Clustering of temporal sport training curves: a comparison of FDA and LDA approaches
Résumé
Functional data analysis (FDA) and longitudinal data analysis (LDA) are the main approaches to analyze repeated measures data (in which multiple measurements are made on the same subject across time). Typically, FDA is applied when the data are dense, assumed to be observed in the continuum, and without noise. LDA is usually applied when data are sparse, possibly with different number of measurements across individuals, and subject to error.
In elite sport, the parameters of the training program (intensity, volume, frequency, distribution and duration of high-intensity, recovery, and competition periods) should be manipulated systematically to optimize performance and reduce the risk of injury. Sport training data are recorded densely over time. However, measurements, such as duration of follow-up or duration of the season, vary among subjects. Subject-specific variations may introduce substantial measurement error.
The statistical objectives of this study were the following:
- First, to review the literature on the most commonly used methods for clustering of time evolution curves with a publicly available R code.
- Second, to implement FDA and LDA methods presenting publicly available R code: k-means based on the standard Euclidian distance, a discrete Frèchet distance, and a distance of functions; Gaussian mixture model - based clustering for standard, longitudinal and functional data; and latent class mixed models.
- Third, using data from a twenty - year longitudinal study of training practices of elite athletes, to perform a clustering analysis using relevant methods.
- Fourth, to compare the results and interpret them. Comparison criteria were mainly based on computational and practical aspects.
The practical goal of this project was to identify training profiles and to characterize them to provide relevant tools for supporting decision-making in monitoring athletes' training programs.