The variance needed to accurately describe jump height from vertical ground reaction force data

Area of Science:

• Biomechanics
• Functional Data Analysis
• Sports Science

Background:

• Functional principal component analysis (fPCA) is used to reduce dimensionality in functional data, like vertical ground reaction force (vGRF) curves.
• The selection of a threshold to determine the number of retained principal components in fPCA can significantly impact subsequent analyses.
• Previous studies have used various thresholds without consistent evaluation, leading to potential variability in results.

Purpose of the Study:

• To determine the optimal fPCA threshold for preserving information critical to accurately predicting jump height from vGRF curves.
• To evaluate the impact of different fPCA thresholds on the accuracy of jump height prediction models.
• To provide evidence-based recommendations for threshold selection in biomechanical analyses of jumping.

Main Methods:

• Vertical ground reaction force (vGRF) data from jump movements were analyzed using functional principal component analysis (fPCA).
• A neural network model was employed to predict jump height using features derived from vGRF curves at various fPCA thresholds.
• Prediction errors for jump height were systematically compared across different thresholds to identify the optimal range.

Main Results:

• The optimal fPCA threshold range for predicting jump height was found to be between 99% and 99.9% of preserved information.
• This optimal range corresponds to retaining 6 to 11 principal components.
• Thresholds within this range resulted in significantly lower jump height prediction errors compared to other tested thresholds.

Conclusions:

• An fPCA threshold between 99% and 99.9% is recommended for analyses aiming to predict jump height from vGRF data.
• Proper threshold selection in fPCA is essential for maximizing the predictive power of biomechanical variables.
• This study provides a data-driven approach to optimize functional data analysis in sports biomechanics.