%0 Journal Article
%T Metrics for generalized persistence modules
%A Peter Bubenik
%A Vin de Silva
%A Jonathan Scott
%J Mathematics
%D 2013
%I arXiv
%R 10.1007/s10208-014-9229-5
%X 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.
%U http://arxiv.org/abs/1312.3829v3