Multiparameter Persistent Homology

Date

2023-6-09

Author

Cantürk, Uğur Bektaş

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The amount of the existing data is increasing rapidly and any way to understand the shape of the given data is welcomed. In this thesis, we examine a method of Topological Data Analysis which is called Persistent Homology. After a detailed overview of 1-parameter case, we extend the structures to the multiparameter case arising as a natural necessity. We present the similarities and differences between 1- parameter and multiparameter persistent homology in an expository way. At the last stage, we work on the interleaving, bottleneck, matching distances and their stability properties. We also analyze the relations between these pseudometrics, and consider some examples that help us to calculate them.

Subject Keywords

Persistent homology, Distance, Stability, Multiparameter

URI

https://hdl.handle.net/11511/104358

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Graduate School of Natural and Applied Sciences, Thesis