Barcodes: The persistent topology of data

被引：677

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.

引用

页码：61 / 75

页数：15

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