TL;DR
This paper introduces an efficient algorithm for computing the image of morphisms in persistent homology, leveraging clearing optimization, applicable to various types of persistent homology, and implemented in Ripser for Vietoris-Rips complexes.
Contribution
The paper presents a novel algorithm for computing image persistence in filtered chain complexes, enhancing efficiency and applicability in topological data analysis.
Findings
Algorithm improves computation speed for image persistence.
Applicable to absolute and relative persistent homology.
Implemented successfully in Ripser for Vietoris-Rips complexes.
Abstract
We present an algorithm for computing the barcode of the image of a morphisms in persistent homology induced by an inclusion of filtered finite-dimensional chain complexes. These algorithms make use of the clearing optimization and can be applied to inclusion-induced maps in persistent absolute homology and persistent relative cohomology for filtrations of pairs of simplicial complexes. They form the basis for our implementation for Vietoris-Rips complexes in the framework of the software Ripser.
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