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… 
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