Parameter clustering in Bayesian functional PCA of neuroscientific data
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Date
22/07/2020Author
Margaritella, Nicoló
Metadata
Abstract
This thesis provides novel methodologies for functional Principal Component Analysis
of dependent time series (curves) with particular emphasis on those arising from neuroscientific experiments. In this context, the extraordinary advances in neuroscientific
technology for brain recordings over the last decades have led to increasingly complex
spatio-temporal datasets. We propose new models that merge ideas from Functional
Data Analysis and Bayesian nonparametrics to obtain a flexible exploration of spatiotemporal data.
In the first part of the thesis, we developed a Dirichlet process Gaussian
mixture model to cluster functional Principal Component scores within the standard
Bayesian functional Principal Component Analysis framework. This approach allows
us to capture the structure of spatial dependence among smoothed curves and its interaction with the time domain. Moreover, by moving the mixture from data to functional
Principal Component scores, we obtain a more general clustering procedure, allowing
a substantially finer curve classification and higher level of intricate insight and understanding of the data. We present results from a Monte Carlo simulation study
showing improvements in curve and correlation reconstruction compared with different
Bayesian and frequentist functional Principal Component Analysis models, Further, we
apply our method to a resting-state fMRI data analysis providing a rich exploration of
the spatio-temporal patterns in brain time series. In the second part of the thesis, we
extend our model to the challenging case of multilevel functional data where multiple
curves are nested within subjects, and subjects are divided in groups. We develop a
method based on a parsimonious trade-off between group behaviours and individual deviations, returning a comprehensive exploration of intricate multilevel functional data.
We obtained excellent classification and improved curve reconstruction with high-noise
level due to the eigen-dimension-specific borrowing of strength among subjects’ functional scores in the same group. Finally, we discuss future extensions in the direction
of a general and flexible modelling framework for complex spatio-temporal data.