统计学系系列讲座之272期

 

时间:2017 年 9月21日(星期四)15:00-16:00

地点:史带楼503室

主持人:朱仲义教授 复旦大学管理学院统计学系

主题:Intrinsic Riemannian Functional Data Analysis

主讲人:Zhenhua Lin PhD

University of Toronto, Canada

摘要:Data of random paths on a Riemannian manifold is often encountered in real-world applications. Examples include trajectories of bird migration, the dynamics of brain functional connectivity, etc. In this talk, I will present the framework of intrinsic Riemannian functional data analysis, which provides a rigorous and sound theoretical foundation for statistical analysis on random paths from a Riemannian manifold. The key concept of the proposed framework is a novel tensor Hilbert space along a curve on the manifold, based on which principal component analysis and Karhunen-Loève expansion for Riemannian random paths are then developed. The framework also features a novel proposal for proper comparison of objects from different tensor Hilbert spaces, which paves the way for intrinsic asymptotic analysis of estimation procedures for Riemannian functional data analysis. Being completely built on top of intrinsic geometric concepts such as vector field, Levi-Civita connection and parallel transport on Riemannian manifolds, the proposed framework embraces full generality of applications and proper handle of intrinsic geometric concepts. As an application of the framework, I will discuss a functional linear regression approach to model Riemannian random paths and their associated response variables, including estimation, asymptotics and the application to the study of brain functional connectivity.

 

 

统计学系

2017-9-18