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Dissertation
Embargoed Access, Embargo ends: 01/22/2027
Dissertation
Stable Measures of Time-Varying Data Using Persistent Homology
Doctor of Philosophy (PhD), Washington State University
2026
Abstract
In this work we leverage the stability of persistent homology to construct stable measures of time-varying data, particularly univariate time-series similarity and exponential divergence between multivariate time series from dynamical systems. Persistent homology is the study of holes in different dimensions which appear in point cloud data as these points are 'thickened' over time. The lifetimes of each of these holes can be summarized as intervals in a stable topological summary called a persistence barcode. Theoretical stability of such barcodes has been proven in the literature, particularly guaranteeing that small perturbations in point cloud data guarantee small changes in the bars of the persistence barcode upon the 'thickening' of the point cloud. We construct theoretically stable measures of univariate time series similarity using the lifetimes of 1-dimensional holes and exponential divergence for multivariate time series using the lifetimes of 0-dimensional holes.
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Details
- Title
- Stable Measures of Time-Varying Data Using Persistent Homology
- Creators
- Elizabeth Thompson
- Contributors
- Bala Krishnamoorthy (Advisor)David Makin (Committee Member)Xueying Wang (Committee Member)Yuan Wang (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Department of Mathematics and Statistics
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Number of pages
- 118
- Identifiers
- 99901394204201842
- Language
- English
- Resource Type
- Dissertation