June 2024 Investigating swimming technical skills by a double partition clustering of multivariate functional data allowing for dimension selection
Antoine Bouvet, Salima El Kolei, Matthieu Marbac
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Ann. Appl. Stat. 18(2): 1750-1772 (June 2024). DOI: 10.1214/23-AOAS1857


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 error terms resulting from the functional basis decomposition. Indeed, after decomposing into functional basis with finite number of elements both the original signal (measuring the swimming pattern) and the signal of squared error terms (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.

Funding Statement

This research was funded by the French Agence Nationale de la Recherche, grant number ANR-19-STPH-004, and conducted within the framework of the PIA EUR DIGISPORT project (ANR-18-EURE-0022). The first author was supported by a Ph.D. scholarship from the Ecole Normale Supérieure de Rennes and affiliated to the MIMETIC team at Inria Rennes Bretagne Atlantique and the CREST.


The authors would like to thank the Editor, the Associate Editor and three anonymous referees for their helpful comments.


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Antoine Bouvet. Salima El Kolei. Matthieu Marbac. "Investigating swimming technical skills by a double partition clustering of multivariate functional data allowing for dimension selection." Ann. Appl. Stat. 18 (2) 1750 - 1772, June 2024. https://doi.org/10.1214/23-AOAS1857


Received: 1 March 2023; Revised: 1 November 2023; Published: June 2024
First available in Project Euclid: 5 April 2024

Digital Object Identifier: 10.1214/23-AOAS1857

Keywords: clustering , Feature selection , functional data , Mixture models , sport performance

Rights: Copyright © 2024 Institute of Mathematical Statistics


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Vol.18 • No. 2 • June 2024
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