Functional Manifold Data Analysis
Hyun Bin Kang

Many scientific areas are faced with the challenge of extracting information from large, complex, and highly structured data sets.  A great deal of modern statistical work focuses on developing tools for handling such data.  This talk will present a new subfield of functional data analysis, FDA, which we call Functional Manifold Data Analysis, or FMDA.  FMDA is concerned with the statistical analysis of samples where one or more variables measured on each unit is a manifold, thus resulting in as many manifolds as we have units.  We propose a framework that converts manifolds into functional objects, a functional principal component method, and a manifold-on-scalar regression model.  This work is motivated by an anthropological application involving 3D facial imaging data, which will be discussed extensively throughout the talk.  The proposed framework is used to understand how individual characteristics, such as age and genetic ancestry, influence the shape of the human face.