Abstract
The aim of this paper is to present a method for computing persistent homology that performs well at large filtration values. To this end we introduce the concept of filtered covers. Given a parameter \(\delta \) with \(0 < \delta \le 1\) we introduce the concept of a \(\delta \)-filtered cover and show that its filtered nerve is interleaved with the Čech complex. We introduce a particular \(\delta \)-filtered cover, the divisive cover. The special feature of the divisive cover is that it is constructed top-down. If we disregard fine scale structure and \(X\) is a finite subspace of Euclidean space, then we obtain a filtered simplicial complex whose size makes computing persistent homology feasible.
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This research was supported by the Research Council of Norway through Grant 248840.
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Blaser, N., Brun, M. Divisive Cover. Math.Comput.Sci. 13, 21–29 (2019). https://doi.org/10.1007/s11786-018-0352-6
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DOI: https://doi.org/10.1007/s11786-018-0352-6