Shapes Analysis of Functional Data
Anuj Srivastava, Department of Statistics, Florida State University, USA
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 ignores the shapes of these functions. 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. I will present some statistical procedures resulting from their framework, including estimation of shape-constrained densities, ANOVA on shape space of curves, shape estimation and analysis of large biomolecules, and shape analysis of brain anatomical structures.