Abstract
In Topological Data Analysis, filtered chain complexes enter the persistence pipeline between the initial filtering of data and the final persistence invariants extraction. It is known that they admit a tame class of indecomposables, called interval spheres. In this paper, we provide an algorithm to decompose filtered chain complexes into such interval spheres. This algorithm provides geometric insights into various aspects of the standard persistence algorithm and two of its runtime optimizations. Moreover, since it works for any filtered chain complexes, our algorithm can be applied in more general cases. As an application, we show how to decompose filtered kernels with it.
Original language | English |
---|---|
Article number | 101938 |
Journal | Computational Geometry: Theory and Applications |
Volume | 109 |
DOIs | |
Publication status | Published - 2023 |
Keywords
- Clear and compress
- Filtered chain complexes
- Filtered kernels
- Interval spheres
- Persistence algorithms
- Topological data analysis
ASJC Scopus subject areas
- Computational Mathematics
- Control and Optimization
- Geometry and Topology
- Computer Science Applications
- Computational Theory and Mathematics