Barcodes: The persistent topology of data

被引：676
作者：
Ghrist, Robert [1 ]
机构：
[1] Univ Illinois, Dept Math, Coordinated Sci Lab, Urbana, IL 61801 USA
来源：
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 45卷 / 01期
关键词：
D O I：
10.1090/s0273-0979-07-01191-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This article surveys recent work of Carlsson and collaborators on applications of computational algebraic topology to problems of feature detection and shape recognition in high-dimensional data. The primary mathematical tool considered is a homology theory for point-cloud data sets-persistent homology-and a novel representation of this algebraic characterization barcodes. We sketch an application of these techniques to the classification of natural images.
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页码：61 / 75
页数：15
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