Muscle Activity Analysis Using Higher-Order Tensor Decomposition: Application to Muscle Synergy Extraction

Abstract

Higher-order tensor decompositions have hardly been used in muscle activity analysis despite multichannel electromyography (EMG) datasets naturally occurring as multi-way structures. Here, we seek to demonstrate and discuss the potential of tensor decompositions as a framework to estimate muscle synergies from 3 rd -order EMG tensors built by stacking repetitions of multi-channel EMG for several tasks. We compare the two most widespread tensor decomposition models -Parallel Factor Analysis (PARAFAC) and Tucker -in muscle synergy analysis of the wrist's three main Degree of Freedoms (DoFs) using the public first Ninapro database. Furthermore, we proposed a constrained Tucker decomposition (consTD) method for efficient synergy extraction building on the power of tensor decompositions. This method is proposed as a direct novel approach for shared and task-specific synergy estimation from two biomechanically related tasks. Our approach is compared with the current standard approach of repetitively applying non-negative matrix factorisation (NMF) to a series of the movements. The results show that the consTD method is suitable for synergy extraction compared to PARAFAC and Tucker. Moreover, exploiting the multi-way structure of muscle activity, the proposed methods successfully identified shared and taskspecific synergies for all three DoFs tensors. These were found to be robust to disarrangement with regard to task-repetition information, unlike the commonly used NMF. In summary, we demonstrate how to use tensors to characterise muscle activity and develop a new consTD method for muscle synergy extraction that could be used for shared and task-specific synergies identification. We expect that this study will pave the way for the development of novel muscle activity analysis methods based on higher-order techniques.

Speed-dependent and mode-dependent modulations of spatiotemporal modules in human locomotion extracted via tensor decomposition

“…A few previous studies have attempted to demonstrate the effectiveness of tensor decomposition in analyzing joint angle and EMG data [17][18][19][20][21] . In a previous study, tensor decomposition was applied to wrist EMG data, and the results demonstrated the task-dependent modulation of the spatiotemporal modules 17 . That study relied on a variant of Tucker decomposition, which is a more general type of tensor decomposition that subsumes CP decomposition.…”

Consistency of Muscle Synergies Extracted via Higher-Order Tensor Decomposition Towards Myoelectric Control

“…It is implemented in the iteration phase by setting the negative values of computed components to zero by the end of each iteration to force the algorithm to converge into a non-negative solution. A similar constrained set-up have been used in previous study [15] to extract shared muscle synergies. Moreover, the algorithm would run for 10 times to ensure that the model is not converged into local minima and the decomposition with the highest explained variance is chosen.…”

Detecting task-dependent modulation of spatiotemporal module via tensor decomposition: application to kinematics and EMG data for walking and running at various speed

“…A few studies have attempted to demonstrate the effectiveness of tensor decomposition in analyzing the joint angle and EMG data [17–19]. A previous study applied tensor decomposition to wrist EMG data and demonstrated the task-dependent modulation of the spatiotemporal module [19].…”

“…A few studies have attempted to demonstrate the effectiveness of tensor decomposition in analyzing the joint angle and EMG data [17–19]. A previous study applied tensor decomposition to wrist EMG data and demonstrated the task-dependent modulation of the spatiotemporal module [19]. Despite the detailed description of mathematical and historical aspects of tensor decomposition, a description of movements and tasks is lacking; the significance of the tensor decomposition in discussing the task-dependent modulation of the spatiotemporal module is unclear.…”

“…Other studies [17,18] applied a matrix tri-factorization to EMG data and revealed how each spatiotemporal module was modulated depending on the task. Although the tri-factorization algorithm and their new experimental paradigm [18] are sophisticated, the algorithm is a reduced version of tensor decomposition (a detailed description is given in [19]). Additionally, although the modulation patterns were estimated in an unsupervised manner (i.e., no experimental information is necessary), additional analysis for interpreting the modulation was based on a supervised method (i.e., experimental information should be required) [17,18].…”