scholarly journals Matrix Factorization Algorithms for the Identification of Muscle Synergies: Evaluation on Simulated and Experimental Data Sets

2006 ◽  
Vol 95 (4) ◽  
pp. 2199-2212 ◽  
Author(s):  
Matthew C. Tresch ◽  
Vincent C. K. Cheung ◽  
Andrea d'Avella
Keyword(s):  
Matrix Factorization ◽  
Muscle Activation ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Muscle Synergies ◽  
Data Sets ◽  
Data Set ◽  
Activation Patterns ◽  
Muscle Activation Patterns ◽  
Factorization Algorithms

Several recent studies have used matrix factorization algorithms to assess the hypothesis that behaviors might be produced through the combination of a small number of muscle synergies. Although generally agreeing in their basic conclusions, these studies have used a range of different algorithms, making their interpretation and integration difficult. We therefore compared the performance of these different algorithms on both simulated and experimental data sets. We focused on the ability of these algorithms to identify the set of synergies underlying a data set. All data sets consisted of nonnegative values, reflecting the nonnegative data of muscle activation patterns. We found that the performance of principal component analysis (PCA) was generally lower than that of the other algorithms in identifying muscle synergies. Factor analysis (FA) with varimax rotation was better than PCA, and was generally at the same levels as independent component analysis (ICA) and nonnegative matrix factorization (NMF). ICA performed very well on data sets corrupted by constant variance Gaussian noise, but was impaired on data sets with signal-dependent noise and when synergy activation coefficients were correlated. Nonnegative matrix factorization (NMF) performed similarly to ICA and FA on data sets with signal-dependent noise and was generally robust across data sets. The best algorithms were ICA applied to the subspace defined by PCA (ICAPCA) and a version of probabilistic ICA with nonnegativity constraints (pICA). We also evaluated some commonly used criteria to identify the number of synergies underlying a data set, finding that only likelihood ratios based on factor analysis identified the correct number of synergies for data sets with signal-dependent noise in some cases. We then proposed an ad hoc procedure, finding that it was able to identify the correct number in a larger number of cases. Finally, we applied these methods to an experimentally obtained data set. The best performing algorithms (FA, ICA, NMF, ICAPCA, pICA) identified synergies very similar to one another. Based on these results, we discuss guidelines for using factorization algorithms to analyze muscle activation patterns. More generally, the ability of several algorithms to identify the correct muscle synergies and activation coefficients in simulated data, combined with their consistency when applied to physiological data sets, suggests that the muscle synergies found by a particular algorithm are not an artifact of that algorithm, but reflect basic aspects of the organization of muscle activation patterns underlying behaviors.

The flexible recruitment of muscle synergies depends on the required force-generating capability

2014 ◽  
Vol 112 (2) ◽  
pp. 316-327 ◽  
Author(s):  
Shota Hagio ◽  
Motoki Kouzaki
Keyword(s):  
Central Nervous System ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Isometric Force ◽  
Nonnegative Matrix ◽  
Muscle Synergies ◽  
Joint Angles ◽  
Activation Patterns ◽  
The Central Nervous System ◽  
Low Dimensional

To simplify redundant motor control, the central nervous system (CNS) may modularly organize and recruit groups of muscles as “muscle synergies.” However, smooth and efficient movements are expected to require not only low-dimensional organization, but also flexibility in the recruitment or combination of synergies, depending on force-generating capability of individual muscles. In this study, we examined how the CNS controls activations of muscle synergies as changing joint angles. Subjects performed multidirectional isometric force generations around right ankle and extracted the muscle synergies using nonnegative matrix factorization across various knee and hip joint angles. As a result, muscle synergies were selectively recruited with merging or decomposition as changing the joint angles. Moreover, the activation profiles, including activation levels and the direction indicating the peak, of muscle synergies across force directions depended on the joint angles. Therefore, we suggested that the CNS selects appropriate muscle synergies and controls their activation patterns based on the force-generating capability of muscles with merging or decomposing descending neural inputs.

scholarly journals Subject-Specific Muscle Synergies in Human Balance Control Are Consistent Across Different Biomechanical Contexts

2010 ◽  
Vol 103 (6) ◽  
pp. 3084-3098 ◽  
Author(s):  
Gelsy Torres-Oviedo ◽  
Lena H. Ting
Keyword(s):  
Muscle Activation ◽  
Balance Control ◽  
Nonnegative Matrix ◽  
The Body ◽  
Muscle Synergy ◽  
Muscle Synergies ◽  
Support Surface ◽  
Activation Patterns ◽  
Muscle Activation Patterns ◽  
Specific Muscle

