Abstract
Topological data analysis is an expanding field that attempts to obtain qualitative information from a data set using topological ideas. There are two common methods of topological data analysis: persistent homology and the Mapper algorithm; the focus of this thesis is on the latter. In this thesis, we will be discussing the key ideas behind the Mapper algorithm, following the flow from Morse Theory to Reeb graphs to the topological version of the algorithm and finally to the statistical version. Lastly, we will present an application of Mapper to the USAIR97 data set using the RTDAmapper package.
Notes
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Graduation Date
2023
Semester
Summer
Advisor
Lee, Junho
Degree
Master of Science (M.S.)
College
College of Sciences
Department
Mathematics
Degree Program
Mathematical Science
Identifier
CFE0009732; DP0027840
URL
https://purls.library.ucf.edu/go/DP0027840
Language
English
Release Date
August 2023
Length of Campus-only Access
None
Access Status
Masters Thesis (Open Access)
STARS Citation
Girard, Jessica, "Topological Data Analysis Using the Mapper Algorithm" (2023). Electronic Theses and Dissertations, 2020-. 1822.
https://stars.library.ucf.edu/etd2020/1822