an:07244727
Zbl 1447.55006
Oudot, Steve; Solomon, Elchanan
Inverse problems in topological persistence
EN
Baas, Nils (ed.) et al., Topological data analysis. Proceedings of the Abel symposium 2018, Geiranger, Norway, June 4--8, 2018. Cham: Springer. Abel Symp. 15, 405-433 (2020).
2020
a
55N31 55-02 68T09 62R07
machine learning; extraction; persistent homology; topological data analysis; survey; barcode; stability; inverses; point cloud; transform
Summary: In this survey, we review the literature on inverse problems in topological persistence theory. The first half of the survey is concerned with the question of surjectivity, i.e. the existence of right inverses, and the second half focuses on injectivity, i.e. left inverses. Throughout, we highlight the tools and theorems that underlie these advances, and direct the reader's attention to open problems, both theoretical and applied.
For the entire collection see [Zbl 1448.62008].