The Theory of the Interleaving Distance on Multidimensional Persistence Modules

@article{Lesnick2015TheTO,
  title={The Theory of the Interleaving Distance on Multidimensional Persistence Modules},
  author={Michael Lesnick},
  journal={Foundations of Computational Mathematics},
  year={2015},
  volume={15},
  pages={613-650}
}
  • Michael Lesnick
  • Published 2015
  • Mathematics, Computer Science
  • Foundations of Computational Mathematics
  • In 2009, Chazal et al. introduced $$\epsilon $$ϵ-interleavings of persistence modules. $$\epsilon $$ϵ-interleavings induce a pseudometric $$d_\mathrm{I}$$dI on (isomorphism classes of) persistence modules, the interleaving distance. The definitions of $$\epsilon $$ϵ-interleavings and $$d_\mathrm{I}$$dI generalize readily to multidimensional persistence modules. In this paper, we develop the theory of multidimensional interleavings, with a view toward applications to topological data analysis… CONTINUE READING
    130 Citations

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