This talk is in the SIAM PNW (Pacific Northwest) Section Virtual Seminar series.
ABSTRA CT: Hypergraphs capture multi-way relationships in data, and they have consequently seen a number of applications in higher-order network analysis, computer vision, geometry processing, and machine learning. First, we study hypergraph visualization via its topological simplification. We put vertex simplification and hyperedge simplification in a unifying framework using tools from topological data analysis. In simplifying a hypergraph, we allow vertices to be combined if they belong to almost the same set of hyperedges, and hyperedges to be merged if they share almost the same set of vertices. Second, we develop the theoretical foundations in studying the space of hypergraphs using ingredients from optimal transport. By enriching a hypergraph with probability measures on its nodes and hyperedges, as well as relational information capturing local and global structure, we obtain a general and robust framework for studying the collection of all hypergraphs. We first introduce a hypergraph distance based on the co-optimal transport framework of Redko et al. and study its theoretical properties. We then formalize common methods for transforming a hypergraph into a graph as maps from the space of hypergraphs to the space of graphs and study their functorial properties and Lipschitz bounds. Finally, we demonstrate the versatility of our Hypergraph Co-Optimal Transport (HyperCOT) framework through various examples. This talk is based on joint works with Youjia Zhou, Archit Rathore, Emilie Purvine, Samir Chowdhury, Tom Needham, and Ethan Semrad. See https://arxiv.org/abs/2104.11214 and https://arxiv.org/abs/2112.03904.
BIO: Bei Wang is an assistant professor in the School of Computing, a faculty member in the Scientific Computing and Imaging (SCI) Institute, and an adjunct assistant professor in the Department of Mathematics, University of Utah. She obtained her Ph.D. from Duke University. She is interested in the analysis and visualization of large and complex data. Her research interests include topological data analysis, data visualization, computational topology, machine learning, and data mining. Some of her current research activities draw inspirations from topology, geometry, and machine learning, in studying vector fields, tensor fields, high-dimensional point clouds, networks, and multivariate ensembles. She is a recipient of the DOE Early Career Award in 2020.