Buchet, Mickaël
[Author];
B. Dornelas, Bianca
[Author];
Kerber, Michael
[Author]
;
Mickaël Buchet and Bianca B. Dornelas and Michael Kerber
[Contributor]
Footnote:
Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
Description:
For a finite set of balls of radius r, the k-fold cover is the space covered by at least k balls. Fixing the ball centers and varying the radius, we obtain a nested sequence of spaces that is called the k-fold filtration of the centers. For k = 1, the construction is the union-of-balls filtration that is popular in topological data analysis. For larger k, it yields a cleaner shape reconstruction in the presence of outliers. We contribute a sparsification algorithm to approximate the topology of the k-fold filtration. Our method is a combination and adaptation of several techniques from the well-studied case k = 1, resulting in a sparsification of linear size that can be computed in expected near-linear time with respect to the number of input points.