# Metrics for Generalized Persistence Modules

@article{Bubenik2015MetricsFG, title={Metrics for Generalized Persistence Modules}, author={Peter Bubenik and Vin de Silva and Jonathan A. Scott}, journal={Foundations of Computational Mathematics}, year={2015}, volume={15}, pages={1501-1531} }

We consider the question of defining interleaving metrics on generalized persistence modules over arbitrary preordered sets. Our constructions are functorial, which implies a form of stability for these metrics. We describe a large class of examples, inverse-image persistence modules, which occur whenever a topological space is mapped to a metric space. Several standard theories of persistence and their stability can be described in this framework. This includes the classical case of…

## 118 Citations

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We present a generalization of the induced matching theorem of as reported by Bauer and Lesnick (in: Proceedings of the thirtieth annual symposium computational geometry 2014) and use it to prove a…

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- 2014

This work redevelops persistent homology (topological persistence) from a categorical point of view and gives a natural construction of a category of ε-interleavings of $\mathbf {(\mathbb {R},\leq)}$-indexed diagrams in some target category and shows that if the target category is abelian, so is this category of interleavments.

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This work gives a more accurate statement of the original Representation Theorem and provides a complete and self-contained proof and generalizes the statement from the case of linear sequences of R- modules to R-modules indexed over more general monoids.

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