Topology of surface electromyogram signals: hand gesture decoding on Riemannian manifolds

TL;DR

The article addresses the problem of decoding hand gestures from surface EMG in the presence of non-Euclidean covariance structure and substantial inter-subject variability. It proposes representing EMG as covariance matrices on the SPD manifold and performing classification directly in the Riemannian geometry via Cholesky-space embeddings, using manifold MDM, SVM, and k-medoids, with parallel transport for cross-subject alignment. Across three datasets (Ninapro Database 2 Exercise 1, high-density EMG, and UCD-MyoVerse-Hand-0), the approach yields high gesture-discrimination performance (e.g., MDM and SVM accuracies around $0.92$–$0.93$ on Ninapro and high-density EMG), while providing interpretable geometry-driven insights and visualization with t-SNE on SPD covariances. The work demonstrates that EMG covariance features on the SPD manifold are powerful, data-efficient, and amenable to cross-subject deployment and potential zero-/few-shot adaptation for EMG-based wrist interfaces.

Abstract

$\textit{Objective.}$ In this article, we present data and methods for decoding hand gestures using surface electromyogram (EMG) signals. EMG-based upper limb interfaces are valuable for amputee rehabilitation, artificial supernumerary limb augmentation, gestural control of computers, and virtual and augmented reality applications. $\textit{Approach.}$ To achieve this, we collect EMG signals from the upper limb using surface electrodes placed at key muscle sites involved in hand movements. Additionally, we design and evaluate efficient models for decoding EMG signals. $\textit{Main results.}$ Our findings reveal that the manifold of symmetric positive definite (SPD) matrices serves as an effective embedding space for EMG signals. Moreover, for the first time, we quantify the distribution shift of these signals across individuals. $\textit{Significance.}$ Overall, our approach demonstrates significant potential for developing efficient and interpretable methods for decoding EMG signals. This is particularly important as we move toward the broader adoption of EMG-based wrist interfaces.

Figures (8)

• Figure 1: Ten gestures included in the UCD-MyoVerse-Hand-0 experiment. From top-left: up, down, left, right, index point, two finger pinch, power grasp, middle finger pinch, splay, index finger pinch.
• Figure 2: t-SNE of SPD covariance matrices using Riemannian distance indicates that the SPD matrices from different subjects lie in different neighborhoods of the manifold. This is due to shift in EMG signals owing to the combined effect of various anatomical, physiological, and circumstantial factors. Embedding is for Ninapro: Database 2-Exercise 1. Embedding is colored according to subjects. Each of the 40 subjects performed 102 trials (17 gestures, each repeated 6 times).
• Figure 3: Riemannian geodesic distance between the centroids of SPD covariance matrices of 40 subjects in Ninapro: Database 2-Exercise 1. Geodesic distance quantifies the differences in EMG signals between subjects due to the combined effect of various physiological and anatomical factors. The centroid of a given subject is calculated as the Log-Cholesky average of SPD covariance matrices of all 102 trials (17 gestures, each repeated 6 times). X and Y axes are numbered according to subjects.
• Figure 4: t-SNE of SPD matrices of subject 0 from Ninapro: Database 2-Exercise 1 shows that different gestures within a subject have contrasting spatial patterns. We can classify these distinct gestures with supervised algorithms such as minimum distance to mean (MDM) and support vector machine (SVM) or unsupervised algorithms such as k-medoids clustering using Riemannian distance. Classification accuracy using the above methods is presented in appendix \ref{['apd:res2']} for all 40 subjects. Embedding is colored according to gestures. The subject performed 17 gestures with each gesture repeated six times. The gestures are: 0: thumb up, 1: extension of index and middle - flexion of the others, 2: flexion of ring and little finger - extension of the others, 3: thumb opposing base of little finger, 4: abduction of all fingers, 5: fingers flexed together in fist, 6: pointing index, 7: adduction of extended fingers, 8: wrist supination (axis: middle finger), 9: wrist pronation (axis: middle finger), 10: wrist supination (axis: little finger), 11: wrist pronation (axis: little finger), 12: wrist flexion, 13: wrist extension, 14: wrist radial deviation, 15: wrist ulnar deviation, and 16: wrist extension with closed hand.
• Figure 5: t-SNE of SPD covariance matrices using Riemannian distance without accounting for intersubject differences reveals that the SPD matrices for the same gesture from different subjects do not cluster together. This is the same embedding in figure \ref{['fig:tSNE40Subjects']} colored according to gestures (instead of subjects). Each of the 40 subjects performed 102 trials (17 gestures, each repeated 6 times). The gestures are: 0: thumb up, 1: extension of index and middle - flexion of the others, 2: flexion of ring and little finger - extension of the others, 3: thumb opposing base of little finger, 4: abduction of all fingers, 5: fingers flexed together in fist, 6: pointing index, 7: adduction of extended fingers, 8: wrist supination (axis: middle finger), 9: wrist pronation (axis: middle finger), 10: wrist supination (axis: little finger), 11: wrist pronation (axis: little finger), 12: wrist flexion, 13: wrist extension, 14: wrist radial deviation, 15: wrist ulnar deviation, and 16: wrist extension with closed hand.