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

Abraham, Ivan T.

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

Description

Title

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

Author(s)

Abraham, Ivan T.

Issue Date

2022-08-10

Director of Research (if dissertation) or Advisor (if thesis)

• Baryshnikov, Yuliy M
• Belabbas, Mohamed-Ali

Doctoral Committee Chair(s)

• Baryshnikov, Yuliy M
• Belabbas, Mohamed-Ali

Committee Member(s)

• Husain, Fatima T
• Zhao, Zhizhen

Department of Study

Electrical & Computer Eng

Discipline

Electrical & Computer Engr

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

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

Abstract

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.

Graduation Semester

2022-12

Type of Resource

Thesis

Copyright and License Information

Copyright 2022 Ivan T. Abraham

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