Filtrated common functional principal component analysis of multigroup functional data

Local field potentials (LFPs) are signals that measure electrical activities in localized cortical regions and are collected from multiple tetrodes implanted across a patch on the surface of cortex. Hence, they can be treated as multigroup functional data, where the trajectories collected across temporal epochs from one tetrode are viewed as a group of functions. In many cases multitetrode LFP trajectories contain both global variation patterns (which are shared by most groups, due to signal synchrony) and idiosyncratic variation patterns (common only to a small subset of groups), and such structure is very informative to the data mechanism. Therefore, one goal in this paper is to develop an efficient algorithm that is able to capture and quantify both global and idiosyncratic features. We develop the novel filtrated common functional principal components (filt-fPCA) method, which is a novel forest -structured fPCA for multigroup functional data. A major advantage of the proposed filtfPCA method is its ability to extract the common components in a flexible "multiresolution" manner. The proposed approach is highly data -driven, and no prior knowledge of "ground -truth" data structure is needed, making it suitable for analyzing complex multigroup functional data. In addition, the filtfPCA method is able to produce parsimonious, interpretable, and efficient functional reconstruction (low reconstruction error) for multigroup functional data with orthonormal basis functions. Here the proposed filt-fPCA method is employed to study the impact of a shock (induced stroke) on the synchrony structure of rat brain. The proposed filt-fPCA is general and inclusive that can be readily applied to analyze any multigroup functional data, such as multivariate functional data, spatial -temporal data, and longitudinal functional data.