Date of Award

5-2024

Degree Type

Thesis

Degree Name

Master of Science

Department

Math and Computer Science

Program

Mathematics (MS)

First Advisor/Chairperson

Josh Thompson

Abstract

Persistent homology is a prominent tool in topological data analysis. This thesis is designed to be an introduction and guide to a beginner in persistent homology. This comprehensive overview discusses the math used behind it, the code needed to apply it, and its current place in the field. We explain and demonstrate the algebraic topology which fuels persistent homology. Homotopies inspire homology groups, which are able to determine how many holes a shape has. By visualizing data as a shape, persistent homology determines what type of holes are present.

We demonstrate this by using the package TDA in the manipulation software R on controlled datasets. A kernel density estimate diagram presents the results. We showcase applying TDA to an external, uncontrolled dataset. The limits on memory allowed us to process no more than four columns of data at a time. To more thoroughly explore the dataset, we analyzed several four-column subsets, but found no special features aside from a base level of closeness.

Access Type

Open Access

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