Metrics for Generalized Persistence Modules

  title={Metrics for Generalized Persistence Modules},
  author={Peter Bubenik and V. D. Silva and J. Scott},
  journal={Foundations of Computational Mathematics},
  • Peter Bubenik, V. D. Silva, J. Scott
  • Published 2015
  • Mathematics, Computer Science
  • Foundations of Computational Mathematics
  • 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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