Studying the Space of Persistence Diagrams Using Optimal Partial Transport II

Explore the intersection of optimal transport theory and topological data analysis in this 30-minute conference talk by Vincent Divol and Théo Lacombe. Delve into the second part of their presentation on studying persistence diagrams using optimal partial transport. Discover how viewing persistence diagrams as measures in a space allows for the introduction of a generalized form: Radon measures supported on the upper half plane. Examine the applications of this formalism, including characterizing convergence in the space of persistence diagrams and its implications for continuous linear representations. Gain insights into new results regarding persistence diagrams in random settings, exploring concepts like expected persistence diagrams and associated convergence rates and stability results. Based on the work "Understanding the topology and the geometry of the persistence diagram space via optimal partial transport," this talk bridges theoretical foundations with practical applications in topological data analysis.