Computing Persistence Diagram Bundles

10/12/2022
by   Abigail Hickok, et al.
0

Persistence diagram (PD) bundles, a generalization of vineyards, were recently introduced as a way of studying the persistent homology of a set of filtrations parameterized by a topological space 𝒯. In this paper, I present an algorithm for computing piecewise-linear PD bundles, a wide class that includes many of the PD bundles that one may encounter in practice. I give full implementation details for the case in which (𝒯) ≤ 2, and I outline the generalization to higher dimensions.

READ FULL TEXT

page 8

page 9

page 11

page 14

research
10/11/2022

Persistence Diagram Bundles: A Multidimensional Generalization of Vineyards

A persistence diagram (PD) summarizes the persistent homology of a filtr...
research
01/11/2023

Fast persistent homology computation for functions on ℝ

0-dimensional persistent homology is known, from a computational point o...
research
05/15/2023

Wavelet-Based Density Estimation for Persistent Homology

Persistent homology is a central methodology in topological data analysi...
research
05/31/2021

Persistent Homology Captures the Generalization of Neural Networks Without A Validation Set

The training of neural networks is usually monitored with a validation (...
research
11/10/2020

Topological Regularization via Persistence-Sensitive Optimization

Optimization, a key tool in machine learning and statistics, relies on r...
research
12/03/2020

A Sparse Delaunay Filtration

We show how a filtration of Delaunay complexes can be used to approximat...
research
01/27/2020

An efficient algorithm for 1-dimensional (persistent) path homology

This paper focuses on developing an efficient algorithm for analyzing a ...

Please sign up or login with your details

Forgot password? Click here to reset