8 papers
A Hilbert space embedding of persistence diagrams and barcodes
Peter Bubenik
For p in , we show that the persistence landscape gives 1-Lipschitz embeddings of metric spaces of countable persistence diagrams and barcodes with p-Wasserstein distan…
Relative Optimal Transport
Peter Bubenik, Alex Elchesen
We develop a theory of optimal transport relative to a distinguished subset, which acts as a reservoir of mass, allowing us to compare measures of different total variation. This r…
Continuous persistence landscapes
Wanchen Zhao, Peter Bubenik
As the size of data increase, persistence diagrams often exhibit structured asymptotic behavior, converging weakly to a Radon measure. However, conventional vector summaries such a…
A rank-based distance for interval modules and Wasserstein stability of persistence landscapes
Wanchen Zhao, Peter Bubenik
Barcodes and persistence diagrams have a canonical one-parameter family of distances called Wasserstein distances. These distances depend on a choice of distance for interval modul…
A Schauder Basis for Multiparameter Persistence
Peter Bubenik, Zachariah Ross
Certain classes of multiparameter persistence modules may be encoded as signed barcodes, represented as points in a polyhedral subset of Euclidean space, we refer to as signed pers…
Relative cell complexes in closure spaces
Peter Bubenik
We give necessary and sufficient conditions for certain pushouts of topological spaces in the category of Cech's closure spaces to agree with their pushout in the category of topol…