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Quantification of symmetry for functional data with application to equine lameness classification

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  • Helle Sørensen
  • Anders Tolver
  • Maj Halling Thomsen
  • Pia Haubro Andersen

Abstract

This paper presents a study on symmetry of repeated bi-phased data signals, in particular, on quantification of the deviation between the two parts of the signal. Three symmetry scores are defined using functional data techniques such as smoothing and registration. One score is related to the L 2 -distance between the two parts of the signal, whereas the other two are constructed to specifically measure differences in amplitude and phase. Moreover, symmetry scores based on functional principal component analysis (PCA) are examined. The scores are applied to acceleration signals from a study on equine gait. The scores turn out to be highly associated with lameness, and their applicability for lameness quantification and detection is investigated. Four classification approaches turn out to give similar results. The scores describing amplitude and phase variation turn out to outperform the PCA scores when it comes to the classification of lameness.

Suggested Citation

  • Helle Sørensen & Anders Tolver & Maj Halling Thomsen & Pia Haubro Andersen, 2012. "Quantification of symmetry for functional data with application to equine lameness classification," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 337-360, May.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:2:p:337-360
    DOI: 10.1080/02664763.2011.590189
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    References listed on IDEAS

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    1. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
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    Cited by:

    1. Mousavi, Seyed Nourollah & Sørensen, Helle, 2017. "Multinomial functional regression with wavelets and LASSO penalization," Econometrics and Statistics, Elsevier, vol. 1(C), pages 150-166.
    2. Pini, Alessia & Sørensen, Helle & Tolver, Anders & Vantini, Simone, 2023. "Local inference for functional linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).

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