Divisive Cover
Nello Blaser, Morten Brun · Mathematics in Computer Science · 2018
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.