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Smoothing and Differentiation of Kinematic Data Using Functional Data Analysis Approach: An Application of Automatic and Subjective Methods
oleh: Muhammad Athif Mat Zin, Azmin Sham Rambely, Noratiqah Mohd Ariff, Muhammad Shahimi Ariffin
| Format: | Article |
|---|---|
| Diterbitkan: | MDPI AG 2020-04-01 |
Deskripsi
Smoothing is one of the fundamental procedures in functional data analysis (FDA). The smoothing parameter <inline-formula> <math display="inline"> <semantics> <mi>λ</mi> </semantics> </math> </inline-formula> 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 <inline-formula> <math display="inline"> <semantics> <mi>λ</mi> </semantics> </math> </inline-formula> 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>λ</mi> <mo>.</mo> </mrow> </semantics> </math> </inline-formula> CV and GCV were applied prior to the subjective assessment with various values of <inline-formula> <math display="inline"> <semantics> <mi>λ</mi> </semantics> </math> </inline-formula> together with cubic and quintic spline (B-spline) bases using the FDA approach. The selection of optimal <inline-formula> <math display="inline"> <semantics> <mi>λ</mi> </semantics> </math> </inline-formula> was based on smoothed and well-fitted first and second derivatives. The chosen optimal <inline-formula> <math display="inline"> <semantics> <mi>λ</mi> </semantics> </math> </inline-formula> was <inline-formula> <math display="inline"> <semantics> <mrow> <mn>1</mn> <mo>×</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>12</mn> </mrow> </msup> </mrow> </semantics> </math> </inline-formula> 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>λ</mi> <mo>,</mo> </mrow> </semantics> </math> </inline-formula> forcing subjective assessment to be employed instead.