Practical limits on muscle synergy identification by non-negative matrix factorization in systems with mechanical constraints

Statistical decomposition, including non-negative matrix factorization (NMF), is a convenient tool for identifying patterns of structured variability within behavioral motor programs, but it is unclear how the resolved factors relate to actual neural structures. Factors can be extracted from a uniformly sampled, low-dimension command space. In practical application, the command space is limited, either to those activations that perform some task(s) successfully or to activations induced in response to specific perturbations. NMF was applied to muscle activation patterns synthesized from low dimensional, synergy-like control modules mimicking simple task performance or feedback activation from proprioceptive signals. In the task-constrained paradigm, the accuracy of control module recovery was highly dependent on the sampled volume of control space, such that sampling even 50% of control space produced a substantial degradation in factor accuracy. In the feedback paradigm, NMF was not capable of extracting more than four control modules, even in a mechanical model with seven internal degrees of freedom. Reduced access to the low-dimensional control space imposed by physical constraints may result in substantial distortion of an existing low dimensional controller, such that neither the dimensionality nor the composition of the recovered/extracted factors match the original controller.