Title: Filtrated common functional principal components of multi-group functional data
Authors: Shuhao Jiao - KAUST (Saudi Arabia) [presenting]
Hernando Ombao - KAUST (Saudi Arabia)
Abstract: Local field potentials (LFPs) are signals that measure electrical activity in localized cortical regions from implanted tetrodes in the human or animal brain. These LFP signals are curves that are observed at multiple tetrodes which are spread across a patch on the surface of the cortex. Hence, they are treated as multi-group functional data. Most multi-group functional data contain both global features (which are shared in common to all curves) and isolated features (common only to a small subset of curves). One goal is to develop a procedure that captures these global features. We propose a novel tree-structured functional principal components (filt-fPC) model through low-dimensional functional representation -- specifically via filtration. Ordinary fPCA can only capture major information from one population and hence fails to reveal the similarity of variation pattern across different groups. In contrast, a major advantage of the proposed filt-fPC method is the ability to extract components that are common to multiple groups and simultaneously preserves the idiosyncratic individual features of the different groups. Thus, the filt-PC method produces a parsimonious and interpretable low dimensional representation of multi-group functional data. The proposed filt-fPC method is employed to study the impact of a shock (induced stroke) on the functional organization structure of the rat brain.