Investigating technical skills of swimmers is a challenge for performance improvement, that can be achieved by analyzing multivariate functional data recorded by Inertial Measurement Units (IMU). To investigate technical levels of front-crawl swimmers, a new model-based approach is introduced to obtain two complementary partitions reflecting, for each swimmer, its swimming pattern and its ability to reproduce it. Contrary to the usual approaches for functional data clustering, the proposed approach also considers the information of the residuals resulting from the functional basis decomposition. Indeed, after decomposing into functional basis both the original signal (measuring the swimming pattern) and the signal of squared residuals (measuring the ability to reproduce the swimming pattern), the method fits the joint distribution of the coefficients related to both decompositions by considering dependency between both partitions. Modeling this dependency is mandatory since the difficulty of reproducing a swimming pattern depends on its shape. Moreover, a sparse decomposition of the distribution within components that permits a selection of the relevant dimensions during clustering is proposed. The partitions obtained on the IMU data aggregate the kinematical stroke variability linked to swimming technical skills and allow relevant biomechanical strategy for front-crawl sprint performance to be identified.

翻译：探究游泳运动员的技术技能是提升运动表现的关键挑战，可通过分析惯性测量单元（IMU）记录的多元函数数据来实现。为研究自由泳运动员的技术水平，本文提出一种基于模型的新方法，以获取两种互补划分，分别反映每位运动员的游泳模式及其复现该模式的能力。与常规函数数据聚类方法不同，本方法还考虑了函数基分解产生的残差信息。具体而言，在将原始信号（用于测量游泳模式）和平方残差信号（用于测量复现游泳模式的能力）分别进行函数基分解后，该方法通过考虑两种划分之间的依赖关系，拟合与两种分解相关的系数的联合分布。建模这种依赖关系是必要的，因为复现游泳模式的难度取决于其形状。此外，本文还提出了一种分量内的稀疏分解方法，可在聚类过程中实现相关维度的选择。基于IMU数据获得的划分汇聚了与游泳技术技能相关的运动划水变异性，并有助于识别与自由泳短距离运动表现相关的生物力学策略。