Coordinate Dependence of Variability Analysis

Abstract

Analysis of motor performance variability in tasks with redundancy affords insight about synergies underlying central nervous system (CNS) control. Preferential distribution of variability in ways that minimally affect task performance suggests sophisticated neural control. Unfortunately, in the analysis of variability the choice of coordinates used to represent multi-dimensional data may profoundly affect analysis, introducing an arbitrariness which compromises its conclusions. This paper assesses the influence of coordinates. Methods based on analyzing a covariance matrix are fundamentally dependent on an investigator's choices. Two reasons are identified: using anisotropy of a covariance matrix as evidence of preferential distribution of variability; and using orthogonality to quantify relevance of variability to task performance. Both are exquisitely sensitive to coordinates. Unless coordinates are known a priori, these methods do not support unambiguous inferences about CNS control. An alternative method uses a two-level approach where variability in task execution (expressed in one coordinate frame) is mapped by a function to its result (expressed in another coordinate frame). An analysis of variability in execution using this function to quantify performance at the level of results offers substantially less sensitivity to coordinates than analysis of a covariance matrix of execution variables. This is an initial step towards developing coordinate-invariant analysis methods for movement neuroscience.

An Uncontrolled Manifold Analysis of Arm Joint Variability in Virtual Planar Position and Orientation Telemanipulation

“…Recently, Sternad et al [29] demonstrated that the UCM analysis is sensitive to the choice of the coordinates that are used to define the task related and unrelated manifolds. An elegant solution to this problem was recently proposed [30], but it was only applied to static tasks to date.…”

A Brief Survey on the Role of Dimensionality Reduction in Manipulation Learning and Control

“…Although commonly employed in robotics, such decoupling is a limiting factor to encode gestures and sensorimotor streams, because it does not fully exploit principles underlying coordination, synergies and actionperception couplings [39], [40], [41].…”

Compliant skills acquisition and multi-optima policy search with EM-based reinforcement learning

“…In the case of human movements, it has been shown that redundancy provides a way to cope with noise at a motor level by channeling it in directions that have minimal effect on achieving the task goal [39]. Skilled performers can take advantage of this redundancy and align their actions with the solution manifold corresponding to a given task goal, i.e., the space in which noise and variability have little or no effect on the end result.…”

“…We take inspiration from the proposal addressed in [39] that variability may offer a way to quantify error tolerance via the shape of the result function. Indeed, one obvious reason to prefer some locations over others in the policy parameters space is the sensitivity of the result to variability (tolerance to errors).…”

“…Human studies show that early attempts at playing the table skittle game can converge to an initial solution that can, with more substantial training, be shifted towards a solution subspace that is more robust to perturbations [39]. Inspired by these studies, we take here the perspective that instead of a single point, the GMM representation can approximate the local shape of several optimal regions, whose covariance information is not only used to generate stochastic samples, but can also be exploited to identify subspaces in the policy parameters space characterized by high reward and high tolerances to errors (see also illustrative example in Fig.…”