Title: Recent advances in elastic functional data analysis
Authors: Anuj Srivastava - Florida State University (United States) [presenting]
Abstract: One of the most important challenges in functional data analysis (FDA) is the the phase variability, the lack of registration in the amplitudes of given functions. Elastic functional data analysis (EFDA) is a branch of FDA that deals with recognizes and deals with this problem directly. While earlier works in EFDA focused on separation of phase and amplitude components, i.e. registration of functions using time warping, and their individual modeling using functional PCA (FPCA), the more recent techniques focus on combining phase-amplitude separation with other statistical techniques. We will summarize progress in EFDA in the following topics: (1) Elastic FPCA: one performs PCA while seeking function registration at the same time. (2) Elastic Functional Regression Models: This problem involves using functional predictors where response variable is scalar, and functional linear regression is a commonly used model. In the elastic approach, one either removes phase components from the predictors during estimation of model parameters, or separates them to form additional predictors. We will describe a single index model that uses elastic functional predictors and a polynomial index term to result in a powerful regression model. (3) If time permits, we will also list some recent advances in shape analysis of complex objects using elastic shape metrics.