Document Type
Honors Project - Open Access
Abstract
A central problem in data-driven scientific inquiry is how to interpret structure in noisy, high-dimensional data. Topological data analysis (TDA) provides a solution via the language of persistent homology, which encodes features of interest as holes within a filtration of the data. The recently presented U-Match Decomposition places the standard persistence computation in a flexible form, allowing for straight-forward extensions of the algorithm to variations of persistent homology. We describe U-Match Decomposition in the context of persistent homology, and extend it to an algorithm for persistent relative homology, providing proofs for the correctness and stability of the presented algorithm.
Recommended Citation
Lentz, Christian J., "Persistent Relative Homology for Topological Data Analysis" (2024). Mathematics, Statistics, and Computer Science Honors Projects. 85.
https://digitalcommons.macalester.edu/mathcs_honors/85
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