  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
called parameter clustering functional Principal Component Analysis (PCl-fPCA)
that merges ideas from Functional Data Analysis and Bayesian nonparametrics to
obtain a flexible and computationally feasible signal reconstruction and
exploration of spatio-temporal neuroscientific data. In particular, we use a
Dirichlet process Gaussian mixture model to cluster functional principal
component scores within the standard Bayesian functional PCA framework. This
approach captures the spatial dependence structure among smoothed time series
(curves) and its interaction with the time domain without imposing a prior
spatial structure on the data. Moreover, by moving the mixture from data to
functional principal component scores, we obtain a more general clustering
procedure, thus allowing a higher level of intricate insight and understanding
of the data. We present results from a simulation study showing improvements in
curve and correlation reconstruction compared with different Bayesian and
frequentist fPCA models and we apply our method to functional Magnetic
Resonance Imaging and Electroencephalogram data analyses providing a rich
exploration of the spatio-temporal dependence in brain time series.
