Filtration Simplification for Persistent Homology via Edge Contraction

Persistent homology is a popular data analysis technique that is used to capture the changing homology of an indexed sequence of simplicial complexes. These changes are summarized in persistence diagrams. A natural problem is to contract edges in complexes in the initial sequence to obtain a sequence of simplified complexes while controlling the perturbation between the original and simplified persistence diagrams. This paper is an extended version of Dey and Slechta (in: Discrete geometry for computer imagery, Springer, New York, 2019), where we developed two contraction operators for the case where the initial sequence is a filtration. In addition to the content in the original version, this paper presents proofs relevant to the filtration case and develops contraction operators for towers and multiparameter filtrations.