Topological Data Analysis and Cosheaves
Justin Curry
TL;DR
This paper provides an overview of persistent homology in topological data analysis and introduces an alternative foundation for level-set persistence using sheaves and cosheaves.
Contribution
It offers an expository account of persistent homology and proposes a new foundation for level-set persistence based on sheaves and cosheaves.
Findings
Persistent homology is useful for topological data analysis.
Sheaves and cosheaves offer an alternative foundation for level-set persistence.
The paper enhances understanding of topological methods in data analysis.
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.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Neuroinflammation and Neurodegeneration Mechanisms · Homotopy and Cohomology in Algebraic Topology