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A robust algorithm for template curve estimation based on manifold embedding

Author

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  • Dimeglio, Chloé
  • Gallón, Santiago
  • Loubes, Jean-Michel
  • Maza, Elie

Abstract

The problem of finding a template function that represents the common pattern of a sample of curves is considered. To address this issue, a novel algorithm based on a robust version of the isometric featuring mapping (Isomap) algorithm is developed. When the functional data lie on an unknown intrinsically low-dimensional smooth manifold, the corresponding empirical Fréchet median function is chosen as an intrinsic estimator of the template function. However, since the geodesic distance is unknown, it has to be estimated. For this, a version of the Isomap procedure is proposed, which has the advantage of being parameter free and easy to use. The feature estimated with this method appears to be a good pattern for the data, capturing the inner geometry of the curves. Comparisons with other methods, with both simulated and real datasets, are provided.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:70:y:2014:i:c:p:373-386
    DOI: 10.1016/j.csda.2013.09.030
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    References listed on IDEAS

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    8. Simone Vantini, 2012. "On the definition of phase and amplitude variability in functional data analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 676-696, December.
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    Cited by:

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    3. 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.

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