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Persistent Homology in Analysis of Point-Cloud Data Open Access


Other title
Type of item
Degree grantor
University of Alberta
Author or creator
Kovacev-Nikolic, Violeta
Supervisor and department
Gannon, Terry (Mathematical and Statistical Sciences)
Heo, Giseon (Dentistry)
Examining committee member and department
Bubenik, Peter (Dept. of Mathematics, Cleveland State University)
Hooper, Peter (Mathematical and Statistical Sciences)
Department of Mathematical and Statistical Sciences
Date accepted
Graduation date
Master of Science
Degree level
The main goal of this thesis is to explore various applications of persistent homology in statistical analysis of point-cloud data. In the introduction, after a brief historical overview, we provide some of the underlying concepts of persistence. Starting from Chapter 2 the focus is on analysis of point-clouds sampled from a surface of a torus and a sphere; our first exploratory tool is a homology plot. In Chapter 3 we calculate the Wasserstein distances in order to visualize existing relationships among samples of data. Chapter 4 introduces a new approach in topological statistical inference, based on the notion of persistence landscapes. In Chapter 5 the method of persistence landscapes is applied to non-perturbed data; following that, data in Chapter 6 involve a component of noise which allows us to demonstrate the efficiency of the new method. To test hypotheses, we implement suitable permutation tests. Last but not least, in Chapter 7 we work with real data of samples of HIV-1 protease some of which feature drug resistance. We truly hope that with the results presented, we offer convincing evidence that testifies in favor of applications of topology in statistical data analysis.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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