A1067
Title: On advances in shape-based functional data analysis
Authors: Anuj Srivastava - Florida State University (United States) [presenting]
Abstract: Functional data analysis (FDA) is a fast-growing area of research and development in statistics. While most FDA literature imposes the classical $l_2$ Hilbert structure on function spaces, there is an emergent need for a different, shape-based approach for analyzing functional data. Fundamental geometrical concepts are reviewed and developed to help connect traditionally diverse fields of shape and functional analysis. It showcases that focusing on shapes is often more appropriate when structural features (number of peaks and valleys and their heights) carry salient information in data. It recaps recent mathematical representations and associated procedures for comparing, summarizing, and testing the shapes of functions. Specifically, it discusses shape regression models that extract and focus on the shapes of functions during regression. The ensuing results provide better interpretations and tend to preserve geometric structures.
