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Zigzag Persistence

被引：157
作者：
Carlsson, Gunnar [1 ]
de Silva, Vin [2 ]
机构：
[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA
[2] Pomona Coll, Dept Math, Claremont, CA 91711 USA
来源：
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS | 2010年 / 10卷 / 04期
关键词：
Applied topology; Persistent topology; Quiver representations;
D O I：
10.1007/s10208-010-9066-0
中图分类号：
TP301 [理论、方法];
学科分类号：
080201 [机械制造及其自动化];
摘要：
We describe a new methodology for studying persistence of topological features across a family of spaces or point-cloud data sets, called zigzag persistence. Building on classical results about quiver representations, zigzag persistence generalises the highly successful theory of persistent homology and addresses several situations which are not covered by that theory. In this paper we develop theoretical and algorithmic foundations with a view towards applications in topological statistics.
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收藏
页码：367 / 405
页数：39
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