Evaluation of Methods for the Extraction of Spatial Muscle Synergies

Abstract

Muscle synergies have been largely used in many application fields, including motor control studies, prosthesis control, movement classification, rehabilitation, and clinical studies. Due to the complexity of the motor control system, the full repertoire of the underlying synergies has been identified only for some classes of movements and scenarios. Several extraction methods have been used to extract muscle synergies. However, some of these methods may not effectively capture the nonlinear relationship between muscles and impose constraints on input signals or extracted synergies. Moreover, other approaches such as autoencoders (AEs), an unsupervised neural network, were recently introduced to study bioinspired control and movement classification. In this study, we evaluated the performance of five methods for the extraction of spatial muscle synergy, namely, principal component analysis (PCA), independent component analysis (ICA), factor analysis (FA), nonnegative matrix factorization (NMF), and AEs using simulated data and a publicly available database. To analyze the performance of the considered extraction methods with respect to several factors, we generated a comprehensive set of simulated data (ground truth), including spatial synergies and temporal coefficients. The signal-to-noise ratio (SNR) and the number of channels (NoC) varied when generating simulated data to evaluate their effects on ground truth reconstruction. This study also tested the efficacy of each synergy extraction method when coupled with standard classification methods, including K-nearest neighbors (KNN), linear discriminant analysis (LDA), support vector machines (SVM), and Random Forest (RF). The results showed that both SNR and NoC affected the outputs of the muscle synergy analysis. Although AEs showed better performance than FA in variance accounted for and PCA in synergy vector similarity and activation coefficient similarity, NMF and ICA outperformed the other three methods. Classification tasks showed that classification algorithms were sensitive to synergy extraction methods, while KNN and RF outperformed the other two methods for all extraction methods; in general, the classification accuracy of NMF and PCA was higher. Overall, the results suggest selecting suitable methods when performing muscle synergy-related analysis.

Keywords: autoencoder (AE); factor analysis (FA); independent component analysis (ICA); muscle synergy; non-negative matrix factorization (NMF); principal component analysis (PCA).

FIGURE 1

Overview of the study design.

FIGURE 2

Schematic representation of the extraction methods considered in this study. Principal component analysis (PCA), independent component analysis (ICA), factor analysis (FA), and non-negative matrix factorization (NMF) follow a similar procedure for synergy extraction, which factorizes muscle activations (M) into a set of muscle synergies and corresponding activation coefficients. The topology structure of the autoencoders used in this study is also shown.

FIGURE 3

The variance accounted for (VAF) of the five extraction methods under different settings: SNR (A) and NoC (B). For FA, when four synergies are extracted, at least eight muscles should be included. Thus, three bars are shown for FA. “^∗”, “^∗∗”, and “^∗∗∗” indicate the significance levels are 0.05, 0.01, and 0.001, respectively.

FIGURE 4

The synergy similarity of the extraction methods and random data. Three panels from top to bottom are synergy vector similarity (SVS), activation coefficient similarity (ACS), and principal angle (PA). The last bar in each panel “Rand” is the similarity between randomly generated data and the simulated data. The star shows the significance level between methods and Rand. “^∗∗∗” indicate the significance levels are 0.05, 0.01, and 0.001, respectively.

FIGURE 5

The SVS of extraction methods under different settings, (A) SNR and (B) NoC. The fine line on the bar is the standard error between trials. “^∗”, “^∗∗”, and “^∗∗∗” indicate the significance levels are 0.05, 0.01, and 0.001, respectively.

FIGURE 6

Activation coefficient similarity of extraction methods under different settings, (A) SNR and (B) NoC. The fine line on the bar is the standard error between trials. “^∗”, “^∗∗”, and “^∗∗∗” indicate the significance levels are below 0.05, 0.01, and 0.001, respectively.

FIGURE 7

Principal angles of extracting methods under different settings, (A) SNR and (B) NoC. The fine line on the bar is the standard error between trials. “^∗”, “^∗∗”, and “^∗∗∗” indicate the significance levels are 0.05, 0.01, and 0.001, respectively.

FIGURE 8

Classification accuracy of different classification algorithms for each synergy extraction method. “^∗∗” and “^∗∗∗” indicate the significance levels are 0.01 and 0.001, respectively.