3 papers
math.AT2025
Kan Approximations of the Persistent Homology Transform
Shreya Arya, Justin Curry
The persistent homology transform (PHT) of a subset is a map from the unit sphere to the space of persist…
math.AT2024
Decomposing the Persistent Homology Transform of Star-Shaped Objects
Shreya Arya, Barbara Giunti, Abigail Hickok +3
In this paper, we study the geometric decomposition of the degree- Persistent Homology Transform (PHT) as viewed as a persistence diagram bundle. We focus on star-shaped objects…
cs.CG2021
Dimensionality Reduction for -Distance Applied to Persistent Homology
Shreya Arya, Jean-Daniel Boissonnat, Kunal Dutta +1
Given a set P of n points and a constant k, we are interested in computing the persistent homology of the Cech filtration of P for the k-distance, and investigate the effectiveness…