---
_id: '3981'
abstract:
- lang: eng
text: Building on the work of Martinetz, Schulten and de Silva, Carlsson, we introduce
a 2-parameter family of witness complexes and algorithms for constructing them.
This family can be used to determine the gross topology of point cloud data in
R-d or other metric spaces. The 2-parameter family is sensitive to differences
in sampling density and thus amenable to detecting patterns within the data set.
It also lends itself to theoretical analysis. For example, we can prove that in
the limit, when the witnesses cover the entire domain, witness complexes in the
family that share the first, scale parameter have the same homotopy type.
acknowledgement: Research by the authors is partially supported by DARPA under grant
HR0011-05-1-0007, by CNRS under grant PICS-3416 and by IST Program of the EU under
Contract IST-2002-506766.
alternative_title:
- LNCS
author:
- first_name: Dominique
full_name: Attali, Dominique
last_name: Attali
- first_name: Herbert
full_name: Herbert Edelsbrunner
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: John
full_name: Harer, John
last_name: Harer
- first_name: Yuriy
full_name: Mileyko, Yuriy
last_name: Mileyko
citation:
ama: 'Attali D, Edelsbrunner H, Harer J, Mileyko Y. Alpha-beta witness complexes.
In: Vol 4619. Springer; 2007:386-397. doi:10.1007/978-3-540-73951-7_34'
apa: 'Attali, D., Edelsbrunner, H., Harer, J., & Mileyko, Y. (2007). Alpha-beta
witness complexes (Vol. 4619, pp. 386–397). Presented at the WADS: International
Workshop on Algrithms and Data Structures, Springer. https://doi.org/10.1007/978-3-540-73951-7_34'
chicago: Attali, Dominique, Herbert Edelsbrunner, John Harer, and Yuriy Mileyko.
“Alpha-Beta Witness Complexes,” 4619:386–97. Springer, 2007. https://doi.org/10.1007/978-3-540-73951-7_34.
ieee: 'D. Attali, H. Edelsbrunner, J. Harer, and Y. Mileyko, “Alpha-beta witness
complexes,” presented at the WADS: International Workshop on Algrithms and Data
Structures, 2007, vol. 4619, pp. 386–397.'
ista: 'Attali D, Edelsbrunner H, Harer J, Mileyko Y. 2007. Alpha-beta witness complexes.
WADS: International Workshop on Algrithms and Data Structures, LNCS, vol. 4619,
386–397.'
mla: Attali, Dominique, et al. Alpha-Beta Witness Complexes. Vol. 4619, Springer,
2007, pp. 386–97, doi:10.1007/978-3-540-73951-7_34.
short: D. Attali, H. Edelsbrunner, J. Harer, Y. Mileyko, in:, Springer, 2007, pp.
386–397.
conference:
name: 'WADS: International Workshop on Algrithms and Data Structures'
date_created: 2018-12-11T12:06:15Z
date_published: 2007-08-21T00:00:00Z
date_updated: 2021-01-12T07:53:38Z
day: '21'
doi: 10.1007/978-3-540-73951-7_34
extern: 1
intvolume: ' 4619'
month: '08'
page: 386 - 397
publication_status: published
publisher: Springer
publist_id: '2149'
quality_controlled: 0
status: public
title: Alpha-beta witness complexes
type: conference
volume: 4619
year: '2007'
...