Notes on an Elementary Proof for the Stability of Persistence Diagrams
Primoz Skraba, Katharine Turner
TL;DR
This paper provides a concise, self-contained proof demonstrating the stability of persistence diagrams, which are crucial tools in topological data analysis for understanding data shape.
Contribution
It offers a new elementary proof of the stability theorem for persistence diagrams, simplifying previous complex arguments.
Findings
Proof confirms stability under perturbations
Simplifies understanding of persistence diagram stability
Applicable to various data analysis contexts
Abstract
These notes are a self-contained short proof of the stability of persistence diagrams.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology · Advanced Neuroimaging Techniques and Applications