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On V-filtration, Hodge filtration and Fourier transform
- Award ID(s):
- 1840234
- PAR ID:
- 10531656
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Selecta Mathematica
- Volume:
- 29
- Issue:
- 4
- ISSN:
- 1022-1824
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Buchin, Kevin and (Ed.)We show how a filtration of Delaunay complexes can be used to approximate the persistence diagram of the distance to a point set in ℝ^d. Whereas the full Delaunay complex can be used to compute this persistence diagram exactly, it may have size O(n^⌈d/2⌉). In contrast, our construction uses only O(n) simplices. The central idea is to connect Delaunay complexes on progressively denser subsamples by considering the flips in an incremental construction as simplices in d+1 dimensions. This approach leads to a very simple and straightforward proof of correctness in geometric terms, because the final filtration is dual to a (d+1)-dimensional Voronoi construction similar to the standard Delaunay filtration. We also, show how this complex can be efficiently constructed.more » « less
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s00029-023-00850-1
