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Pairwise curve synchronization for functional data

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  • Rong Tang
  • Hans-Georg Müller

Abstract

Data collected by scientists are increasingly in the form of trajectories or curves. Often these can be viewed as realizations of a composite process driven by both amplitude and time variation. We consider the situation in which functional variation is dominated by time variation, and develop a curve-synchronization method that uses every trajectory in the sample as a reference to obtain pairwise warping functions in the first step. These initial pairwise warping functions are then used to create improved estimators of the underlying individual warping functions in the second step. A truncated averaging process is used to obtain robust estimation of individual warping functions. The method compares well with other available time-synchronization approaches and is illustrated with Berkeley growth data and gene expression data for multiple sclerosis. Copyright 2008, Oxford University Press.

Suggested Citation

  • Rong Tang & Hans-Georg Müller, 2008. "Pairwise curve synchronization for functional data," Biometrika, Biometrika Trust, vol. 95(4), pages 875-889.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:4:p:875-889
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    File URL: http://hdl.handle.net/10.1093/biomet/asn047
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    Citations

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    Cited by:

    1. Weiyi Xie & Sebastian Kurtek & Karthik Bharath & Ying Sun, 2017. "A Geometric Approach to Visualization of Variability in Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 979-993, July.
    2. Dimeglio, Chloé & Gallón, Santiago & Loubes, Jean-Michel & Maza, Elie, 2014. "A robust algorithm for template curve estimation based on manifold embedding," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 373-386.
    3. Alonso González, Pablo, 2013. "Dependency evolution in Spanish disabled population : a functional data analysis approach," DES - Working Papers. Statistics and Econometrics. WS ws130403, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Tucker, J. Derek & Wu, Wei & Srivastava, Anuj, 2013. "Generative models for functional data using phase and amplitude separation," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 50-66.
    5. Boudaoud, S. & Rix, H. & Meste, O., 2010. "Core Shape modelling of a set of curves," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 308-325, February.
    6. Jason Cleveland & Wei Wu & Anuj Srivastava, 2016. "Norm-preserving constraint in the Fisher--Rao registration and its application in signal estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 338-359, June.
    7. Marco Grasso & Bianca Maria Colosimo & Fugee Tsung, 2017. "A phase I multi-modelling approach for profile monitoring of signal data," International Journal of Production Research, Taylor & Francis Journals, vol. 55(15), pages 4354-4377, August.
    8. Arribas-Gil, Ana & Müller, Hans-Georg, 2014. "Pairwise dynamic time warping for event data," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 255-268.
    9. Cleveland, Jason & Zhao, Weilong & Wu, Wei, 2018. "Robust template estimation for functional data with phase variability using band depth," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 10-26.

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