.
In this talk, I will show how topological and geometric ideas can be used to analyze graph data, which occurs ubiquitously across science and engineering. Graphs could be geometric in nature, such as road networks in GIS, or relational and abstract. I will particularly focus on the reconstruction of hidden geometric graphs from noisy data, as well as graph matching and classification. I will discuss the motivating applications, algorithm development, and theoretical guarantees for these methods. Through these topics, I aim to illustrate the important role that geometric and topological ideas can play in data analysis.
Yusu Wang is Professor of Computer Science and Engineering Department at the Ohio State University, and co-director for the Foundations Research CoP (Community of Practice) at Translational Data Analytics Institute at OSU. She obtained her PhD degree from Duke University in 2004, where she received the Best PhD Dissertation Award at the Computer Science Department. Before joining OSU in 2005, she was a post-doctoral fellow at Stanford University. Yusu Wang primarily works in the fields of Computational geometry, and Computational and applied topology. She is particularly interested in developing effective and theoretically justified algorithms for data analysis using geometric and topological ideas and methods, as well as in applying them to practical domains. Yusu Wang received DOE Early Career Principal Investigator Award in 2006, and NSF Career Award in 2008. Her work received several best paper awards. She is on the editorial boards for SIAM Journal on Computing (SICOMP) and Journal of Computational Geometry (JoCG).