Abstract
Smoothing is one of the fundamental procedures in functional data analysis (FDA). The smoothing parameter λ influences data smoothness and fitting, which is governed by selecting automatic methods, namely, cross-validation (CV) and generalized cross-validation (GCV) or subjective assessment. However, previous biomechanics research has only applied subjective assessment in choosing optimal λ without using any automatic methods beforehand. None of that research demonstrated how the subjective assessment was made. Thus, the goal of this research was to apply the FDA method to smoothing and differentiating kinematic data, specifically right hip flexion/extension (F/E) angle during the American kettlebell swing (AKS) and determine the optimal λ . CV and GCV were applied prior to the subjective assessment with various values of λ together with cubic and quintic spline (B-spline) bases using the FDA approach. The selection of optimal λ was based on smoothed and well-fitted first and second derivatives. The chosen optimal λ was 1 × 10 − 12 with a quintic spline (B-spline) basis and penalized fourth-order derivative. Quintic spline is a better smoothing and differentiation method compared to cubic spline, as it does not produce zero acceleration at endpoints. CV and GCV did not give optimal λ , forcing subjective assessment to be employed instead.
Highlights
Signals from motion analysis systems are contaminated with noise or error, resulting from electrical interference in the system, skin motion, and inaccurate data digitization
The noise has features that are different from the actual signal: low amplitude, nondeterministic, and diverse frequency range [1]
The first and second derivatives were used as indicators for determining the optimal smoothing parameter λ
Summary
Signals from motion analysis systems are contaminated with noise or error, resulting from electrical interference in the system, skin motion, and inaccurate data digitization. The noise has features that are different from the actual signal: low amplitude, nondeterministic, and diverse frequency range [1]. Raw signals or data must be smoothed or filtered to eradicate such noise while preserving the original signal traits. Biomechanics data, displacement data, were smoothed to obtain velocity and acceleration using several methods such as polynomial, splines, and Fourier series, as well as digital filtering. Cubic spline has been proven to be a better smoothing technique than polynomial as a second derivative; that is, the acceleration of displacement data is well-fitted by using cubic spline rather than orthogonal polynomial [2] and Chebyshev polynomial [3]. Polynomial produces an oversmoothed acceleration curve, which provides unrealistic acceleration values in running events [3], and an oversmoothed angular acceleration curve, which attenuates the peaks and falsifies the time histories
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