Abstract:

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. In this talk, we develop the theoretical foundations for 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 will discuss the potential applications of using such a framework in studying datasets that arise from biology and materials science. This is based on joint work with Samir Chowdhury, Tom Needham, Ethan Semrad, and Youjia Zhou.