Metrics for Generalized Persistence Modules
@article{Bubenik2015MetricsFG, title={Metrics for Generalized Persistence Modules}, author={Peter Bubenik and V. D. Silva and J. 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… CONTINUE READING
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