An algebraic Wasserstein distance for generalized persistence modules
Year: 2018
Type: preprint
Abstract: The Wasserstein distances are a family of $L^p$ distances, with $1 \leq p \leq \infty$, for persistence diagrams. We define Wasserstein distances for persistence modules, the algebraic counterpart to persistence diagrams, and prove the following isometry theorem. The $p$-Wasserstein distance of a persistence module and its persistence diagram agree. Since our algebraic Wasserstein distances do not require computing a persistence diagram, they apply to persistence modules that are not interval decomposable and also to generalized persistence modules, such as multi-parameter persistence modules. We also prove structure theorems for maps from an interval module and maps to an interval module and show that for monomorphisms and epimorphisms of persistence modules there is an induced algebraic matching.
Source: arXiv (Cornell University)
Authors: Peter Bubenik, Jonathan Scott, Donald Stanley
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3038254990