Analyzing Variance in Multi-Degree-of-Freedom Movements: Uncovering Structure versus Extracting Correlations

in Motor Control
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An important aspect of the study of multi-degree-of-freedom motor control is the analysis of high-dimensional variance data. Through the “uncontrolled manifold” (UCM) approach the structure in such data can be discovered and interpreted. The covariation by randomization (CR) approach provides nonlinear and potentially multi-dimensional measures of covariance. We critically examine these two approaches and compare them relative to the three fundamental issues of choice of variables, choice of model, and adoption of either a geometrical or a correlational view of variance. The UCM approach is a geometrical approach that seeks to discover the structure of variance in multi-degree-of-freedom task spaces in which all degrees of freedom have a common metric. The structure of variance in that space is interpreted in terms of its meaning for task variables. The CR approach seeks to uncover correlations between interpretable elemental variables. It requires a defined and common metric in the space of task variables, but not the elemental variables. Although the CR approach is better suited for systems with strong nonlinearities, variance structure that is not caused by correlation but by different amounts of variance in the different elemental variables is undetected by this approach.

Schöner is with the Institut für Neuroinformatik, Ruhr-Universität Bochum, 44780 Bochum, Germany. Scholz is with the Dept of Physical Therapy and Biomechanics and Movement Science Program, University of Delaware, Newark, DE 19717.

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