# Parameter clustering in Bayesian functional PCA of fMRI data

## TL;DR

This paper introduces PCl-fPCA, a novel Bayesian functional PCA method with parameter clustering for analyzing complex brain imaging data, capturing spatial-temporal dependencies without predefined spatial structures.

## Contribution

It combines Bayesian nonparametrics with functional PCA to enable flexible clustering of principal component scores, enhancing analysis of spatio-temporal neuroscientific data.

## Key findings

- Improved curve and correlation reconstruction over existing models
- Effective clustering captures spatial dependence in brain data
- Applied successfully to fMRI and EEG datasets

## Abstract

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.