Topological spaces of persistence modules and their properties

被引：0

作者：

Bubenik P. ^{[1
]}

Vergili T. ^{[2
]}

机构：

[1] Department of Mathematics, University of Florida, Gainesville

[2] Department of Mathematics, Ege University, Izmir

来源：

Journal of Applied and Computational Topology | 2018年 / 2卷 / 3-4期

基金：

美国国家科学基金会;

关键词：

Interleaving distance; Persistence modules; Persistent homology;

D O I：

10.1007/s41468-018-0022-4

中图分类号：

学科分类号：

摘要：

Persistence modules are a central algebraic object arising in topological data analysis. The notion of interleaving provides a natural way to measure distances between persistence modules. We consider various classes of persistence modules, including many of those that have been previously studied, and describe the relationships between them. In the cases where these classes are sets, interleaving distance induces a topology. We undertake a systematic study the resulting topological spaces and their basic topological properties. © 2018, Springer Nature Switzerland AG.

引用

页码：233 / 269

页数：36

共 38 条

[1]

Bauer U., Lesnick M., Induced matchings and the algebraic stability of persistence barcodes, J. Comput. Geom., 6, 2, pp. 162-191, (2015)

[2]

Lesnick, M.: Persistence Diagrams as Diagrams: A Categorification of the Stability Theorem (, (2016)

[3]

Bjerkevik H.B., Botnan M.B., Computational complexity of the interleaving distance. In: 34th International Symposium on, Computational Geometry, 12, (2017)

[4]

Lesnick, M.: Universality of the Homotopy Interleaving Distance (2017).

[5]

Blumberg A.J., Gal I., Mandell M.A., Pancia M., Robust statistics, hypothesis testing, and confidence intervals for persistent homology on metric measure spaces, Found. Comput. Math., 14, 4, pp. 745-789, (2014)

[6]

Botnan M., Lesnick M., Algebraic stability of zigzag persistence modules, Algebra Geom. Topol., 18, 6, pp. 3133-3204, (2018)

[7]

Bubenik P., Statistical topological data analysis using persistence landscapes, J. Mach. Learn. Res., 16, pp. 77-102, (2015)

[8]

Bubenik P., Dlotko P., A persistence landscapes toolbox for topological statistics, J. Symb. Comput., 78, pp. 91-114, (2017)

[9]

Bubenik P., Scott J.A., Categorification of persistent homology, Discrete Comput. Geom., 51, 3, pp. 600-627, (2014)

[10]

Bubenik P., de Silva V., Scott J., Metrics for generalized persistence modules, Found. Comput. Math., 15, 6, pp. 1501-1531, (2015)

← 1 2 3 4 →