The reflection distance between zigzag persistence modules

被引：0
|
作者：
Elchesen A. [1 ]
Mémoli F. [2 ]
机构：
[1] Department of Mathematics, The University of Florida, Gainesville
[2] Departments of Mathematics, Computer Science and Engineering, The Ohio State University, Columbus
来源：
Journal of Applied and Computational Topology | 2019年 / 3卷 / 3期
基金：
美国国家科学基金会;
关键词：
Reflection distance; Reflection functors; Zigzag persistence;
D O I：
10.1007/s41468-019-00031-0
中图分类号：
学科分类号：
摘要：
By invoking the reflection functors introduced by Bernstein et al. (Russ Math Surv 28(2):17–32, 1973), in this paper we define a metric on the space of all zigzag modules of a given length, which we call the reflection distance. We show that the reflection distance between two given zigzag modules of the same length is an upper bound for the ℓ1-bottleneck distance between their respective persistence diagrams. © 2019, Springer Nature Switzerland AG.
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页码：185 / 219
页数：34
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