Topological Data Analysis
نویسندگان
چکیده
This paper explores the new and growing field of topological data analysis (TDA). TDA is a data analysis method that provides information about the ’shape’ of data. The paper describes what types of shapes TDA detects and why these shapes having meaning. Additionally, concepts from algebraic topology, the mathematics behind TDA, will be discussed. Specifically, the concepts of persistent homology and barcodes will be developed. Finally, the paper will show how these concepts from algebraic topology can be applied to analyze data. Acknowledgments I would first like to thank my advisor, Scott Taylor. He provided me with guidance and support throughout this year long project. Second, I would like to acknowledge my reader, Jim Scott. His input, especially concerning statistical matters, was very valuable. Additionally, I would like to thank Randy Downer for helping me with Perseus, a software packages for topological data analysis. Finally, I would like to thank Xiaojie (Jackie) Chen and Dan Medici, both of whom provided me with support and helped me with LaTeX, the system that was used to typeset this document.
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