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Signed visibility graphs of time series and their application to brain networks

University of British Columbia

Time series have been extensively studied and used in many fields to describe time-dependent observations such as rainfall levels, stock market, and even our brain signals. In this thesis, we extend previous network based approach to the analysis of time series, by introducing signs to the edges that describe the visibility graph. The resulting signed visibility graph contains more information about the properties of time series than standard visibility graphs. We designed a dynamic programming algorithm that creates optimal, non-overlapping and time-respecting clusters/partitions in signed visibility graphs. Our method differs from existing approaches of standard network partitioning or community detection methods that do not take into consideration the time-order in a visibility graph. Our signed visibility graph approach can also be used to define mutual information based measure for comparing the correlation between two time series. By taking into consideration the information of a node due to both positive and negative edges in the graphs, our measure is more accurate than the existing correlation measure. As an application, we applied our framework of signed visibility graph to brain networks and studied the clustering of brain time series for various sets of patients suffering from ADHD, Schizophrenia, Bipolar Disorder, and Epilepsy (with & without seizures), compared with normal human brain signals. For fMRI data, these comparisons are done on various levels: starting from individual Regions of Interest (ROIs) of the brain, to groups of ROIs, and lastly to Resting State Networks (RSNs; brain sub-networks/regions). These comparisons gave some interesting results showing differences in various metrics of brain network. For instance, differences were found in the average number of clusters, cluster size, average mutual information measure, average jaccard index values of clusters, with extreme values in certain sub-networks and in certain disease-sets, etc.

Text

2019-04-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69978

Computer Science

University of British Columbia

UBCO

http://creativecommons.org/licenses/by-nc-nd/4.0/