2 papers
math.CO2026
Maximum Persistent Betti Numbers of Äech Complexes
Herbert Edelsbrunner, Matthew Kahle, Shu Kanazawa
This note proves that only a linear number of holes in a Äech complex of points in can persist over an interval of constant length. Specifically, for any fixed…
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…