Publication Date

Summer 7-28-2026

Abstract

Mapper is a data visualization tool commonly used in topological data analysis to study large, often high-dimensional datasets. Mapper operates through the selection of a lens function, a clustering algorithm, and a cover. The Mapper graph is constructed using the nerve of the cover after the clustering algorithm is performed; it is therefore useful to study nerves to better understand Mapper. In this thesis, we will utilize the properties of nerves to find the minimal point set that produces a given graph. We will then extend this to Mapper to determine what Mapper graphs may be constructed over a given dataset, both in the case of Mapper taken over point clouds, and Mapper taken over graphs. Finally, I will demonstrate my contributions to the ceREEBerus Python package's Mapper functionality.

Degree Name

Mathematics

Level of Degree

Masters

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Sarah Percival

Second Committee Member

James Degnan

Third Committee Member

Maria Cristina Pereyra

Language

English

Keywords

Mapper, TDA, Topology

Document Type

Thesis

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