June 2024 Filtrated common functional principal component analysis of multigroup functional data
Shuhao Jiao, Ron Frostig, Hernando Ombao
Author Affiliations +
Ann. Appl. Stat. 18(2): 1160-1177 (June 2024). DOI: 10.1214/23-AOAS1827


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 filt-fPCA 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 filt-fPCA 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.


The authors would like to thank the anonymous referees, the Associate Editor, and the Editor for their constructive comments that substantially improved the quality of this paper.


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Shuhao Jiao. Ron Frostig. Hernando Ombao. "Filtrated common functional principal component analysis of multigroup functional data." Ann. Appl. Stat. 18 (2) 1160 - 1177, June 2024. https://doi.org/10.1214/23-AOAS1827


Received: 1 February 2023; Revised: 1 September 2023; Published: June 2024
First available in Project Euclid: 5 April 2024

Digital Object Identifier: 10.1214/23-AOAS1827

Keywords: Community detection , Dimension reduction , functional principal components , multigroup functional data , network filtration , weighted network

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.18 • No. 2 • June 2024
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