Topology of Surface Electromyography Signals: Decoding Hand Gestures Using Riemannian Manifolds

This paper is authored by Harshavardhana T. Gowda (Department of Electrical and Computer Engineering, University of California, Davis) and Lee M. Miller (Center for Mind and Brain Sciences, Department of Neurophysiology and Behavior, Department of Otolaryngology-Head and Neck Surgery, University of California, Davis). The paper is published in the Journal of Neural Engineering.

Research Background

Surface Electromyogram (sEMG) signals are non-invasively recorded by placing sensors on the skin to capture electrical signals from motor unit (MU) activations. These signals are significant in the application of upper limb gesture decoding for amputee rehabilitation, prosthetic limb enhancement, computer gesture control, and in virtual/augmented reality fields. However, the practical applications of sEMG signals are limited by several factors, such as subcutaneous tissue thickness and signal variability dependent on electrode positioning. Decoding and differentiating various gestures thus pose a challenge, which this paper aims to address.

Paper Source

This paper is authored by Harshavardhana T. Gowda and Lee M. Miller, respectively from the Department of Electrical and Computer Engineering and the Center for Mind and Brain Sciences at the University of California, Davis. The paper is published in the Journal of Neural Engineering.

Research Process

This paper proposes a method to represent the MU activity space distribution by constructing Symmetric Positive Definite (SPD) covariance matrices, operating these matrices on Riemannian manifolds, to understand and process multivariate sEMG time series more naturally. The research includes the following steps:

Definitions and Operations

• Definitions:

  • For a square matrix x of dimension c, various normalized matrix representations are defined.
  • The computations for Frobenius inner product and induced norms are presented.

• Operations on Manifolds of SPD Matrices:

  • The SPD matrix is a convex smooth submanifold of the space of symmetric matrices. Using Cholesky decomposition, SPD matrices can be transformed into lower triangular matrices and equivalently mapped in a one-to-one manner.
  • It introduces how to achieve an isometric mapping between these two manifolds through Cholesky decomposition and its inverse operation.

Riemannian Metric Calculation

• The calculation methods for Riemannian metrics and geodesic distances are proposed to ensure computational efficiency and numerical stability.
• The methods to compute Fréchet means and parallel transport are presented, and a Positive Definite kernel computation method for Support Vector Machines (SVM) is constructed.

Datasets

The research utilizes three datasets: 1. Ninapro: A public dataset provided by Atzori et al., including 40 participants, recorded using 12 electrodes and containing 17 different gestures. 2. High-Density sEMG Signal Dataset: Dataset from Malešević et al., including 19 participants, recorded with 128 electrodes and containing 65 unique gestures. 3. UCD-Myoverse-Hand-0 Dataset: Collected by the authors at UC Davis, involving 30 participants, recorded with 12 electrodes and containing 10 gestures.

Main Results

Dataset 1 - Ninapro

• Data Preprocessing and Gesture Classification
  • Using 2000Hz frequency and 12 electrode sEMG data, different algorithms (MDM, SVM, K-medoids) are used for gesture recognition.
  • Comparing the accuracy of different classification methods, the proposed manifold methods (MDM and SVM) achieved accuracies of 0.92 and 0.93, significantly higher than previous methods.

Dataset 2 - High-Density sEMG Signal Dataset

• Data Preprocessing and Gesture Classification
  • Using 2048Hz frequency and 128 electrode sEMG data, the same algorithms are employed for classification.
  • Comparison results indicate that the proposed methods’ accuracy (0.92 and 0.93) matches the current highest levels but offer higher computational efficiency and are more suitable for deployment across different individuals.

Dataset 3 - UCD-Myoverse-Hand-0

• Data Preprocessing and Gesture Classification
  • Using 2000Hz frequency and 12 electrode sEMG data, the same algorithms are applied for classification.
  • The average accuracies are: MDM 0.82, SVM 0.86, K-medoids 0.70, demonstrating the efficacy of these methods in practical applications.

Conclusions and Implications

This paper, through analyzing sEMG signals on Riemannian manifolds, proposes a natural and low-dimensional gesture classification scheme, demonstrating transparent and definitive methods to adapt to signal variations between individuals and sessions. This research bridges the gap where current deep learning methods require large models and extensive datasets, enabling rapid cross-individual adaptation. Additionally, through parallel transport, a method to adapt to signal variability in real-time is proposed, bringing new hope for real-world sEMG decoding applications.

Highlights

• Innovative Method: For the first time, the introduction of Riemannian manifolds and SPD covariance matrices in sEMG signal research for gesture classification.
• Efficient Computation: Higher computational efficiency and adaptability compared to existing deep learning methods.
• Practical Application Potential: Provides new insights to address adaptability issues of sEMG signals in real-world applications.

This paper experimentally validates the effectiveness and superiority of analyzing sEMG signals on Riemannian manifolds, providing important theoretical and practical basis for gesture decoding in real-world applications.