主题：Filtrated Common Functional Principal Components for Multi-group
焦舒豪，现为香港中文大学副研究员。2019年在加州大学洛杉矶分校获得博士学位，2019年9月至2021年9月在阿卜杜拉国王科技大学从事博士后研究。主要从事神经图像数据的理论与应用研究，在 Journal of the American Statistical Association等统计顶级杂志发表论文。研究方法包括函数型数据分析，网络分析，时间序列分析和机器学习方法。
Local field potentials (LFPs) are signals that measure electrical activity in localized
cortical regions from implanted tetrodes in the human or animal brain. The LFP
signals are curves observed at multiple tetrodes which are implanted across a patch on the surface of the cortex. Hence, they can be treated as multi-group functional data, where the trajectories collected across temporal epochs from one tetrode are viewed as a group of functions. In many cases, multi-tetrode LFP trajectories contain both global variation patterns (which are shared in common to all groups, due to signal synchrony) and isolated variation patterns (common only to a small subset of groups), and such structure is very informative to the analysis of such data. Therefore, one goal in this paper is to develop an efficient procedure that is able to capture and quantify both global and isolated features. We propose a novel tree-structured functional principal components (filt-fPC) analysis through finite-dimensional functional representation – specifically via filtration. A major advantage of the proposed filt-fPC method is the ability to extract the components that are common to multiple groups (or tetrodes) in a flexible "multi-resolution" manner and simultaneously preserve the idiosyncratic individual components of different tetrodes. The proposed filt-fPC approach is highly data-driven and no "ground-truth" model pre-specification is needed, making it a suitable approach for analyzing multi-group functional data that is complex. In addition, the filt-fPC method is able to produce a parsimonious, interpretable, and efficient low dimensional representation of multi-group 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 the rat brain. The proposed filt-fPCA is a general approach that can be readily applied to analyze other complex multi-group functional data, such as multivariate functional data, spatial-temporal data and longitudinal functional data.