On geometric & topological methods for analysis of biophysical time series data

Time series analysis is staple work horse in many fields including climatology, econometrics, stock and derivatives markets, systems engineering, etc. Traditional analysis of time series data is focused on predicting or forecasting future values based on analysis and modeling of past values. In this work we present methods of time series analysis that are based on geometric principles. First cyclicity analysis, a method of analysis of repeating but aperiodic signals is introduced and treated in depth. This method is then used to examine two sets of brain imaging data, specifically functional magnetic resonance imaging data under both resting state and task paradigms. We present results that show our ability to fingerprint individuals using their resting state scans, detect slow cortical waves in the brain and classify between groups in the dataset. Next we apply principles from geometric diffusion process in the context of manifold learning to show how synergy detection in eletcromyography data is best viewed as a nonlinear clustering problem rather than a factor analysis problem. We also present simple kinematic examples where linear methods fail to show that nonlinearity is inherent in even the simplest systems. Finally, we conclude this document with a review of results presented, some comments of a historical nature and ongoing trends in the fields we that supplied the data and what can be expected in the near future.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Abraham, Ivan T.

Contributors dc:contributor

• Baryshnikov, Yuliy M
• Belabbas, Mohamed-Ali
• Husain, Fatima T
• Zhao, Zhizhen

• time-series
• geometric diffusions
• manifold learning
• cyclicity analysis
• fmri
• emg

Statement dc:rights

• Copyright 2022 Ivan T. Abraham

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/117702

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F117702