Applications of Zigzag Persistence to Topological Data Analysis
Andrew Tausz, Gunnar Carlsson
TL;DR
This paper explores three applications of zigzag persistence in topological data analysis, demonstrating its usefulness in bootstrapping, parameter thresholding, and complex comparison.
Contribution
It introduces novel applications of zigzag persistence, expanding its utility in topological data analysis beyond traditional persistent homology.
Findings
Demonstrated topological bootstrapping using zigzag persistence
Applied zigzag persistence for parameter thresholding
Compared witness complexes effectively with zigzag persistence
Abstract
The theory of zigzag persistence is a substantial extension of persistent homology, and its development has enabled the investigation of several unexplored avenues in the area of topological data analysis. In this paper, we discuss three applications of zigzag persistence: topological bootstrapping, parameter thresholding, and the comparison of witness complexes.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Neuroinflammation and Neurodegeneration Mechanisms · Digital Image Processing Techniques