主题：Filtrated Common Functional Principal Components for Multi-group

Functional Data

主讲人：香港中文大学统计系 焦舒豪

主持人：统计学院 陈坤教授

时间：2022年3月29日（周二）上午10:30-11:30

举办地点：腾讯会议，536-364-594

主办单位：统计学院 科研处

主讲人简介：

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。

内容简介：

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.

局部场电位是⽤来监测⼈类或动物⼤脑活动的电讯号，通常是从植⼊于局部⼤脑⽪层的多个电极中获取。我们将局部场电位信号看作多维函数型数据。不同电极产⽣的信号会同时体现相同（由多个不同电极互享）或独⽴（只有少数或单个电极体现）的变化模式。这种结构在分析此类数据时会提供重要信息。因此，这篇⽂章的⼀个⽬标是提取出这些相同和独⽴的变化特征。为此，我们提出⼀种新型的树形公共主成分结构—filt-fPC。此⽅法⾼度由数据导向，不需要提前设定任何模型，⽽且可以提供⼀种简约，可解释，⾼效的主成分结构。我们将filt-fPCA应⽤于分析电位信号的同步性结构以阐述此⽅法的优势。filt-fPCA是⼀种可以被⼴泛应⽤的⽅法，例如在多维函数型数据，时空间数据，以及纵向函数型数据的应⽤。