The musculoskeletal redundancy of the body provides multiple solutions for performing motor tasks. We have proposed that the nervous system solves this unconstrained problem through the recruitment of motor modules or functional muscle synergies that map motor intention to action. Consistent with this hypothesis, we showed that trial-by-trial variations in muscle activation for multidirectional balance control in humans were constrained by a small set of muscle synergies. However, apparent muscle synergy structures could arise from characteristic patterns of sensory input resulting from perturbations or from low-dimensional optimal motor solutions. Here we studied electromyographic (EMG) responses for balance control across a range of biomechanical contexts, which alter not only the sensory inflow generated by postural perturbations, but also the muscle activation patterns used to restore balance. Support-surface translations in 12 directions were delivered to subjects standing in six different postural configurations: one-leg, narrow, wide, very wide, crouched, and normal stance. Muscle synergies were extracted from each condition using nonnegative matrix factorization. In addition, muscle synergies from the normal stance condition were used to reconstruct muscle activation patterns across all stance conditions. A consistent set of muscle synergies were recruited by each subject across conditions. When balance demands were extremely different from the normal stance (e.g., one-legged or crouched stance), task-specific muscle synergies were recruited in addition to the preexisting ones, rather generating de novo muscle synergies. Taken together, our results suggest that muscle synergies represent consistent motor modules that map intention to action, regardless of the biomechanical context of the task.

scholarly journals Accelerating Nonnegative Matrix Factorization Algorithms Using Extrapolation

2019 ◽  
Vol 31 (2) ◽  
pp. 417-439 ◽  
Author(s):  
Andersen Man Shun Ang ◽  
Nicolas Gillis
Keyword(s):  
Least Squares ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
State Of The Art ◽  
Gradient Methods ◽  
Nonnegative Matrix ◽  
Synthetic Image ◽  
Data Sets ◽  
Extrapolation Scheme ◽  
Factorization Algorithms

We propose a general framework to accelerate significantly the algorithms for nonnegative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient methods in convex optimization and from the method of parallel tangents. However, the use of extrapolation in the context of the exact coordinate descent algorithms tackling the nonconvex NMF problems is novel. We illustrate the performance of this approach on two state-of-the-art NMF algorithms: accelerated hierarchical alternating least squares and alternating nonnegative least squares, using synthetic, image, and document data sets.

scholarly journals Comparison of Initialization Techniques for the Accurate Extraction of Muscle Synergies from Myoelectric Signals via Nonnegative Matrix Factorization

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Mumtaz Hussain Soomro ◽  
Silvia Conforto ◽  
Gaetano Giunta ◽  
Simone Ranaldi ◽  
Cristiano De Marchis
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Simulated Data ◽  
Surface Emg ◽  
Muscle Synergies ◽  
Accurate Identification ◽  
Experimental Surface ◽  
Factorization Algorithms

The main goal of this work was to assess the performance of different initializations of matrix factorization algorithms for an accurate identification of muscle synergies. Currently, nonnegative matrix factorization (NNMF) is the most commonly used method to identify muscle synergies. However, it has been shown that NNMF performance might be affected by different kinds of initialization. The present study aims at optimizing the traditional NNMF initialization for data with partial or complete temporal dependencies. For this purpose, three different initializations are used: random, SVD-based, and sparse. NNMF was used to identify muscle synergies from simulated data as well as from experimental surface EMG signals. Simulated data were generated from synthetic independent and dependent synergy vectors (i.e., shared muscle components), whose activation coefficients were corrupted by simulating controlled degrees of correlation. Similarly, EMG data were artificially modified, making the extracted activation coefficients temporally dependent. By measuring the quality of identification of the original synergies underlying the data, it was possible to compare the performance of different initialization techniques. Simulation results demonstrate that sparse initialization performs significantly better than all other kinds of initialization in reconstructing muscle synergies, regardless of the correlation level in the data.

scholarly journals On identifying kinematic and muscle synergies: a comparison of matrix factorization methods using experimental data from the healthy population

2017 ◽  
Vol 117 (1) ◽  
pp. 290-302 ◽  
Author(s):  
Navid Lambert-Shirzad ◽  
H. F. Machiel Van der Loos
Keyword(s):  
Principal Component Analysis ◽  
Matrix Factorization ◽  
Muscle Activation ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Principal Component ◽  
Component Analysis ◽  
Data Sets ◽  
Motor Synergies ◽  
Factorization Methods

