Shape Analysis of Functional Data

Xiaoyang Guo () and Anuj Srivastava ()
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Xiaoyang Guo: Florida State University
Anuj Srivastava: Florida State University

Chapter Chapter 13 in Handbook of Variational Methods for Nonlinear Geometric Data, 2020, pp 379-394 from Springer

Abstract: Abstract Functional data is one of the most common types of data in our digital society. Such data includes scalar or vector time series, Euclidean curves, surfaces, or trajectories on nonlinear manifolds. Rather than applying past statistical techniques developed using standard Hilbert norm, we focus on analyzing functions according to their shapes. We summarize recent developments in the field of elastic shape analysiselastic shape analysis of functional data, with a perspective on statistical inferences. The key idea is to use metrics, with appropriate invariance properties, to register corresponding parts of functions and to use this registration in quantification of shape differences. Furthermore, one introduces square-root representations of functions to help simplify computations and facilitate efficient algorithms for large-scale data analysis. We will demonstrate these ideas using simple examples from common application domains.

Date: 2020
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DOI: 10.1007/978-3-030-31351-7_13

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