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arXiv · 1312.3829

Metrics for generalized persistence modules

Peter Bubenik·Vin de Silva·Jonathan Scott
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Abstract

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 sublevelset persistent homology. We introduce a distinction between `soft' and `hard' stability theorems. While our treatment is direct and elementary, the approach can be explained abstractly in terms of monoidal functors.

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Peter Bubenik, Vin de Silva, Jonathan Scott. 2015-02-05. Metrics for generalized persistence modules. https://doi.org/10.1007/s10208-014-9229-5

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