Quantification of symmetry for functional data with application to equine lameness classification |
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Authors: | Helle Sørensen Anders Tolver Maj Halling Thomsen Pia Haubro Andersen |
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Affiliation: | 1. Department of Mathematical Sciences , University of Copenhagen , Universitetsparken 5, DK-2100, Copenhagen East, Denmark;2. Department of Natural Sciences and Environment , University of Copenhagen (LIFE) , Copenhagen, Denmark;3. Department of Large Animal Sciences , University of Copenhagen (LIFE) , Copenhagen, Denmark |
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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. |
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Keywords: | acceleration signals classification classification and regression trees equine lameness functional data analysis linear discriminant analysis principal component analysis symmetry |
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