Contributions to Persistence Theory
Du Dong
Annals of the West University of Timisoara: Mathematics and Computer Science · 2014
doi:10.2478/awutm-2014-0012 (opens in a new tab)
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Abstract
Persistence theory discussed in this paper is an application of algebraic topology (Morse Theory [29]) to Data Analysis, precisely to qualitative understanding of point cloud data, or PCD for short. PCD can be geometrized as a filtration of simplicial complexes (Vietoris-Rips complex [25] [36]) and the homology changes of these complexes provide qualitative information about the data. Bar codes describe the changes in homology with coefficients in a fixed field. When the coefficient field is ℤ
Abstract licence: CC BY-NC-ND
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