Investigating swimming technical skills by a double partition clustering of multivariate functional data allowing for dimension selection

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.