An Objective, Information-Based Approach for Selecting the Number of Muscle Synergies to be Extracted via Non-Negative Matrix Factorization

Muscle synergy analysis is a useful tool for the evaluation of the motor control strategies and for the quantification of motor performance. Among the parameters that can be extracted, most of the information is included in the rank of the modular control model (i.e. the number of muscle synergies that can be used to describe the overall muscle coordination). Even though different criteria have been proposed in literature, an objective criterion for the model order selection is needed to improve reliability and repeatability of MSA results. In this paper, we propose an Akaike Information Criterion (AIC)-based method for model order selection when extracting muscle synergies via the original Gaussian Non-Negative Matrix Factorization algorithm. The traditional AIC definition has been modified based on a correction of the likelihood term, which includes signal dependent noise on the neural commands, and a Discrete Wavelet decomposition method for the proper estimation of the number of degrees of freedom of the model, reduced on a synergy-by-synergy and event-by-event basis. We tested the performance of our method in comparison with the most widespread ones, proving that our criterion is able to yield good and stable performance in selecting the correct model order in simulated EMG data. We further evaluated the performance of our AIC-based technique on two distinct experimental datasets confirming the results obtained with the synthetic signals, with performances that are stable and independent from the nature of the analysed task, from the signal quality and from the subjective EMG pre-processing steps.