Year: 2017
Type: dissertation
Abstract: Topological data analysis (TDA) has been used to discover qualitative, deformation invariant features of point-cloud data. Generally, TDA is sensitive to the choice of various parameters, with the "true" underlying topology of the data only recovered by a certain range of settings. A method for analyzing time series, involving a time-delay embedding (lift) of that signal to a higher dimension, creates additional considerations: a parameter td which determines the length of the lag in this lift, and the embedding dimension k. It is argued that rather than attempting to determine optimal values for td or k, useful information can be obtained by considering embeddings across a range of td choices, as dimension increases. This work has two primary outcomes: the first is distinguishing periodic and chaotic behaviour. The second is to apply time-delay embeddings to ECG signals. The results indicate a promising direction for the study of ECG signals, and to provide further insight into more general time series, such as those occuring in numerous biomedical and geospatial applications.
Source: TSpace (University of Toronto)
Author: Benjamin A. Fraser
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3144895798