Alpha-beta witness complexes
Publication
, Journal Article
Attali, D; Edelsbrunner, H; Harer, J; Mileyko, Y
Published in: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
January 1, 2007
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 ℝd 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. © Springer-Verlag Berlin Heidelberg 2007.
Duke Scholars
Published In
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
DOI
EISSN
1611-3349
ISSN
0302-9743
Publication Date
January 1, 2007
Volume
4619 LNCS
Start / End Page
386 / 397
Related Subject Headings
- Artificial Intelligence & Image Processing
- 46 Information and computing sciences
Citation
APA
Chicago
ICMJE
MLA
NLM
Attali, D., Edelsbrunner, H., Harer, J., & Mileyko, Y. (2007). Alpha-beta witness complexes. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 4619 LNCS, 386–397. https://doi.org/10.1007/978-3-540-73951-7_34
Attali, D., H. Edelsbrunner, J. Harer, and Y. Mileyko. “Alpha-beta witness complexes.” Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 4619 LNCS (January 1, 2007): 386–97. https://doi.org/10.1007/978-3-540-73951-7_34.
Attali D, Edelsbrunner H, Harer J, Mileyko Y. Alpha-beta witness complexes. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 2007 Jan 1;4619 LNCS:386–97.
Attali, D., et al. “Alpha-beta witness complexes.” Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4619 LNCS, Jan. 2007, pp. 386–97. Scopus, doi:10.1007/978-3-540-73951-7_34.
Attali D, Edelsbrunner H, Harer J, Mileyko Y. Alpha-beta witness complexes. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). 2007 Jan 1;4619 LNCS:386–397.
Published In
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
DOI
EISSN
1611-3349
ISSN
0302-9743
Publication Date
January 1, 2007
Volume
4619 LNCS
Start / End Page
386 / 397
Related Subject Headings
- Artificial Intelligence & Image Processing
- 46 Information and computing sciences