The Theory of the Interleaving Distance on Multidimensional Persistence Modules

Understand

In 2009, Chazal et al.

• introduced $\epsilon$-interleavings of persistence modules.
• $\epsilon$-interleavings induce a pseudometric $d_I$ on (isomorphism classes of) persistence modules, the interleaving distance.
• The definitions of $\epsilon$-interleavings and $d_I$ generalize readily to multidimensional persistence modules.