Interleaving by Parts: Join Decompositions of Interleavings and Join-Assemblage of Geodesics

Woojin Kim, Facundo Mémoli, Anastasios Stefanou

Metrics of interest in topological data analysis (TDA) are often explicitly or implicitly in the form of an interleaving distance $d_{\mathrm{I}}$ between poset maps (i.e. order-pr…