Topological Data Analysis and Cosheaves

Abstract

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.

arXiv commentversion 2 has 30 pages, 18 figures; 25 pages, 17 figures, submitted to the Japan Journal of Industrial and Applied Mathematics

References in corpus (2)

• Metrics for generalized persistence modules
• Persistent homology analysis of brain artery trees

Cited by in corpus (1)

• Variable sets over an algebra of lifetimes: a contribution of lattice theory to the study of computational topology