Plumbing the Depths of the Shallow End: Exploring Persistent Homology Using Small Data

<p>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.</p> <p>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.</p>

Name thesis:degree_name

Master of Science

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Math and Computer Science

Year dc:date.available

2024

Author dc:creator

• Flynn, R. Anne

Contributors dc:contributor

• Josh Thompson

• TDA
• topological data analysis
• topology
• data science
• persistence
• persistent homology
• algebraic topology
• R
• Geometry and Topology

Repository record dc:identifier

https://commons.nmu.edu/theses/844

OAI identifier oai:identifier

oai:commons.nmu.edu:theses-1834