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Shape Analysis of Functional Data

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Handbook of Variational Methods for Nonlinear Geometric Data

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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 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.

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Authors and Affiliations

  1. Florida State University, Tallahassee, FL, USA

    Xiaoyang Guo & Anuj Srivastava

Authors
  1. Xiaoyang Guo
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  2. Anuj Srivastava
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Correspondence to Xiaoyang Guo .

Editor information

Editors and Affiliations

  1. Faculty of Mathematics, University of Vienna, Wien, Austria

    Philipp Grohs

  2. Institute of Mathematics and Scientific Computing, University of Graz, Graz, Austria

    Martin Holler

  3. Department of Mathematics and Natural Sciences, Hochschule Darmstadt, Darmstadt, Germany

    Andreas Weinmann

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Guo, X., Srivastava, A. (2020). Shape Analysis of Functional Data. In: Grohs, P., Holler, M., Weinmann, A. (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, Cham. https://doi.org/10.1007/978-3-030-31351-7_13

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