Structure in Variability – Searching Coordinate-Insensitive Methods to Characterize Motor Control

Abstract

Motor variability is an intrinsic feature of all human movements and can serve as a window into the determinants of skill acquisition and control. Variability is specifically informative when a task is redundant, i.e. the same result can be obtained in many different ways. The typical approach to analyze structure of variability is to use dimensionality-reduction techniques such as principal component analysis (PCA). We previously highlighted that covariance-based variability analyses are sensitive to the choice of coordinates and even linear coordinate transformations alter the results. If the aim of the analysis is to identify structure in data to reveal features of the central nervous system, this coordinate dependence presents a problem as the coordinates of the central nervous system are unknown. Coordinate-insensitive methods are needed. At the example of a throwing task with known redundancy we previously introduced another technique which decomposed variability into three different aspects: optimizing tolerance to error (Tolerance), channeling noise into dimensions that do not affect the result (Covariation), and minimizing random variability (Noise). The present study illustrates this technique in a throwing task where variability in performance decreases with practice. We compare the results for Tolerance, Noise and Covariation in different coordinates and show that this analysis is less sensitive to changes in coordinates. We also present a new way to quantify Covariation to make this measure less sensitive to the choice of coordinates.