Barcodes: The persistent topology of data
Barcodes: The persistent topology of data
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DOI：
10.1090/s0273-0979-07-01191-3
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发表时间：
2008-01-01
影响因子：
1.3
通讯作者：
Ghrist, Robert
中科院分区：
文献类型：
--
作者：
Ghrist, Robert
本文综述了Carlsson及其合作者在高维数据特征检测和形状识别问题中应用计算代数拓扑的最新工作。考虑的主要数学工具是点云数据集的同源性理论-持久同源性-和这种代数表征条形码的新表示。我们勾勒出这些技术的自然图像的分类应用。
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.