506 citations · 1.6k across the 45 of their papers we have counts for
46 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…
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 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…
A rank-based distance for interval modules and Wasserstein stability of persistence landscapes
Peter Bubenik, Wanchen Zhao
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…
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…
Exact weights and path metrics for triangulated categories and the derived category of persistence modules
Peter Bubenik, Jose A. Velez-Marulanda
We define exact weights on a triangulated category to be nonnegative functions on objects satisfying a subadditivity condition with respect to exact triangles. Such weights induce…