seminars:stat:dec1_2022
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| + | ^ **TITLE:**| Manifold Data Analysis with Applications to High-Frequency 3D Imaging | | ||
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| + | 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 paper presents a new | ||
| + | subfield of functional data analysis, FDA, which we call Manifold Data Analysis, or | ||
| + | MDA. MDA 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, an efficient 2-step 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 is discussed extensively throughout the | ||
| + | paper. The proposed framework is used to understand how individual characteristics, | ||
| + | such as age and genetic ancestry, influence the shape of the human face. | ||
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