Topological data analysis and cosheaves

被引：0
作者：
Justin Michael Curry
机构：
[1] Duke University,Department of Mathematics
来源：
Japan Journal of Industrial and Applied Mathematics | 2015年 / 32卷
关键词：
Topological data analysis; Persistent homology; Sheaves and cosheaves; Barcodes; o-minimal topology; 55U99; 46M20; 32S60; 16G20; 62-07; 03C64;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper contains an expository account of persistent homology and its usefulness for topological data analysis. An alternative foundation for level set persistence is presented using sheaves and cosheaves.
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页码：333 / 371
页数：38
相关论文
共 21 条
[1]  
Bott R(1988)Morse theory indomitable Publications Mathématiques de l’IHÉS 68 99-114
[2]  
Carlsson G(2008)On the local behavior of spaces of natural images Int. J. Comput. Vis. 76 1-12
[3]  
Ishkhanov T(2009)The theory of multidimensional persistence Discret. Comput. Geom. 42 71-93
[4]  
De Silva V(2007)Stability of persistence diagrams Discret. Comput. Geom. 37 103-120
[5]  
Zomorodian A(2005)Quiver representations Not. AMS 52 200-206
[6]  
Carlsson G(1998)Verdier and strict thom stratifications in o-minimal structures Ill. J. Math. 42 347-356
[7]  
Zomorodian A(2012)Notes on topological stability Bull. (New Ser.) Am. Math. Soc. 49 475-506
[8]  
Cohen-Steiner D(2011)Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival Proc. Natl. Acad. Sci. 108 7265-7270
[9]  
Edelsbrunner H(2007)Coverage in sensor networks via persistent homology Algebr. Geom. Topol. 7 24-274
[10]  
Harer J(2005)Computing persistent homology Discret. Comput. Geom. 33 249-undefined
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