Title: Shape-motivated functional data analysis
Authors: Anuj Srivastava - Florida State University (United States) [presenting]
Abstract: Functional data has a growing presence in all branches of science and engineering, partly due to tremendous advances made in data collection and storage technologies. Such data is mostly analyzed using the classical Hilbert structure of square-integrable function spaces, but that setup ignored shapes of functions and leads to counter intuitive results. Shape implies the ordering and the heights of peaks and valleys but is flexible on their exact locations. To focus on shapes of functions, we have introduced Elastic functional data analysis that allows time warpings of functions in order to register functional data, i.e. match their peaks and valleys. This, in turn, requires elastic Riemannian metrics that enable comparisons and testing of shape data modulo warping group action. We will present some statistical tools resulting from this framework, including estimation of shape-constrained functions and probability densities.