Exercise & Sport Science, University of Sydney, Australia; People Development & Wellbeing, Australian Institute of Sport, Australia.
Department of Mathematics & Statistics, University of Limerick, Ireland.
J Biomech. 2021 Feb 12;116:110106. doi: 10.1016/j.jbiomech.2020.110106. Epub 2020 Oct 31.
Principal components analysis (PCA) of waveforms and functional PCA (fPCA) are statistical approaches used to explore patterns of variability in biomechanical curve data, with fPCA being an accepted statistical method grounded within the functional data analysis (FDA) statistical framework. This technical note demonstrates that PCA of waveforms is the most rudimentary form of FDA, and consequently can be rationalised within the FDA framework of statistical processes. Mathematical proofing applied demonstrations of both techniques, and an example of when fPCA may be of greater benefit to control over smoothing of functional principal components is provided using an open access motion sickness dataset. Finally, open access software is provided with this paper as means of priming the biomechanics community for using these methods as a part of future functional data explorations.
主成分分析（PCA）和功能主成分分析（fPCA）是用于探索生物力学曲线数据变异性模式的统计方法，其中 fPCA 是基于功能数据分析（FDA）统计框架的一种公认的统计方法。本技术说明表明，波形的 PCA 是 FDA 的最基本形式，因此可以在 FDA 的统计过程框架内进行合理化。这两种技术都应用了数学证明，并且提供了一个示例，说明在什么情况下 fPCA 可能比平滑功能主成分更有优势，该示例使用了一个公开访问的运动病数据集。最后，本文提供了开放访问软件，作为为生物力学界提供的一种手段，以便他们将来在功能数据探索中使用这些方法。
