Analysis of Postural Control Using Principal Component Analysis: The Relevance of Postural Accelerations and of Their Frequency Dependency for Selecting the Number of Movement Components.

One criterion when selecting the number of principal components (PCs) to be considered in a principal component analysis (PCA) is the fraction of overall variance that each PC represents. When applying a PCA to kinematic marker data in postural control research, this criterion relates to the amplitude of postural changes, recently often called "principal (postural) positions" (PPs). However, in the assessment of postural control, important aspects are also how fast posture changes and the acceleration of postural changes, i.e., "principal accelerations" (PAs). The current study compared how much of the total position variance each PP explained (PP_rVAR) and how much of the total acceleration variance each PA explained (PA_rVAR). Furthermore, the frequency content of PP and PA signals were evaluated. Postural movements of 26 participants standing on stable ground or balancing on a multiaxial balance board were analyzed by applying a PCA on 90 marker coordinates. For each PC, PP_rVAR, PA_rVAR, and the Fourier transformations of the PP and PA time series were calculated. The PP_rVAR and the PA_rVAR-distributions differed substantially. The PP-frequency domain was observed well below 5 Hz, the PA-frequency domain up to 5 Hz for stable standing and up to 10 Hz on the balance board. These results confirm that small-amplitude but fast movement components can have a higher impact on postural accelerations-and thus on the forces active in the system-than large-amplitude but slow lower-order movement components. Thus, PA variance and its dependence on filter frequencies should be considered in dimensionality reduction decisions.