<![CDATA[The complexity of the physical and biomechanical variables of runners often makes it difficult to identify the main factors that contribute to performance. Primary Component Analysis (PCA) and functional PCA (fPCA) offer a multivariate approach to reducing data dimensions without losing important information. This study aims to analyze the basic components of physical exercise and evaluate its effect on the physical condition of runners using the PCA and fPCA approaches. A total of 78 runners (ages 18–40) were observed for eight weeks. Twelve exercise variables (intensity, duration, RPE, speed, acceleration, etc.) as well as soil reaction force biomechanical data were analyzed using PCA and fPCA. The analysis was carried out after z-score normalization and validation through bootstrap and cross-validation. PCA produces three main components such as Volume-Intensity, Neuromuscular, and Internal Efficiency which explains 81.4% of the total variance. The Neuromuscular component showed a significant association with increased VO₂max (β = 0.37, p < 0.001) and 5 km running time (β = –0.42, p < 0.001). The fPCA's analysis of the ground reaction force curve revealed two main modes of vertical force variation and propulsive timing that relate to the biomechanical efficiency of experienced runners. PCA and fPCA are effective in identifying key exercise and biomechanical patterns that affect the physical condition of runners. The Neuromuscular component is the main determinant of increased VO₂max and running performance, while the efficient biomechanical pattern (low vertical force, short contact time) shows optimal adaptation. This approach can be applied as a diagnostic tool and data-driven training design in modern athletic coaching.]]>
