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Persistent Homology in Analysis of Point-Cloud Data

  • Author / Creator
    Kovacev-Nikolic, Violeta
  • 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.

  • Subjects / Keywords
  • Graduation date
    2012-09
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R3RP90
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Statistics
  • Supervisor / co-supervisor and their department(s)
    • Heo, Giseon (Dentistry)
    • Gannon, Terry (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Bubenik, Peter (Dept. of Mathematics, Cleveland State University)
    • Hooper, Peter (Mathematical and Statistical Sciences)