Advanced Neuroscience Data Analysis using Functional Data Analysis Methods
Type of DegreePhD Dissertation
Mathematics and Statistics
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There has been a growing interest in neuroscience data, encompassing fields like engineering, bioengineering, and neurophysiology. Researchers increasingly utilize neural signals, including electroencephalography (EEG) signals and functional Magnetic Resonance Imaging (fMRI), for various applications like control systems, communication, and medical diagnostics. While numerous models have been developed to explain the relationship between these signals and motor or mental activities, it is still unclear how much information can be decoded from them. Thus, the exploration of neural signal data is still in progress. Neural signals are inherently characterized as time series data. Most analysis prioritize frequency domain information over time domain. Even when exploring the time domain, these signals are often treated as discrete time points for multivariate analysis, neglecting essential functional dynamics such as continuity and smoothness. Functional data analysis (FDA) facilitates the extraction of information from both the time and frequency domains while considering the temporal dependencies inherent in neural signals. Hence, employing FDA to analyze neural signals is a promising approach. In this dissertation, we focus on the development of neural signal data analysis with FDA. Specifically, we explore the application of FDA across every phase of signal processing for EEG data, which is a representative data type in neural signal analysis. Firstly, we develop a comprehensive three-stage classification algorithm rooted in functional data analysis, offering the distinct advantage of interpretability. Next, we introduce a robust determination method to automatically identifying the optimal number of ICs. Notably, this method is designed to seamlessly integrate with a variety of ICA techniques, thus ensuring the consistent and reliable generation of results. Furthermore, we propose a robust functional ICA (fICA) method, that significantly enhances the accuracy and reliability of subsequent analysis pertaining to recovered ICs. In summary, this dissertation encompasses the introduction of a functional classification algorithm, dimension reduction techniques, and robust fICA methods tailored for the neuroscience data analysis.