Kernel Principal Component Analysis for Identification of Between-Group Differences and Changes in Running Gait Patterns

Abstract

The identification of between-group differences and changes in gait mechanics are useful for injury prevention. Previous studies suggest the differences in gait biomechanical variables may interact in a complex non-linear fashion rather than a simple linear fashion. A non-linear multivariate analysis technique is therefore necessary to unravel the inherent structure in the gait data. Kernel principal component analysis (KPCA) is an extension of principal component analysis (PCA), the most widely used method in this field, and can provide inside into non-linear relationships of the variables of interest. Despite the growing use of PCA in running gait research, no prior studies have evaluated the utility of KPCA in determining the between-group differences in running gait patterns. Therefore, the objective of this study was to compare the performance of KPCA and PCA in identifying differences between male and female runners and as well between young and older runners in running gait kinematics. Running kinematic data were analysed on a gender group (female, n = 50; male, n = 50) and an age group (young, n = 50; older, n = 50) for discrete variables and waveform data. The following key results were obtained: (1) the performance of the KPCA for the identification of gender and age differences in running gait kinematics increased as compared to using the linear PCA; (2) the Gaussian function often performed better than the polynomial function for these two experiments; (3) there was no consistent optimal value of either the width σ of the Gaussian kernel or the degree d of the polynomial kernel for different data types and experiments. These results suggest that non-linear features extracted by KPCA could be potentially useful in identifying and discriminating between-group differences and changes in running gait patterns, and could provide useful information about the intrinsic non-linear dynamics of running movement.