Coreduction homology algorithm for inclusions and persistent homology

Authors:
Marian Mrozek;Thomas Wanner
Affiliations:
Institute of Computer Science, Jagiellonian University, ul. St. Łojasiewicza 6, 30-348 Kraków, Poland and Division of Computational Mathematics, WSB-NLU, ul. Zielona 27, 33-300 Nowy Sacz ...;Department of Mathematical Sciences, George Mason University, 4400 University Drive, MS 3F2, Fairfax, VA 22030, USA
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

We present an algorithm for computing the homology of inclusion maps which is based on the idea of coreductions and leads to significant speed improvements over current algorithms. It is shown that this algorithm can be extended to compute both persistent homology and an extension of the persistence concept to two-sided filtrations. In addition to describing the theoretical background, we present results of numerical experiments, as well as several applications to concrete problems in materials science.