Geodesic
Erosion distance for generalized persistence modules
Homology, homotopy, and applications, Tome 22 (2020) no. 1, pp. 233-254.

Voir la notice de l'article provenant de la source International Press of Boston

The persistence diagram of Cohen–Steiner, Edelsbrunner, and Harer was recently generalized by Patel to the case of constructible persistence modules with values in a symmetric monoidal category with images. Patel also introduced a distance for persistence diagrams, the erosion distance. Motivated by this work, we extend the erosion distance to a distance of rank invariants of generalized persistence modules by using the generalization of the interleaving distance of Bubenik, de Silva, and Scott as a guideline. This extension of the erosion distance also gives, as a special case, a distance for multidimensional persistent homology groups with torsion introduced by Frosini. We show that the erosion distance is stable with respect to the interleaving distance, and that it gives a lower bound for the natural pseudo-distance in the case of sublevel set persistent homology of continuous functions.
DOI : 10.4310/HHA.2020.v22.n1.a14
Classification : 55U99
Keywords: persistence module, persistent homology 
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     language = {en},
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Ville Puuska. Erosion distance for generalized persistence modules. Homology, homotopy, and applications, Tome 22 (2020) no. 1, pp. 233-254. doi : 10.4310/HHA.2020.v22.n1.a14. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2020.v22.n1.a14/

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