Michael Lesnick (5/3/21): l_p-Metrics on Multiparameter Persistence Modules скачать в хорошем качестве

Michael Lesnick (5/3/21): l_p-Metrics on Multiparameter Persistence Modules

Motivated both by theoretical and practical considerations in topological data analysis, we generalize the p-Wasserstein distance on barcodes to multi-parameter persistence modules. For each p ? [1,?], we in fact introduce two such generalizations d_I^p and d_M^p, such that d_I^? equals the interleaving distance and d_M^? equals the matching distance. These distances turn out to have several good properties. We use them to study the continuity of (2-parameter) multicover persistent homology, revealing nuances to the stability theory for multicover persistence which are not seen by the interleaving distance. Joint work with Havard Bjerkevik. This talk was part of the workshop on "Topological Data Analysis - Theory and Applications" supported by the Tutte Institute and Western University: https://math.sci.uwo.ca/~jardine/TDA-...