The application of principal component analysis to quantify technique in sports

Analyzing an athlete's technique, sport scientists often focus on preselected variables that quantify important aspects of movement. In contrast, coaches and practitioners typically describe movements in terms of basic postures and movement components using subjective and qualitative features. A challenge for sport scientists is finding an appropriate quantitative methodology that incorporates the holistic perspective of human observers. Using alpine ski racing as an example, this study explores principal component analysis (PCA) as a mathematical method to decompose a complex movement pattern into its main movement components. Ski racing movements were recorded by determining the three-dimensional coordinates of 26 points on each skier which were subsequently interpreted as a 78-dimensional posture vector at each time point. PCA was then used to determine the mean posture and principal movements (PMk) carried out by the athletes. The first four PMk contained 95.5 +/- 0.5% of the variance in the posture vectors which quantified changes in body inclination, vertical or fore-aft movement of the trunk, and distance between skis. In summary, calculating PMk offered a data-driven, quantitative, and objective method of analyzing human movement that is similar to how human observers such as coaches or ski instructors would describe the movement.