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

Abstract

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.

Toward a unifying framework for the modeling and identification of motor primitives

“…Interestingly, a similar procedure can also allow to make inference about the most suitable smoothness priors for a given data set. A more recent AIC-based approach for the estimation of the number of motor primitives extracted with NMF is introduced by Ranaldi et al ( 2021 ).…”

Optimal Identification of Muscle Synergies From Typical Sit-to-Stand Clinical Tests

“…Synergies have been extracted via Non-Negative Matrix Factorization [24] and the number of synergies \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$N_{syn}$\end{document} has been selected from each signal according to the optimal Akaike Information Criterion (AIC) method presented in [22] . The modified AIC criterion is written in the mathematical form as: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{} \begin{align*} AIC(k) \!=&\!\!…”

“…Synergies have been extracted via Non-Negative Matrix Factorization [24] and the number of synergies N syn has been selected from each signal according to the optimal Akaike Information Criterion (AIC) method presented in [22]. The modified AIC criterion is written in the mathematical form as:…”

“…The accurate and thorough extraction of muscle synergies from multi-muscle surface electromyography (sEMG) recordings requires a precise tuning of the methodologies that process and factorize the raw signals. The importance of a correct methodological workflow has already been studied for the sEMG amplitude estimation [18] , [19] , [20] , for factorization algorithm performance [21] or for model selection criteria [22] , [23] . In all the mentioned study, the main result is that of a critical importance of having either objective or optimal methods for the synergy analysis in order to capture clinically relevant information from the coordinated structure of muscle activity; non optimality of the methods adopted have been proven to yield errors in the identification of both the number and the structure of the muscle synergies, thus generating wrong interpretation of their clinical meaning.…”

Muscle synergies for evaluating upper limb in clinical applications: A systematic review

“…These methods assume different constraints on the input signals, and factorization results are affected by the noise level, signal characteristics, and the number of channels [ [72] , [73] , [74] ]. When identifying the optimal number of synergies, a predefined threshold based on the variance accounted for (VAF) [ 75 ] or the coefficient of determination (R 2 ) [ 76 ] is commonly used, but other criteria have also been used [ 29 , 36 , 59 , 65 , [76] , [77] , [78] , [79] , [80] ].…”