Persistent Homology on Time series

  • Author / Creator
  • Topology is a useful tool of mathematics studying how objects are related to one another by investigating their qualitative structural properties, such as connectivity and shape. In this thesis, we applied the method of topological data analysis (TDA) on sequence data and adopt the theory of persistent homology for time series, based on topological features computed over the persistence diagram. Aiming to analyze sequence data from diverse views, we investigate topological features (in a persistent homology perspective) of both traditional statistical tools (i.e. time series) and machine learning methods (i.e. random forest). Combining the advantages of three different ideas, we finally have a way to solve clustering (unsupervised learning) and predicting problems (supervised learning) for our two datasets respectively. There are two main contributions in this thesis. In Chapter 2, we applied persistent homology on the cross correlation matrices and partial correlation matrices of time series, and obtain topological features from the persistence diagrams and barcodes. With this information, we generated consistent clusters and loops from our data and this solution for unsupervised learning problems of unlabeled datasets constitutes my first contribution in this thesis. The second contribution lies in considering landscape as an important covariate for supervised learning problems. In Chapter 3, we applied persistent homology on polysomnography (PSG) time series and took the integrals of landscapes as covariates generated from time series. A random forest model is built with these covariates to predict Obstructive Apnea-Hypopnea (3\% desaturation) Index of new incoming patient.

  • Subjects / Keywords
  • Graduation date
  • Type of Item
  • Degree
    Master of Science
  • DOI
  • 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
  • Institution
    University of Alberta
  • Degree level
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Statistical Machine Learning
  • Supervisor / co-supervisor and their department(s)
    • Giseon Heo (Dentistry)
  • Examining committee members and their departments
    • Ivor Cribben (Alberta Scholl of Business)
    • Bei Jiang (Mathematical and Statistical Sciences)
    • Ivan Mizera (Mathematical and Statistical Sciences)
    • Giseon Heo (Dentistry)