Abstract
Topological Data Analysis (TDA) is a collection of techniques for data analysis that leverages topological invariants of spaces formed from data points. These methods excel at extracting useful information from noisy or sparse data, making them attractive to many mathematicians, statisticians, and scientists. In this thesis, we explore TDA on three fronts: algebraic foundations, statistical applications, and metric properties. Throughout, the central object of study is the Persistence Diagram (PD), a summary of the changes in homology that occur as one builds simplicial complexes from the data by increasing a parameter.
Committee Chair
Ben Wormleighton
Committee Members
Ari Stern, Ulugbek Kamilov
Degree
Master of Science (MS)
Author's Department
Electrical & Systems Engineering
Document Type
Thesis
Date of Award
Spring 5-2025
Language
English (en)
DOI
https://doi.org/10.7936/yk3v-zd81
Author's ORCID
https://orcid.org/0009-0007-2630-2567
Recommended Citation
Kler, Eugene, "The Little Diagram That Could: Geometric Properties and Statistical Applications of Persistence Diagrams in Topological Data Analysis" (2025). McKelvey School of Engineering Theses & Dissertations. 1211.
The definitive version is available at https://doi.org/10.7936/yk3v-zd81
Included in
Applied Mathematics Commons, Data Science Commons, Engineering Commons, Statistical Theory Commons