A Scale Mixture-Based Stochastic Model of Surface EMG Signals With Variable Variances

Abstract

Objective: Surface electromyogram (EMG) signals have typically been assumed to follow a Gaussian distribution. However, the presence of non-Gaussian signals associated with muscle activity has been reported in recent studies, and there is no general model of the distribution of EMG signals that can explain both non-Gaussian and Gaussian distributions within a unified scheme. Methods: In this paper, we describe the formulation of a non-Gaussian EMG model based on a scale mixture distribution. In the model, an EMG signal at a certain time follows a Gaussian distribution, and its variance is handled as a random variable that follows an inverse gamma distribution. Accordingly, the probability distribution of EMG signals is assumed to be a mixture of Gaussians with the same mean but different variances. The EMG variance distribution is estimated via marginal likelihood maximization. Results: Experiments involving nine participants revealed that the proposed model provides a better fit to recorded EMG signals than conventional EMG models. It was also shown that variance distribution parameters may reflect underlying motor unit activity. Conclusion: This study proposed a scale mixture distribution-based stochastic EMG model capable of representing changes in non-Gaussianity associated with muscle activity. A series of experiments demonstrated the validity of the model and highlighted the relationship between the variance distribution and muscle force. Significance: The proposed model helps to clarify conventional wisdom regarding the probability distribution of surface EMG signals within a unified scheme.

EMG Pattern Recognition via Bayesian Inference with Scale Mixture-Based Stochastic Generative Models

“…Although the GMM, LDA, and GNB approaches are generative classifiers, similar to the proposed method, they are based on simple Gaussian distributions. Recent studies have suggested that EMG signals follow distributions that are more heavily tailed than Gaussian distributions, which is believed to be due to the variation in EMG variance caused by muscle force changes (Furui et al, 2019b) and muscle fatigue (Furui & Tsuji, 2019). The Gaussian distribution-based classifiers cannot take such variations into account, resulting in relatively low generalization performance.…”

“…The scale mixture model of surface EMG signals is a stochastic model for raw EMG signals recorded from a pair of electrodes (Furui et al, 2019b). However, EMG pattern classification typically involves the use of EMG signals from multichannel electrodes.…”

“…4 depicts examples of EMG signals and the corresponding density histograms from the second electrode for Participant 1 during hand supination. It also shows the fitted distributions obtained using the original scale mixture model (Furui et al, 2019b) sification accuracy of the proposed method over participants with various initial numbers of components K c and parameters ν. The average classification accuracy reaches a maximum value of 90.75% when K c = 1 and ν = 1.…”

“…However, recent studies have suggested that EMG signals often follow a distribution that is more heavily tailed than a Gaussian distribution (Nazarpour et al, 2013;Messaoudi et al, 2017;Furui et al, 2019b). Such non-Gaussian properties of EMG signals are believed to be due to the variation in EMG variances depending on muscle activity (Milner-Brown & Stein, 1975;Mcgill, 2004;Furui et al, 2019b;Furui & Tsuji, 2019). Therefore, Gaussian distribution-based classification may not be sufficient as a generative approach.…”

“…To develop a classifier that reflects the stochastic nature of EMG signals, such varying non-Gaussianity needs to be considered. Meanwhile, the authors previously proposed a stochastic model of EMG signals based on a scale mixture distribution assuming the EMG variance to be a random variable (Furui et al, 2019b). This model can represent changes in non-Gaussianity associated with muscle activity, thereby explaining both non-Gaussian and Gaussian distributions within a unified scheme.…”