Higher interpolation and extension for persistence modules

Author: 

Bubenik, P
de Silva, V
Nanada, V

Publication Date: 

7 June 2017

Journal: 

SIAM Journal on Applied Algebra and Geometry

Last Updated: 

2020-09-27T20:15:38.757+01:00

Issue: 

1

Volume: 

1

DOI: 

10.1137/16M1100472

page: 

272-284

abstract: 

The use of topological persistence in contemporary data analysis has provided considerable impetus for investigations into the geometric and functional-analytic structure of the space of persistence modules. In this paper, we isolate a coherence criterion which guarantees the extensibility of nonexpansive maps into this space across embeddings of the domain to larger ambient metric spaces. Our coherence criterion is category-theoretic, allowing Kan extensions to provide the desired extensions. Our main construction gives an isometric embedding of a metric space into the metric space of persistence modules with values in the spacetime of this metric space. As a consequence of such “higher interpolation,” it becomes possible to compare Vietoris–Rips and Cech complexes built ˇ within the space of persistence modules.

Symplectic id: 

700961

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article