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Preprints, Working Papers, ... Year : 2022

Swap, Shift and Trim to Edge Collapse a Filtration

Marc Glisse

Abstract

Boissonnat and Pritam introduced an algorithm to reduce a filtration of flag (or clique) complexes, which can in particular speed up the computation of its persistent homology. They used so-called edge collapse to reduce the input flag filtration and their reduction method required only the 1-skeleton of the filtration. In this paper we revisit the usage of edge collapse for efficient computation of persistence homology. We first give a simple and intuitive explanation of the principles underlying that algorithm. This in turn allows us to propose various extensions including a zigzag filtration simplification algorithm. We finally show some experiments to better understand how it behaves.

Dates and versions

hal-03791455 , version 1 (29-09-2022)

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Marc Glisse, Siddharth Pritam. Swap, Shift and Trim to Edge Collapse a Filtration. 2022. ⟨hal-03791455⟩
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