Math @ Duke

Publications [#243581] of John Harer
Papers Published
 Attali, D; Edelsbrunner, H; Harer, J; Mileyko, Y, Alphabeta witness complexes,
Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4619 LNCS
(December, 2007),
pp. 386397, ISSN 03029743
(last updated on 2019/04/26)
Abstract: Building on the work of Martinetz, Schulten and de Silva, Carlsson, we introduce a 2parameter 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 2parameter 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. © SpringerVerlag Berlin Heidelberg 2007.


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