Parameter clustering in Bayesian functional PCA of fMRI data

The extraordinary advancements in neuroscientific technology for brain recordings over the last decades have led to increasingly complex spatio-temporal datasets. To reduce oversimplifications, new models have been developed to be able to identify meaningful patterns and new insights within a highly demanding data environment. To this extent, we propose a new model that merges ideas from Functional Data Analysis and Bayesian nonparametrics to obtain a flexible and computationally feasible exploration of spatio-temporal neuroscientific data. In particular, we make use of a Dirichlet process Gaussian mixture model to cluster functional Principal Component (fPC) scores within the standard Bayesian functional Principal Component Analysis (fPCA) framework; this allows us to capture the structure of spatial dependence among smoothed time series (curves) and its interaction with the time domain. Moreover, by moving the mixture from data to fPC scores, we obtain a more general clustering procedure, thus allowing much 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 curves and correlation reconstruction compared with the standard Bayesian fPCA model before applying our method to a resting-state fMRI data analysis providing a rich exploration of the spatio-temporal dependence in brain time series that offer further insights into the underlying neurophysiological processes.