a Department of Exercise and Sports Science, Faculty of Health Sciences , The University of Sydney, Cumberland Campus , Lidcombe , Australia.
b Department of Physical Education and Sport Sciences , University of Limerick , Limerick , Ireland.
Sports Biomech. 2019 Feb;18(1):10-27. doi: 10.1080/14763141.2017.1384050. Epub 2017 Nov 10.
Sporting performance is often investigated through graphical observation of key technical variables that are representative of whole movements. The presence of differences between athletes in such variables has led to terms such as movement signatures being used. These signatures can be multivariate (multiple time-series observed concurrently), and also be composed of variables measured relative to different scales. Analytical techniques from areas of statistics such as Functional Data Analysis (FDA) present a practical alternative for analysing multivariate signatures. When applied to concurrent bivariate time-series multivariate functional principal components analysis (referred to as bivariate fPCA or bfPCA in this paper) has demonstrated preliminary application in biomechanical contexts. Despite this, given the infancy of bfPCA in sports biomechanics there are still necessary considerations for its use with non-conventional or complex bivariate structures. This paper focuses on the application of bfPCA to the force-angle graph in on-water rowing, which is a bivariate structure composed of variables with different units. A normalisation approach is proposed to investigate and standardise differences in variability between the two variables. The results of bfPCA applied to the non-normalised data and normalised data are then compared. Considerations and recommendations for the application of bfPCA in this context are also provided.
运动表现通常通过观察代表整个运动的关键技术变量的图形来进行研究。运动员在这些变量上存在差异，导致出现了“运动特征”等术语。这些特征可以是多元的（同时观察多个时间序列），也可以由相对于不同尺度测量的变量组成。来自统计学领域的分析技术，如功能数据分析（FDA），为分析多元特征提供了一种实用的替代方法。当应用于同时的双变量时间序列多元函数主成分分析（在本文中称为双变量 fPCA 或 bfPCA）时，它在生物力学背景下已经有了初步的应用。尽管如此，由于 bfPCA 在运动生物力学中的应用还处于起步阶段，对于具有非传统或复杂双变量结构的 bfPCA 仍然需要考虑一些因素。本文重点介绍 bfPCA 在水上划船的力-角度图中的应用，该图是由具有不同单位的变量组成的双变量结构。提出了一种归一化方法来研究和标准化两个变量之间的可变性差异。然后比较应用于非归一化数据和归一化数据的 bfPCA 的结果。本文还提供了在这种情况下应用 bfPCA 的注意事项和建议。
