Smoothing and Differentiation of Kinematic Data Using Functional Data Analysis Approach: An Application of Automatic and Subjective Methods

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.

Kinetics Study in Parachute Landing Fall Technique by Comparing Professional and Amateur Malaysian Army Parachutists Using Kane’s Method

“…The flexion and extension at each joint are important to be identified since it also affect the reading of torque. In the present study, in order to analyse the dynamic pattern, functional data analysis (FDA) was utilised by referring to the procedure by [32][33][34]. The data were smoothed by setting up an order six spline basis with knots at the frame of observation, along with roughness penalty on their fourth derivatives and smoothing parameter of 1 √ 10.…”

Effectiveness of Landmark and Continuous Registrations in Reducing Inter- and Intrasubject Phase Variability

“…The data were transformed into a functional form by smoothing using the penalized fourth-order derivative (roughness penalty approach) and quintic spline (B-spline) basis with an optimal smoothing parameter, ,  set to a value of 12 1 −  before the registration procedures. The step-bystep method of how these smoothing parameters were chosen is explained in [34].…”

Smoothing with the Best Rectangle Window is Optimal for All Tapered Rectangle Windows

“…Smoothing approaches, which are abundant in literature, can help in achieving a more flexible and robust analysis of datasets by constructing their more informative smoothed versions [2]. Because of the acquired more informative data, it has many applications in various fields from data analysis [3]- [7], signal processing [8]- [11], anomaly detection [12]- [15] and machine learning [16]- [23].…”