3 papers
cs.CG2024
Wasserstein convergence of Äech persistence diagrams for samplings of submanifolds
Charles Arnal, David Cohen-Steiner, Vincent Divol
Äech Persistence diagrams (PDs) are topological descriptors routinely used to capture the geometry of complex datasets. They are commonly compared using the Wasserstein distances…
cs.CG2024
Understanding the Topology and the Geometry of the Space of Persistence Diagrams via Optimal Partial Transport
Vincent Divol, Théo Lacombe
Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence dia…
math.DG2024
Critical points of the distance function to a generic submanifold
Charles Arnal, David Cohen-Steiner, Vincent Divol
In general, the critical points of the distance function to a compact submanifold can be poorly behaved. In this article, we show…