Coordinate sensitivity of variability analysis: A revised method to quantify covariation

Analyzing the structure of motor variability is important to understand neural control of movement. Although many previous studies have suggested analysis methods to account for task-relevant variability, it has been revealed that even a simple linear transformation of the coordinate system causes qualitatively different interpretation of the variability analysis. The present study suggests a revised version of the Covariation cost analysis and shows that it has little coordinate sensitivity. The modified algorithm allows more flexible optimization, but does not change mean and standard deviation of the execution variables. We also show that the cost analysis takes anisotropy of execution variables into account regardless of two tested coordinate systems. While not resolving the cause of the coordinate sensitivity, the present study is a step forward to coordinate invariance of variability analysis. Together with Tolerance and Noise cost analyses, which is already known to be coordinate insensitive, it is expected that the analysis will elucidate neural mechanism in goal-directed motor behavior in contexts of motor control, learning and rehabilitation.