Human motor behavior is highly goal directed, requiring the central nervous system to coordinate different aspects of motion generation to achieve the motion goals. The concept of motor synergies provides an approach to quantify the covariation of joint motions and of muscle activations, i.e., elemental variables, during a task. To analyze goal-directed movements, factorization methods can be used to reduce the high dimensionality of these variables while accounting for much of the variance in large data sets. Three factorization methods considered in this paper are principal component analysis (PCA), nonnegative matrix factorization (NNMF), and independent component analysis (ICA). Bilateral human reaching data sets are used to compare the methods, and advantages of each are presented and discussed. PCA and NNMF had a comparable performance on both EMG and joint motion data and both outperformed ICA. However, NNMF's nonnegativity condition for activation of basis vectors is a useful attribute in identifying physiologically meaningful synergies, making it a more appealing method for future studies. A simulated data set is introduced to clarify the approaches and interpretation of the synergy structures returned by the three factorization methods.NEW & NOTEWORTHY Literature on comparing factorization methods in identifying motor synergies using numerically generated, simulation, and muscle activation data from animal studies already exists. We present an empirical evaluation of the performance of three of these methods on muscle activation and joint angles data from human reaching motion: principal component analysis, nonnegative matrix factorization, and independent component analysis. Using numerical simulation, we also studied the meaning and differences in the synergy structures returned by each method. The results can be used to unify approaches in identifying and interpreting motor synergies.

scholarly journals Collaborative Filtering Recommendation Using Nonnegative Matrix Factorization in GPU-Accelerated Spark Platform

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Bing Tang ◽  
Linyao Kang ◽  
Li Zhang ◽  
Feiyan Guo ◽  
Haiwu He
Keyword(s):  
Collaborative Filtering ◽  
Processing Speed ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Experimental Results ◽  
Computational Time ◽  
Data Sets ◽  
Heterogeneous Cluster ◽  
The Matrix

Nonnegative matrix factorization (NMF) has been introduced as an efficient way to reduce the complexity of data compression and its capability of extracting highly interpretable parts from data sets, and it has also been applied to various fields, such as recommendations, image analysis, and text clustering. However, as the size of the matrix increases, the processing speed of nonnegative matrix factorization is very slow. To solve this problem, this paper proposes a parallel algorithm based on GPU for NMF in Spark platform, which makes full use of the advantages of in-memory computation mode and GPU acceleration. The new GPU-accelerated NMF on Spark platform is evaluated in a 4-node Spark heterogeneous cluster using Google Compute Engine by configuring each node a NVIDIA K80 CUDA device, and experimental results indicate that it is competitive in terms of computational time against the existing solutions on a variety of matrix orders. Furthermore, a GPU-accelerated NMF-based parallel collaborative filtering (CF) algorithm is also proposed, utilizing the advantages of data dimensionality reduction and feature extraction of NMF, as well as the multicore parallel computing mode of CUDA. Using real MovieLens data sets, experimental results have shown that the parallelization of NMF-based collaborative filtering on Spark platform effectively outperforms traditional user-based and item-based CF with a higher processing speed and higher recommendation accuracy.

scholarly journals Lower complexity of motor primitives ensures robust control of high-speed human locomotion

2020 ◽  
Author(s):  
Alessandro Santuz ◽  
Antonis Ekizos ◽  
Yoko Kunimasa ◽  
Kota Kijima ◽  
Masaki Ishikawa ◽  
...  
Keyword(s):  
High Speed ◽  
Muscle Activation ◽  
Human Locomotion ◽  
Muscle Synergies ◽  
Activation Patterns ◽  
Motor Primitives ◽  
Muscle Activation Patterns ◽  
Relative Contribution ◽  
Muscle Activations ◽  
Low Dimensional

AbstractWalking and running are mechanically and energetically different locomotion modes. For selecting one or another, speed is a parameter of paramount importance. Yet, both are likely controlled by similar low-dimensional neuronal networks that reflect in patterned muscle activations called muscle synergies. Here, we investigated how humans synergistically activate muscles during locomotion at different submaximal and maximal speeds. We analysed the duration and complexity (or irregularity) over time of motor primitives, the temporal components of muscle synergies. We found that the challenge imposed by controlling high-speed locomotion forces the central nervous system to produce muscle activation patterns that are wider and less complex relative to the duration of the gait cycle. The motor modules, or time-independent coefficients, were redistributed as locomotion speed changed. These outcomes show that robust locomotion control at challenging speeds is achieved by modulating the relative contribution of muscle activations and producing less complex and wider control signals, whereas slow speeds allow for more irregular control.

