2 papers
math.CO2024
Maximum Persistent Betti Numbers of Čech Complexes
Herbert Edelsbrunner, Matthew Kahle, Shu Kanazawa
This note proves that only a linear number of holes in a Čech complex of points in can persist over an interval of constant length. Specifically, for any fixed d…
math.ST2024
Curse of Dimensionality on Persistence Diagrams
Yasuaki Hiraoka, Yusuke Imoto, Shu Kanazawa +1
The stability of persistent homology has led to wide applications of the persistence diagram as a trusted topological descriptor in the presence of noise. However, with the increas…