Abstract
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.
Cite
CITATION STYLE
Attali, D., Edelsbrunner, H., Harer, J., & Mileyko, Y. (2007). Alpha-beta witness complexes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4619 LNCS, pp. 386–397). Springer Verlag. https://doi.org/10.1007/978-3-540-73951-7_34
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