scholarly journals Alterations in upper limb muscle synergy structure in chronic stroke survivors

2013 ◽  
Vol 109 (3) ◽  
pp. 768-781 ◽  
Author(s):  
Jinsook Roh ◽  
William Z. Rymer ◽  
Eric J. Perreault ◽  
Seng Bum Yoo ◽  
Randall F. Beer
Keyword(s):  
Muscle Activation ◽  
Isometric Force ◽  
Muscle Synergy ◽  
Muscle Synergies ◽  
Stroke Survivors ◽  
Activation Patterns ◽  
Force Matching ◽  
Muscle Activation Patterns ◽  
Anterior Deltoid ◽  
Arm Function

Previous studies in neurologically intact subjects have shown that motor coordination can be described by task-dependent combinations of a few muscle synergies, defined here as a fixed pattern of activation across a set of muscles. Arm function in severely impaired stroke survivors is characterized by stereotypical postural and movement patterns involving the shoulder and elbow. Accordingly, we hypothesized that muscle synergy composition is altered in severely impaired stroke survivors. Using an isometric force matching protocol, we examined the spatial activation patterns of elbow and shoulder muscles in the affected arm of 10 stroke survivors (Fugl-Meyer <25/66) and in both arms of six age-matched controls. Underlying muscle synergies were identified using non-negative matrix factorization. In both groups, muscle activation patterns could be reconstructed by combinations of a few muscle synergies (typically 4). We did not find abnormal coupling of shoulder and elbow muscles within individual muscle synergies. In stroke survivors, as in controls, two of the synergies were comprised of isolated activation of the elbow flexors and extensors. However, muscle synergies involving proximal muscles exhibited consistent alterations following stroke. Unlike controls, the anterior deltoid was coactivated with medial and posterior deltoids within the shoulder abductor/extensor synergy and the shoulder adductor/flexor synergy in stroke was dominated by activation of pectoralis major, with limited anterior deltoid activation. Recruitment of the altered shoulder muscle synergies was strongly associated with abnormal task performance. Overall, our results suggest that an impaired control of the individual deltoid heads may contribute to poststroke deficits in arm function.

scholarly journals Sex-specific tuning of modular muscle activation patterns for locomotion in young and older adults

2021 ◽  
Author(s):  
Alessandro Santuz ◽  
Lars Janshen ◽  
Leon Bruell ◽  
Victor Munoz-Martel ◽  
Juri Taborri ◽  
...  
Keyword(s):  
Older Adults ◽  
Motor Control ◽  
Muscle Activation ◽  
Human Locomotion ◽  
Older Age ◽  
Modular Organization ◽  
Muscle Synergies ◽  
Activation Patterns ◽  
Motor Primitives ◽  
Muscle Activation Patterns

There is increasing evidence that including sex as a biological variable is of crucial importance to promote rigorous, repeatable and reproducible science. In spite of this, the body of literature that accounts for the sex of participants in human locomotion studies is small and often produces controversial results. Here, we investigated the modular organization of muscle activation patterns for human locomotion using the concept of muscle synergies with a double purpose: i) uncover possible sex-specific characteristics of motor control and ii) assess whether these are maintained in older age. We recorded electromyographic activities from 13 ipsilateral muscles of the lower limb in young and older adults of both sexes walking (young and old) and running (young) on a treadmill. The data set obtained from the 215 participants was elaborated through non-negative matrix factorization to extract the time-independent (i.e., motor modules) and time-dependent (i.e., motor primitives) coefficients of muscle synergies. We found sparse sex-specific modulations of motor control. Motor modules showed a different contribution of hip extensors, knee extensors and foot dorsiflexors in various synergies. Motor primitives were wider (i.e., lasted longer) in males in the propulsion synergy for walking (but only in young and not in older adults) and in the weight acceptance synergy for running. Moreover, the complexity of motor primitives was similar in younger adults of both sexes, but lower in older females as compared to older males. In essence, our results revealed the existence of small but defined sex-specific differences in the way humans control locomotion and that these strategies are not entirely maintained in older age.

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