Identifying Coordinative Structure Using Principal Component Analysis Based on Coherence Derived From Linear Systems Analysis

ABSTRACT

Principal component analysis is a powerful and popular technique for capturing redundancy in muscle activity and kinematic patterns. A primary limitation of the correlations or covariances between signals on which this analysis is based is that they do not account for dynamic relations between signals, yet such relations—such as that between neural drive and muscle tension—are widespread in the sensorimotor system. Low correlations may thus be obtained and signals may appear independent despite a dynamic linear relation between them. To address this limitation, linear systems analysis can be used to calculate the matrix of overall coherences between signals, which measures the strength of the relation between signals taking dynamic relations into account. Using ankle, knee, and hip sagittal-plane angles from 6 healthy subjects during overground walking at preferred speed, it is shown that with conventional correlation matrices the first principal component accounted for ∼50% of total variance in the data set, while with overall coherence matrices the first component accounted for > 95% of total variance. The results demonstrate that the dimensionality of the coordinative structure can be overestimated using conventional correlation, whereas a more parsimonious structure is identified with overall coherence.

Keywords:

• coordination
• cross-correlation
• dynamic relations
• module
• motor primitive
• synergy

ACKNOWLEDGMENTS

The authors would like to acknowledge Peter Neilson as the originator of the overall coherence measure. They thank Ian Cathers for helpful comments on the analysis.