Statistical kinematic modelling: concepts and model validity

Abstract

Data reduction techniques are applied to reduce the volume of data while maintaining its integrity. For cyclic motion data, a reliable overview comparing these methods is lacking. Therefore, this study aims to evaluate the features of the different data reduction techniques by applying them to large public data sets. The periodicity of cyclic motion can be exploited by either analysing a single cycle or studying a series of cycles. Analysing single cycles requires a pre-processing step to isolate the amplitude variability. Three different alignment techniques were evaluated, namely Linear length normalisation (LLN), piecewise LLN (PLLN) and continuous registration (CR). CR showed to remove the most phase variation. For the data reduction, three techniques were assessed (i.e., principal component analysis (PCA), principal polynomial analysis (PPA) and multivariate functional PCA (MFPCA)) based on the in- and out-of-sample error, the compactness and the computation time. The differences were found to be minimal. From our results, PPA appeared to be most useful for data compression. Further, we recommend PCA and MFPCA for classification and feature extraction purposes. We suggest the use of PCA when computation time is key and we advise the use of MFPCA when the inclusion of different data sources is desired. In contrast, the analysis of a series of cycles requires a pre-processing step to decompose the series. Further, a regression model was used to compensate for the difference in fundamental frequency. PCA on FC and MFPCA with splines were applied on the frequency compensated curves. Both methods performed as good.